diff --git a/dumux/assembly/boxlocalassembler.hh b/dumux/assembly/boxlocalassembler.hh
index 808b1b0d90110f153f3534fcbbdfbf75c69eb6c0..f78804dd4bbcc3418649c6423cdab4c612b1e2b5 100644
--- a/dumux/assembly/boxlocalassembler.hh
+++ b/dumux/assembly/boxlocalassembler.hh
@@ -57,7 +57,7 @@ class BoxLocalAssembler<TypeTag,
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
     using ElementSolutionVector = typename GET_PROP_TYPE(TypeTag, ElementSolutionVector);
     using ElementVolumeVariables = typename GET_PROP_TYPE(TypeTag, ElementVolumeVariables);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using VolumeVariables = typename GET_PROP_TYPE(TypeTag, VolumeVariables);
     using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
     using JacobianMatrix = typename GET_PROP_TYPE(TypeTag, JacobianMatrix);
@@ -431,12 +431,12 @@ private:
     }
 private:
     template<class T = TypeTag>
-    static typename std::enable_if<!GET_PROP_VALUE(T, EnableGlobalVolumeVariablesCache), VolumeVariables&>::type
+    static typename std::enable_if<!GET_PROP_VALUE(T, EnableGridVolumeVariablesCache), VolumeVariables&>::type
     getVolVarAccess(GridVolumeVariables& gridVolVars, ElementVolumeVariables& elemVolVars, const SubControlVolume& scv)
     { return elemVolVars[scv]; }
 
     template<class T = TypeTag>
-    static typename std::enable_if<GET_PROP_VALUE(T, EnableGlobalVolumeVariablesCache), VolumeVariables&>::type
+    static typename std::enable_if<GET_PROP_VALUE(T, EnableGridVolumeVariablesCache), VolumeVariables&>::type
     getVolVarAccess(GridVolumeVariables& gridVolVars, ElementVolumeVariables& elemVolVars, const SubControlVolume& scv)
     { return gridVolVars.volVars(scv.elementIndex(), scv.indexInElement()); }
 
@@ -456,7 +456,7 @@ class BoxLocalAssembler<TypeTag,
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
     using ElementSolutionVector = typename GET_PROP_TYPE(TypeTag, ElementSolutionVector);
     using ElementVolumeVariables = typename GET_PROP_TYPE(TypeTag, ElementVolumeVariables);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using VolumeVariables = typename GET_PROP_TYPE(TypeTag, VolumeVariables);
     using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
     using JacobianMatrix = typename GET_PROP_TYPE(TypeTag, JacobianMatrix);
@@ -798,12 +798,12 @@ private:
     }
 private:
     template<class T = TypeTag>
-    static typename std::enable_if<!GET_PROP_VALUE(T, EnableGlobalVolumeVariablesCache), VolumeVariables&>::type
+    static typename std::enable_if<!GET_PROP_VALUE(T, EnableGridVolumeVariablesCache), VolumeVariables&>::type
     getVolVarAccess(GridVolumeVariables& gridVolVars, ElementVolumeVariables& elemVolVars, const SubControlVolume& scv)
     { return elemVolVars[scv]; }
 
     template<class T = TypeTag>
-    static typename std::enable_if<GET_PROP_VALUE(T, EnableGlobalVolumeVariablesCache), VolumeVariables&>::type
+    static typename std::enable_if<GET_PROP_VALUE(T, EnableGridVolumeVariablesCache), VolumeVariables&>::type
     getVolVarAccess(GridVolumeVariables& gridVolVars, ElementVolumeVariables& elemVolVars, const SubControlVolume& scv)
     { return gridVolVars.volVars(scv.elementIndex(), scv.indexInElement()); }
 
@@ -823,7 +823,7 @@ class BoxLocalAssembler<TypeTag,
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
     using ElementSolutionVector = typename GET_PROP_TYPE(TypeTag, ElementSolutionVector);
     using ElementVolumeVariables = typename GET_PROP_TYPE(TypeTag, ElementVolumeVariables);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using VolumeVariables = typename GET_PROP_TYPE(TypeTag, VolumeVariables);
     using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
     using JacobianMatrix = typename GET_PROP_TYPE(TypeTag, JacobianMatrix);
@@ -1135,7 +1135,7 @@ class BoxLocalAssembler<TypeTag,
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
     using ElementSolutionVector = typename GET_PROP_TYPE(TypeTag, ElementSolutionVector);
     using ElementVolumeVariables = typename GET_PROP_TYPE(TypeTag, ElementVolumeVariables);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using VolumeVariables = typename GET_PROP_TYPE(TypeTag, VolumeVariables);
     using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
     using JacobianMatrix = typename GET_PROP_TYPE(TypeTag, JacobianMatrix);
diff --git a/dumux/assembly/cclocalassembler.hh b/dumux/assembly/cclocalassembler.hh
index 019ef81719942f42db94177531c3584729e77148..dcbce5fcea9bbc376ab70ea1892261aaeacd2290 100644
--- a/dumux/assembly/cclocalassembler.hh
+++ b/dumux/assembly/cclocalassembler.hh
@@ -55,7 +55,7 @@ class CCLocalAssembler<TypeTag,
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
     using ElementSolutionVector = typename GET_PROP_TYPE(TypeTag, ElementSolutionVector);
     using ElementVolumeVariables = typename GET_PROP_TYPE(TypeTag, ElementVolumeVariables);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using VolumeVariables = typename GET_PROP_TYPE(TypeTag, VolumeVariables);
     using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
     using JacobianMatrix = typename GET_PROP_TYPE(TypeTag, JacobianMatrix);
@@ -577,12 +577,12 @@ private:
     }
 private:
     template<class T = TypeTag>
-    static typename std::enable_if<!GET_PROP_VALUE(T, EnableGlobalVolumeVariablesCache), VolumeVariables&>::type
+    static typename std::enable_if<!GET_PROP_VALUE(T, EnableGridVolumeVariablesCache), VolumeVariables&>::type
     getVolVarAccess(GridVolumeVariables& gridVolVars, ElementVolumeVariables& elemVolVars, const SubControlVolume& scv)
     { return elemVolVars[scv]; }
 
     template<class T = TypeTag>
-    static typename std::enable_if<GET_PROP_VALUE(T, EnableGlobalVolumeVariablesCache), VolumeVariables&>::type
+    static typename std::enable_if<GET_PROP_VALUE(T, EnableGridVolumeVariablesCache), VolumeVariables&>::type
     getVolVarAccess(GridVolumeVariables& gridVolVars, ElementVolumeVariables& elemVolVars, const SubControlVolume& scv)
     { return gridVolVars.volVars(scv); }
 };
@@ -600,7 +600,7 @@ class CCLocalAssembler<TypeTag,
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
     using ElementSolutionVector = typename GET_PROP_TYPE(TypeTag, ElementSolutionVector);
     using ElementVolumeVariables = typename GET_PROP_TYPE(TypeTag, ElementVolumeVariables);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using VolumeVariables = typename GET_PROP_TYPE(TypeTag, VolumeVariables);
     using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
     using JacobianMatrix = typename GET_PROP_TYPE(TypeTag, JacobianMatrix);
@@ -917,12 +917,12 @@ private:
     }
 private:
     template<class T = TypeTag>
-    static typename std::enable_if<!GET_PROP_VALUE(T, EnableGlobalVolumeVariablesCache), VolumeVariables&>::type
+    static typename std::enable_if<!GET_PROP_VALUE(T, EnableGridVolumeVariablesCache), VolumeVariables&>::type
     getVolVarAccess(GridVolumeVariables& gridVolVars, ElementVolumeVariables& elemVolVars, const SubControlVolume& scv)
     { return elemVolVars[scv]; }
 
     template<class T = TypeTag>
-    static typename std::enable_if<GET_PROP_VALUE(T, EnableGlobalVolumeVariablesCache), VolumeVariables&>::type
+    static typename std::enable_if<GET_PROP_VALUE(T, EnableGridVolumeVariablesCache), VolumeVariables&>::type
     getVolVarAccess(GridVolumeVariables& gridVolVars, ElementVolumeVariables& elemVolVars, const SubControlVolume& scv)
     { return gridVolVars.volVars(scv); }
 };
@@ -942,7 +942,7 @@ class CCLocalAssembler<TypeTag,
     using JacobianMatrix = typename GET_PROP_TYPE(TypeTag, JacobianMatrix);
     using ElementSolutionVector = typename GET_PROP_TYPE(TypeTag, ElementSolutionVector);
     using ElementVolumeVariables = typename GET_PROP_TYPE(TypeTag, ElementVolumeVariables);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using VolumeVariables = typename GET_PROP_TYPE(TypeTag, VolumeVariables);
     using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
 
@@ -1204,7 +1204,7 @@ class CCLocalAssembler<TypeTag,
     using JacobianMatrix = typename GET_PROP_TYPE(TypeTag, JacobianMatrix);
     using ElementSolutionVector = typename GET_PROP_TYPE(TypeTag, ElementSolutionVector);
     using ElementVolumeVariables = typename GET_PROP_TYPE(TypeTag, ElementVolumeVariables);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using VolumeVariables = typename GET_PROP_TYPE(TypeTag, VolumeVariables);
     using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
 
diff --git a/dumux/assembly/staggeredlocalassembler.hh b/dumux/assembly/staggeredlocalassembler.hh
index 9de574c3a723345cda1ba245d5b8e640889c00d2..b4b6f037a6ca292783d616a29a8dada4bd602451 100644
--- a/dumux/assembly/staggeredlocalassembler.hh
+++ b/dumux/assembly/staggeredlocalassembler.hh
@@ -61,7 +61,7 @@ class StaggeredLocalAssembler<TypeTag,
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
     using ElementSolutionVector = typename GET_PROP_TYPE(TypeTag, ElementSolutionVector);
     using ElementVolumeVariables = typename GET_PROP_TYPE(TypeTag, ElementVolumeVariables);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using VolumeVariables = typename GET_PROP_TYPE(TypeTag, VolumeVariables);
     using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
     using JacobianMatrix = typename GET_PROP_TYPE(TypeTag, JacobianMatrix);
@@ -599,12 +599,12 @@ static void updateGlobalJacobian_(SubMatrix& matrix,
 
 private:
     template<class T = TypeTag>
-    static typename std::enable_if<!GET_PROP_VALUE(T, EnableGlobalVolumeVariablesCache), VolumeVariables&>::type
+    static typename std::enable_if<!GET_PROP_VALUE(T, EnableGridVolumeVariablesCache), VolumeVariables&>::type
     getVolVarAccess(GridVolumeVariables& gridVolVars, ElementVolumeVariables& elemVolVars, const SubControlVolume& scv)
     { return elemVolVars[scv]; }
 
     template<class T = TypeTag>
-    static typename std::enable_if<GET_PROP_VALUE(T, EnableGlobalVolumeVariablesCache), VolumeVariables&>::type
+    static typename std::enable_if<GET_PROP_VALUE(T, EnableGridVolumeVariablesCache), VolumeVariables&>::type
     getVolVarAccess(GridVolumeVariables& gridVolVars, ElementVolumeVariables& elemVolVars, const SubControlVolume& scv)
     { return gridVolVars.volVars(scv); }
 
diff --git a/dumux/common/properties.hh b/dumux/common/properties.hh
index 1aa128345d0b64d995f89faae3dcbf6d54f35cc1..057f8149303523e43f8f6adaf0426986bc72bafd 100644
--- a/dumux/common/properties.hh
+++ b/dumux/common/properties.hh
@@ -91,8 +91,8 @@ NEW_PROP_TAG(EnableFVGridGeometryCache);           //! specifies if geometric da
 
 NEW_PROP_TAG(VolumeVariables);                     //! The secondary variables within a sub-control volume
 NEW_PROP_TAG(ElementVolumeVariables);              //! The type for a local (element/stencil) container for the volume variables
-NEW_PROP_TAG(GlobalVolumeVariables);               //! The type for a global container for the volume variables
-NEW_PROP_TAG(EnableGlobalVolumeVariablesCache);    //! If disabled, the volume variables are not stored (reduces memory, but is slower)
+NEW_PROP_TAG(GridVolumeVariables);                 //! The type for a global container for the volume variables
+NEW_PROP_TAG(EnableGridVolumeVariablesCache);      //! If disabled, the volume variables are not stored (reduces memory, but is slower)
 NEW_PROP_TAG(FluxVariables);                       //! Container storing the different types of flux variables
 NEW_PROP_TAG(FluxVariablesCache);                  //! Stores data associated with flux vars
 NEW_PROP_TAG(ElementFluxVariablesCache);           //! A local vector of flux variable caches per element
diff --git a/dumux/discretization/box/elementvolumevariables.hh b/dumux/discretization/box/elementvolumevariables.hh
index 0ca3960600f732ee734d0c7cc5c04efed9d026e2..5d59105eb6623c65746cf96fcb033478141dfef1 100644
--- a/dumux/discretization/box/elementvolumevariables.hh
+++ b/dumux/discretization/box/elementvolumevariables.hh
@@ -33,7 +33,7 @@ namespace Dumux
  * \ingroup ImplicitModel
  * \brief Base class for the volume variables vector
  */
-template<class TypeTag, bool enableGlobalVolVarsCache>
+template<class TypeTag, bool enableGridVolVarsCache>
 class BoxElementVolumeVariables
 {};
 
@@ -45,7 +45,7 @@ class BoxElementVolumeVariables<TypeTag,/*enableGlobalVolVarCache*/true>
     using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
     using VolumeVariables = typename GET_PROP_TYPE(TypeTag, VolumeVariables);
-    using GlobalVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
     using IndexType = typename GridView::IndexSet::IndexType;
     using FVElementGeometry = typename GET_PROP_TYPE(TypeTag, FVElementGeometry);
@@ -57,14 +57,14 @@ class BoxElementVolumeVariables<TypeTag,/*enableGlobalVolVarCache*/true>
 
 public:
     //! Constructor
-    BoxElementVolumeVariables(const GlobalVolumeVariables& globalVolVars)
-    : globalVolVarsPtr_(&globalVolVars) {}
+    BoxElementVolumeVariables(const GridVolumeVariables& gridVolVars)
+    : gridVolVarsPtr_(&gridVolVars) {}
 
     const VolumeVariables& operator [](IndexType scvIdx) const
-    { return globalVolVars().volVars(eIdx_, scvIdx); }
+    { return gridVolVars().volVars(eIdx_, scvIdx); }
 
     const VolumeVariables& operator [](const SubControlVolume& scv) const
-    { return globalVolVars().volVars(eIdx_, scv.indexInElement()); }
+    { return gridVolVars().volVars(eIdx_, scv.indexInElement()); }
 
     // For compatibility reasons with the case of not storing the vol vars.
     // function to be called before assembling an element, preparing the vol vars within the stencil
@@ -84,11 +84,11 @@ public:
     }
 
     //! The global volume variables object we are a restriction of
-    const GlobalVolumeVariables& globalVolVars() const
-    { return *globalVolVarsPtr_; }
+    const GridVolumeVariables& gridVolVars() const
+    { return *gridVolVarsPtr_; }
 
 private:
-    const GlobalVolumeVariables* globalVolVarsPtr_;
+    const GridVolumeVariables* gridVolVarsPtr_;
     IndexType eIdx_;
 };
 
@@ -101,7 +101,7 @@ class BoxElementVolumeVariables<TypeTag, /*enableGlobalVolVarCache*/false>
     using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
     using VolumeVariables = typename GET_PROP_TYPE(TypeTag, VolumeVariables);
-    using GlobalVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
     using IndexType = typename GridView::IndexSet::IndexType;
     using FVElementGeometry = typename GET_PROP_TYPE(TypeTag, FVElementGeometry);
@@ -112,8 +112,8 @@ class BoxElementVolumeVariables<TypeTag, /*enableGlobalVolVarCache*/false>
 
 public:
     //! Constructor
-    BoxElementVolumeVariables(const GlobalVolumeVariables& globalVolVars)
-    : globalVolVarsPtr_(&globalVolVars) {}
+    BoxElementVolumeVariables(const GridVolumeVariables& gridVolVars)
+    : gridVolVarsPtr_(&gridVolVars) {}
 
     // specialization for box models, simply forwards to the bindElement method
     void bind(const Element& element,
@@ -136,8 +136,8 @@ public:
         for (auto&& scv : scvs(fvGeometry))
         {
             // TODO: INTERFACE SOLVER
-            // globalVolVars().problem().model().boxInterfaceConditionSolver().updateScvVolVars(element, scv, sol);
-            volumeVariables_[scv.indexInElement()].update(elemSol, globalVolVars().problem(), element, scv);
+            // gridVolVars().problem().model().boxInterfaceConditionSolver().updateScvVolVars(element, scv, sol);
+            volumeVariables_[scv.indexInElement()].update(elemSol, gridVolVars().problem(), element, scv);
         }
     }
 
@@ -154,11 +154,11 @@ public:
     { return volumeVariables_[scv.indexInElement()]; }
 
     //! The global volume variables object we are a restriction of
-    const GlobalVolumeVariables& globalVolVars() const
-    { return *globalVolVarsPtr_; }
+    const GridVolumeVariables& gridVolVars() const
+    { return *gridVolVarsPtr_; }
 
 private:
-    const GlobalVolumeVariables* globalVolVarsPtr_;
+    const GridVolumeVariables* gridVolVarsPtr_;
     std::vector<VolumeVariables> volumeVariables_;
 };
 
diff --git a/dumux/discretization/box/globalfluxvariablescache.hh b/dumux/discretization/box/globalfluxvariablescache.hh
index d1196df20e943ac21496ba310d58bf4f3f60f5f7..4961c8dcd632f31077444421f4eca4f1848615e4 100644
--- a/dumux/discretization/box/globalfluxvariablescache.hh
+++ b/dumux/discretization/box/globalfluxvariablescache.hh
@@ -47,7 +47,7 @@ class BoxGlobalFluxVariablesCache<TypeTag, true>
     using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
     using FVGridGeometry = typename GET_PROP_TYPE(TypeTag, FVGridGeometry);
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using IndexType = typename GridView::IndexSet::IndexType;
     using Element = typename GridView::template Codim<0>::Entity;
     using FluxVariablesCache = typename GET_PROP_TYPE(TypeTag, FluxVariablesCache);
@@ -121,7 +121,7 @@ class BoxGlobalFluxVariablesCache<TypeTag, false>
     using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
     using FVGridGeometry = typename GET_PROP_TYPE(TypeTag, FVGridGeometry);
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using IndexType = typename GridView::IndexSet::IndexType;
     using Element = typename GridView::template Codim<0>::Entity;
     using FluxVariablesCache = typename GET_PROP_TYPE(TypeTag, FluxVariablesCache);
diff --git a/dumux/discretization/box/globalvolumevariables.hh b/dumux/discretization/box/globalvolumevariables.hh
index 27e9f0b768804cc53162dee79508d9aac6bcd104..7e3f6abd60db0d043b63a6fb4905a1882b38318c 100644
--- a/dumux/discretization/box/globalvolumevariables.hh
+++ b/dumux/discretization/box/globalvolumevariables.hh
@@ -32,13 +32,13 @@ namespace Dumux
  * \ingroup ImplicitModel
  * \brief Base class for the volume variables vector
  */
-template<class TypeTag, bool enableGlobalVolVarsCache>
-class BoxGlobalVolumeVariables
+template<class TypeTag, bool enableGridVolVarsCache>
+class BoxGridVolumeVariables
 {};
 
 // specialization in case of storing the volume variables
 template<class TypeTag>
-class BoxGlobalVolumeVariables<TypeTag,/*enableGlobalVolVarCache*/true>
+class BoxGridVolumeVariables<TypeTag,/*enableGlobalVolVarCache*/true>
 {
     using Problem = typename GET_PROP_TYPE(TypeTag, Problem);
     using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
@@ -55,7 +55,7 @@ class BoxGlobalVolumeVariables<TypeTag,/*enableGlobalVolVarCache*/true>
     using Element = typename GridView::template Codim<0>::Entity;
 
 public:
-    BoxGlobalVolumeVariables(const Problem& problem) : problemPtr_(&problem) {}
+    BoxGridVolumeVariables(const Problem& problem) : problemPtr_(&problem) {}
 
     void update(const FVGridGeometry& fvGridGeometry, const SolutionVector& sol)
     {
@@ -82,7 +82,7 @@ public:
      *        The local object is only functional after calling its bind/bindElement method
      *        This is a free function that will be found by means of ADL
      */
-    friend inline ElementVolumeVariables localView(const BoxGlobalVolumeVariables& global)
+    friend inline ElementVolumeVariables localView(const BoxGridVolumeVariables& global)
     { return ElementVolumeVariables(global); }
 
     const VolumeVariables& volVars(const IndexType eIdx, const IndexType scvIdx) const
@@ -102,7 +102,7 @@ private:
 
 // Specialization when the current volume variables are not stored
 template<class TypeTag>
-class BoxGlobalVolumeVariables<TypeTag, /*enableGlobalVolVarCache*/false>
+class BoxGridVolumeVariables<TypeTag, /*enableGlobalVolVarCache*/false>
 {
     using Problem = typename GET_PROP_TYPE(TypeTag, Problem);
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
@@ -111,7 +111,7 @@ class BoxGlobalVolumeVariables<TypeTag, /*enableGlobalVolVarCache*/false>
     using FVGridGeometry = typename GET_PROP_TYPE(TypeTag, FVGridGeometry);
 
 public:
-    BoxGlobalVolumeVariables(const Problem& problem) : problemPtr_(&problem) {}
+    BoxGridVolumeVariables(const Problem& problem) : problemPtr_(&problem) {}
 
     void update(const FVGridGeometry& fvGridGeometry, const SolutionVector& sol) {}
 
@@ -120,7 +120,7 @@ public:
      *        The local object is only functional after calling its bind/bindElement method
      *        This is a free function that will be found by means of ADL
      */
-    friend inline ElementVolumeVariables localView(const BoxGlobalVolumeVariables& global)
+    friend inline ElementVolumeVariables localView(const BoxGridVolumeVariables& global)
     { return ElementVolumeVariables(global); }
 
     const Problem& problem() const
diff --git a/dumux/discretization/box/properties.hh b/dumux/discretization/box/properties.hh
index 99953e79425346d5da61eba4ee8966f99322ce94..8714f760d6ab16350b000fd06364214a748f32af 100644
--- a/dumux/discretization/box/properties.hh
+++ b/dumux/discretization/box/properties.hh
@@ -160,12 +160,12 @@ SET_TYPE_PROP(BoxModel, ElementSolutionVector, BoxElementSolution<TypeTag>);
 SET_TYPE_PROP(BoxModel, ElementBoundaryTypes, BoxElementBoundaryTypes<TypeTag>);
 
 //! The global volume variables vector class
-SET_TYPE_PROP(BoxModel, GlobalVolumeVariables, BoxGlobalVolumeVariables<TypeTag,
-                            GET_PROP_VALUE(TypeTag, EnableGlobalVolumeVariablesCache)>);
+SET_TYPE_PROP(BoxModel, GridVolumeVariables, BoxGridVolumeVariables<TypeTag,
+                            GET_PROP_VALUE(TypeTag, EnableGridVolumeVariablesCache)>);
 
 //! The element volume variables vector class
 SET_TYPE_PROP(BoxModel, ElementVolumeVariables, BoxElementVolumeVariables<TypeTag,
-                            GET_PROP_VALUE(TypeTag, EnableGlobalVolumeVariablesCache)>);
+                            GET_PROP_VALUE(TypeTag, EnableGridVolumeVariablesCache)>);
 
 //! The global flux variables cache vector class
 SET_TYPE_PROP(BoxModel, GlobalFluxVariablesCache, BoxGlobalFluxVariablesCache<TypeTag,
diff --git a/dumux/discretization/cellcentered/globalvolumevariables.hh b/dumux/discretization/cellcentered/globalvolumevariables.hh
index 9e2780aba53267e6f3931b5fc51df7c60575c49c..338236cc56c6e2c56b9789ec9d77d5417793f6ea 100644
--- a/dumux/discretization/cellcentered/globalvolumevariables.hh
+++ b/dumux/discretization/cellcentered/globalvolumevariables.hh
@@ -32,13 +32,13 @@ namespace Dumux
  * \ingroup ImplicitModel
  * \brief Base class for the volume variables vector
  */
-template<class TypeTag, bool enableGlobalVolVarsCache>
-class CCGlobalVolumeVariables
+template<class TypeTag, bool enableGridVolVarsCache>
+class CCGridVolumeVariables
 {};
 
 //! specialization in case of storing the volume variables
 template<class TypeTag>
-class CCGlobalVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/true>
+class CCGridVolumeVariables<TypeTag, /*enableGridVolVarsCache*/true>
 {
     using Problem = typename GET_PROP_TYPE(TypeTag, Problem);
     using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
@@ -54,7 +54,7 @@ class CCGlobalVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/true>
     using Element = typename GridView::template Codim<0>::Entity;
 
 public:
-    CCGlobalVolumeVariables(const Problem& problem) : problemPtr_(&problem) {}
+    CCGridVolumeVariables(const Problem& problem) : problemPtr_(&problem) {}
 
     void update(const FVGridGeometry& fvGridGeometry, const SolutionVector& sol)
     {
@@ -102,7 +102,7 @@ public:
      *        The local object is only functional after calling its bind/bindElement method
      *        This is a free function that will be found by means of ADL
      */
-    friend inline ElementVolumeVariables localView(const CCGlobalVolumeVariables& global)
+    friend inline ElementVolumeVariables localView(const CCGridVolumeVariables& global)
     { return ElementVolumeVariables(global); }
 
     const VolumeVariables& volVars(const IndexType scvIdx) const
@@ -137,7 +137,7 @@ private:
 
 //! Specialization when the current volume variables are not stored globally
 template<class TypeTag>
-class CCGlobalVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/false>
+class CCGridVolumeVariables<TypeTag, /*enableGridVolVarsCache*/false>
 {
     using Problem = typename GET_PROP_TYPE(TypeTag, Problem);
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
@@ -145,7 +145,7 @@ class CCGlobalVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/false>
     using FVGridGeometry = typename GET_PROP_TYPE(TypeTag, FVGridGeometry);
 
 public:
-    CCGlobalVolumeVariables(const Problem& problem) : problemPtr_(&problem) {}
+    CCGridVolumeVariables(const Problem& problem) : problemPtr_(&problem) {}
 
     void update(const FVGridGeometry& fvGridGeometry, const SolutionVector& sol) {}
 
@@ -154,7 +154,7 @@ public:
      *        The local object is only functional after calling its bind/bindElement method
      *        This is a free function that will be found by means of ADL
      */
-    friend inline ElementVolumeVariables localView(const CCGlobalVolumeVariables& global)
+    friend inline ElementVolumeVariables localView(const CCGridVolumeVariables& global)
     { return ElementVolumeVariables(global); }
 
     //! The problem we are solving
diff --git a/dumux/discretization/cellcentered/mpfa/elementvolumevariables.hh b/dumux/discretization/cellcentered/mpfa/elementvolumevariables.hh
index d7285035c6ba05ea5dd6ed82e1909c0da17662e5..5d63f8669a43b0c4d65d12cd2f30b15e28826704 100644
--- a/dumux/discretization/cellcentered/mpfa/elementvolumevariables.hh
+++ b/dumux/discretization/cellcentered/mpfa/elementvolumevariables.hh
@@ -30,20 +30,20 @@ namespace Dumux
  * \ingroup ImplicitModel
  * \brief Base class for the local volume variables vector
  */
-template<class TypeTag, bool enableGlobalVolVarsCache>
+template<class TypeTag, bool enableGridVolVarsCache>
 class CCMpfaElementVolumeVariables
 {};
 
 // specialization in case of storing the volume variables globally
 template<class TypeTag>
-class CCMpfaElementVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/true>
+class CCMpfaElementVolumeVariables<TypeTag, /*enableGridVolVarsCache*/true>
 {
     using Problem = typename GET_PROP_TYPE(TypeTag, Problem);
     using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
     using FVElementGeometry = typename GET_PROP_TYPE(TypeTag, FVElementGeometry);
     using VolumeVariables = typename GET_PROP_TYPE(TypeTag, VolumeVariables);
-    using GlobalVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
     using IndexType = typename GridView::IndexSet::IndexType;
 
@@ -52,16 +52,16 @@ class CCMpfaElementVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/true>
 
 public:
     //! Constructor
-    CCMpfaElementVolumeVariables(const GlobalVolumeVariables& globalVolVars)
-    : globalVolVarsPtr_(&globalVolVars) {}
+    CCMpfaElementVolumeVariables(const GridVolumeVariables& gridVolVars)
+    : gridVolVarsPtr_(&gridVolVars) {}
 
     const VolumeVariables& operator [](const SubControlVolume& scv) const
-    { return globalVolVars().volVars(scv.dofIndex()); }
+    { return gridVolVars().volVars(scv.dofIndex()); }
 
     // operator for the access with an index
     // needed for cc methods for the access to the boundary volume variables
     const VolumeVariables& operator [](const IndexType scvIdx) const
-    { return globalVolVars().volVars(scvIdx); }
+    { return gridVolVars().volVars(scvIdx); }
 
     // For compatibility reasons with the case of not storing the vol vars.
     // function to be called before assembling an element, preparing the vol vars within the stencil
@@ -75,17 +75,17 @@ public:
                      const SolutionVector& sol) {}
 
     //! The global volume variables object we are a restriction of
-    const GlobalVolumeVariables& globalVolVars() const
-    { return *globalVolVarsPtr_; }
+    const GridVolumeVariables& gridVolVars() const
+    { return *gridVolVarsPtr_; }
 
 private:
-    const GlobalVolumeVariables* globalVolVarsPtr_;
+    const GridVolumeVariables* gridVolVarsPtr_;
 };
 
 
 // Specialization when the current volume variables are not stored
 template<class TypeTag>
-class CCMpfaElementVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/false>
+class CCMpfaElementVolumeVariables<TypeTag, /*enableGridVolVarsCache*/false>
 {
     using Problem = typename GET_PROP_TYPE(TypeTag, Problem);
     using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
@@ -93,7 +93,7 @@ class CCMpfaElementVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/false>
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
     using ElementSolution = typename GET_PROP_TYPE(TypeTag, ElementSolutionVector);
     using VolumeVariables = typename GET_PROP_TYPE(TypeTag, VolumeVariables);
-    using GlobalVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
     using FVElementGeometry = typename GET_PROP_TYPE(TypeTag, FVElementGeometry);
     using IndexType = typename GridView::IndexSet::IndexType;
@@ -104,8 +104,8 @@ class CCMpfaElementVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/false>
 public:
 
     //! Constructor
-    CCMpfaElementVolumeVariables(const GlobalVolumeVariables& globalVolVars)
-    : globalVolVarsPtr_(&globalVolVars) {}
+    CCMpfaElementVolumeVariables(const GridVolumeVariables& gridVolVars)
+    : gridVolVarsPtr_(&gridVolVars) {}
 
     // Binding of an element, prepares the volume variables within the element stencil
     // called by the local jacobian to prepare element assembly
@@ -113,7 +113,7 @@ public:
               const FVElementGeometry& fvGeometry,
               const SolutionVector& sol)
     {
-        const auto& problem = globalVolVars().problem();
+        const auto& problem = gridVolVars().problem();
         const auto& fvGridGeometry = fvGeometry.fvGridGeometry();
         const auto& gridIvIndexSets = fvGridGeometry.gridInteractionVolumeIndexSets();
 
@@ -245,7 +245,7 @@ public:
         // update the volume variables of the element
         const auto& scv = fvGeometry.scv(eIdx);
         volumeVariables_[0].update(ElementSolution(sol[scv.dofIndex()]),
-                                   globalVolVars().problem(),
+                                   gridVolVars().problem(),
                                    element,
                                    scv);
         volVarIndices_[0] = scv.dofIndex();
@@ -264,11 +264,11 @@ public:
     { return volumeVariables_[getLocalIdx_(scvIdx)]; }
 
     //! The global volume variables object we are a restriction of
-    const GlobalVolumeVariables& globalVolVars() const
-    { return *globalVolVarsPtr_; }
+    const GridVolumeVariables& gridVolVars() const
+    { return *gridVolVarsPtr_; }
 
 private:
-    const GlobalVolumeVariables* globalVolVarsPtr_;
+    const GridVolumeVariables* gridVolVarsPtr_;
 
     //! Computes how many boundary vol vars come into play for flux calculations
     //! on this element. This number is probably almost always higher than the actually
diff --git a/dumux/discretization/cellcentered/mpfa/globalfluxvariablescache.hh b/dumux/discretization/cellcentered/mpfa/globalfluxvariablescache.hh
index 44d334a34fe6bb6849e9a50c461e5273023caea8..e930a936e3043f31e7a229da9da4e4561e5a0ee8 100644
--- a/dumux/discretization/cellcentered/mpfa/globalfluxvariablescache.hh
+++ b/dumux/discretization/cellcentered/mpfa/globalfluxvariablescache.hh
@@ -53,7 +53,7 @@ class CCMpfaGlobalFluxVariablesCache<TypeTag, true>
     using FVGridGeometry = typename GET_PROP_TYPE(TypeTag, FVGridGeometry);
     using FVElementGeometry = typename GET_PROP_TYPE(TypeTag, FVElementGeometry);
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using ElementVolumeVariables = typename GET_PROP_TYPE(TypeTag, ElementVolumeVariables);
     using IndexType = typename GridView::IndexSet::IndexType;
     using FluxVariablesCache = typename GET_PROP_TYPE(TypeTag, FluxVariablesCache);
@@ -211,7 +211,7 @@ class CCMpfaGlobalFluxVariablesCache<TypeTag, false>
     using FVGridGeometry = typename GET_PROP_TYPE(TypeTag, FVGridGeometry);
     using FVElementGeometry = typename GET_PROP_TYPE(TypeTag, FVElementGeometry);
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using ElementVolumeVariables = typename GET_PROP_TYPE(TypeTag, ElementVolumeVariables);
 
 public:
diff --git a/dumux/discretization/cellcentered/mpfa/globalvolumevariables.hh b/dumux/discretization/cellcentered/mpfa/globalvolumevariables.hh
index 853ef04255f44e7c6d28310192e4cdc2c5f88e41..74dad604fa1dbe9533666a246ed97a321a99adde 100644
--- a/dumux/discretization/cellcentered/mpfa/globalvolumevariables.hh
+++ b/dumux/discretization/cellcentered/mpfa/globalvolumevariables.hh
@@ -33,13 +33,13 @@ namespace Dumux
  * \ingroup ImplicitModel
  * \brief Base class for the volume variables vector
  */
-template<class TypeTag, bool enableGlobalVolVarsCache>
-class CCMpfaGlobalVolumeVariables
+template<class TypeTag, bool enableGridVolVarsCache>
+class CCMpfaGridVolumeVariables
 {};
 
 //! specialization in case of storing the volume variables
 template<class TypeTag>
-class CCMpfaGlobalVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/true>
+class CCMpfaGridVolumeVariables<TypeTag, /*enableGridVolVarsCache*/true>
 {
     // The local class needs to access and change volVars
     friend typename GET_PROP_TYPE(TypeTag, ElementVolumeVariables);
@@ -108,7 +108,7 @@ public:
      *        The local object is only functional after calling its bind/bindElement method
      *        This is a free function that will be found by means of ADL
      */
-    friend inline ElementVolumeVariables localView(const CCMpfaGlobalVolumeVariables& global)
+    friend inline ElementVolumeVariables localView(const CCMpfaGridVolumeVariables& global)
     { return ElementVolumeVariables(global); }
 
     const VolumeVariables& volVars(const IndexType scvIdx) const
@@ -128,7 +128,7 @@ private:
 
 //! Specialization when the current volume variables are not stored globally
 template<class TypeTag>
-class CCMpfaGlobalVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/false>
+class CCMpfaGridVolumeVariables<TypeTag, /*enableGridVolVarsCache*/false>
 {
     // local class needs access to the problem
     friend typename GET_PROP_TYPE(TypeTag, ElementVolumeVariables);
@@ -145,7 +145,7 @@ public:
      *        The local object is only functional after calling its bind/bindElement method
      *        This is a free function that will be found by means of ADL
      */
-    friend inline ElementVolumeVariables localView(const CCMpfaGlobalVolumeVariables& global)
+    friend inline ElementVolumeVariables localView(const CCMpfaGridVolumeVariables& global)
     { return ElementVolumeVariables(global); }
 
 private:
diff --git a/dumux/discretization/cellcentered/mpfa/properties.hh b/dumux/discretization/cellcentered/mpfa/properties.hh
index 793953f337a4cc318517e6422eeee5cfffc23b95..fad5670078dedf622c5dd6678804ecbd96d353aa 100644
--- a/dumux/discretization/cellcentered/mpfa/properties.hh
+++ b/dumux/discretization/cellcentered/mpfa/properties.hh
@@ -107,10 +107,10 @@ SET_TYPE_PROP(CCMpfaModel,
 //! The global previous volume variables vector class
 SET_TYPE_PROP(CCMpfaModel,
               ElementVolumeVariables,
-              CCMpfaElementVolumeVariables<TypeTag, GET_PROP_VALUE(TypeTag, EnableGlobalVolumeVariablesCache)>);
+              CCMpfaElementVolumeVariables<TypeTag, GET_PROP_VALUE(TypeTag, EnableGridVolumeVariablesCache)>);
 
 //! The global current volume variables vector class
-SET_TYPE_PROP(CCMpfaModel, GlobalVolumeVariables, CCGlobalVolumeVariables<TypeTag, GET_PROP_VALUE(TypeTag, EnableGlobalVolumeVariablesCache)>);
+SET_TYPE_PROP(CCMpfaModel, GridVolumeVariables, CCGridVolumeVariables<TypeTag, GET_PROP_VALUE(TypeTag, EnableGridVolumeVariablesCache)>);
 
 //! The sub control volume
 SET_PROP(CCMpfaModel, SubControlVolume)
diff --git a/dumux/discretization/cellcentered/tpfa/elementvolumevariables.hh b/dumux/discretization/cellcentered/tpfa/elementvolumevariables.hh
index 76f66a92c0de5136895ba5a87d82a94a00c54f9d..35e2ddf7b6d6da7ad75b079344ee548f8881abc5 100644
--- a/dumux/discretization/cellcentered/tpfa/elementvolumevariables.hh
+++ b/dumux/discretization/cellcentered/tpfa/elementvolumevariables.hh
@@ -32,13 +32,13 @@ namespace Dumux
  * \ingroup ImplicitModel
  * \brief Base class for the volume variables vector
  */
-template<class TypeTag, bool enableGlobalVolVarsCache>
+template<class TypeTag, bool enableGridVolVarsCache>
 class CCTpfaElementVolumeVariables
 {};
 
 // specialization in case of storing the volume variables globally
 template<class TypeTag>
-class CCTpfaElementVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/true>
+class CCTpfaElementVolumeVariables<TypeTag, /*enableGridVolVarsCache*/true>
 {
     using Problem = typename GET_PROP_TYPE(TypeTag, Problem);
     using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
@@ -46,7 +46,7 @@ class CCTpfaElementVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/true>
     using ElementSolution = typename GET_PROP_TYPE(TypeTag, ElementSolutionVector);
     using FVElementGeometry = typename GET_PROP_TYPE(TypeTag, FVElementGeometry);
     using VolumeVariables = typename GET_PROP_TYPE(TypeTag, VolumeVariables);
-    using GlobalVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
     using IndexType = typename GridView::IndexSet::IndexType;
 
@@ -55,16 +55,16 @@ class CCTpfaElementVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/true>
 
 public:
     //! Constructor
-    CCTpfaElementVolumeVariables(const GlobalVolumeVariables& globalVolVars)
-    : globalVolVarsPtr_(&globalVolVars) {}
+    CCTpfaElementVolumeVariables(const GridVolumeVariables& gridVolVars)
+    : gridVolVarsPtr_(&gridVolVars) {}
 
     const VolumeVariables& operator [](const SubControlVolume& scv) const
-    { return globalVolVars().volVars(scv.dofIndex()); }
+    { return gridVolVars().volVars(scv.dofIndex()); }
 
     // operator for the access with an index
     // needed for cc methods for the access to the boundary volume variables
     const VolumeVariables& operator [](const IndexType scvIdx) const
-    { return globalVolVars().volVars(scvIdx); }
+    { return gridVolVars().volVars(scvIdx); }
 
     // For compatibility reasons with the case of not storing the vol vars.
     // function to be called before assembling an element, preparing the vol vars within the stencil
@@ -80,24 +80,24 @@ public:
     {}
 
     //! The global volume variables object we are a restriction of
-    const GlobalVolumeVariables& globalVolVars() const
-    { return *globalVolVarsPtr_; }
+    const GridVolumeVariables& gridVolVars() const
+    { return *gridVolVarsPtr_; }
 
 private:
-    const GlobalVolumeVariables* globalVolVarsPtr_;
+    const GridVolumeVariables* gridVolVarsPtr_;
 };
 
 
 // Specialization when the current volume variables are not stored
 template<class TypeTag>
-class CCTpfaElementVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/false>
+class CCTpfaElementVolumeVariables<TypeTag, /*enableGridVolVarsCache*/false>
 {
     using Problem = typename GET_PROP_TYPE(TypeTag, Problem);
     using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
     using ElementSolution = typename GET_PROP_TYPE(TypeTag, ElementSolutionVector);
     using VolumeVariables = typename GET_PROP_TYPE(TypeTag, VolumeVariables);
-    using GlobalVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
     using FVElementGeometry = typename GET_PROP_TYPE(TypeTag, FVElementGeometry);
     using IndexType = typename GridView::IndexSet::IndexType;
@@ -108,8 +108,8 @@ class CCTpfaElementVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/false>
 public:
 
     //! Constructor
-    CCTpfaElementVolumeVariables(const GlobalVolumeVariables& globalVolVars)
-    : globalVolVarsPtr_(&globalVolVars) {}
+    CCTpfaElementVolumeVariables(const GridVolumeVariables& gridVolVars)
+    : gridVolVarsPtr_(&gridVolVars) {}
 
     // Binding of an element, prepares the volume variables within the element stencil
     // called by the local jacobian to prepare element assembly
@@ -119,7 +119,7 @@ public:
     {
         clear();
 
-        const auto& problem = globalVolVars().problem();
+        const auto& problem = gridVolVars().problem();
         const auto& fvGridGeometry = fvGeometry.fvGridGeometry();
         const auto globalI = fvGridGeometry.elementMapper().index(element);
         const auto& connectivityMapI = fvGridGeometry.connectivityMap()[globalI];
@@ -213,7 +213,7 @@ public:
         // update the volume variables of the element
         auto&& scv = fvGeometry.scv(eIdx);
         volumeVariables_[0].update(ElementSolution(sol[eIdx]),
-                                   globalVolVars().problem(),
+                                   gridVolVars().problem(),
                                    element,
                                    scv);
         volVarIndices_[0] = scv.dofIndex();
@@ -232,8 +232,8 @@ public:
     { return volumeVariables_[getLocalIdx_(scvIdx)]; }
 
     //! The global volume variables object we are a restriction of
-    const GlobalVolumeVariables& globalVolVars() const
-    { return *globalVolVarsPtr_; }
+    const GridVolumeVariables& gridVolVars() const
+    { return *gridVolVarsPtr_; }
 
     //! Clear all local storage
     void clear()
@@ -242,7 +242,7 @@ public:
         volumeVariables_.clear();
     }
 private:
-    const GlobalVolumeVariables* globalVolVarsPtr_;
+    const GridVolumeVariables* gridVolVarsPtr_;
 
     int getLocalIdx_(const int volVarIdx) const
     {
diff --git a/dumux/discretization/cellcentered/tpfa/globalfluxvariablescache.hh b/dumux/discretization/cellcentered/tpfa/globalfluxvariablescache.hh
index d8f8f20d71e23264c831fb011d5003dbb60da73c..2bf5e2f5eeebc6c2a6e61c2fa38ab3ee35d9d4f2 100644
--- a/dumux/discretization/cellcentered/tpfa/globalfluxvariablescache.hh
+++ b/dumux/discretization/cellcentered/tpfa/globalfluxvariablescache.hh
@@ -47,7 +47,7 @@ class CCTpfaGlobalFluxVariablesCache<TypeTag, true>
     using FVGridGeometry = typename GET_PROP_TYPE(TypeTag, FVGridGeometry);
     using FVElementGeometry = typename GET_PROP_TYPE(TypeTag, FVElementGeometry);
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using ElementVolumeVariables = typename GET_PROP_TYPE(TypeTag, ElementVolumeVariables);
     using IndexType = typename GridView::IndexSet::IndexType;
     using Element = typename GridView::template Codim<0>::Entity;
@@ -157,7 +157,7 @@ class CCTpfaGlobalFluxVariablesCache<TypeTag, false>
     using FVGridGeometry = typename GET_PROP_TYPE(TypeTag, FVGridGeometry);
     using FVElementGeometry = typename GET_PROP_TYPE(TypeTag, FVElementGeometry);
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using ElementVolumeVariables = typename GET_PROP_TYPE(TypeTag, ElementVolumeVariables);
 
 public:
diff --git a/dumux/discretization/cellcentered/tpfa/properties.hh b/dumux/discretization/cellcentered/tpfa/properties.hh
index fb182ede1d3b3c2c75736287678587ba42ffbd4a..186601ca63ed6ae8873f1acb480669deb0bdf3a3 100644
--- a/dumux/discretization/cellcentered/tpfa/properties.hh
+++ b/dumux/discretization/cellcentered/tpfa/properties.hh
@@ -75,13 +75,13 @@ SET_TYPE_PROP(CCTpfaModel, GlobalFluxVariablesCache, CCTpfaGlobalFluxVariablesCa
 SET_TYPE_PROP(CCTpfaModel, FVElementGeometry, CCTpfaFVElementGeometry<TypeTag, GET_PROP_VALUE(TypeTag, EnableFVGridGeometryCache)>);
 
 //! The global previous volume variables vector class
-SET_TYPE_PROP(CCTpfaModel, ElementVolumeVariables, CCTpfaElementVolumeVariables<TypeTag, GET_PROP_VALUE(TypeTag, EnableGlobalVolumeVariablesCache)>);
+SET_TYPE_PROP(CCTpfaModel, ElementVolumeVariables, CCTpfaElementVolumeVariables<TypeTag, GET_PROP_VALUE(TypeTag, EnableGridVolumeVariablesCache)>);
 
 //! The local flux variables cache vector class
 SET_TYPE_PROP(CCTpfaModel, ElementFluxVariablesCache, CCTpfaElementFluxVariablesCache<TypeTag, GET_PROP_VALUE(TypeTag, EnableGlobalFluxVariablesCache)>);
 
 //! The global current volume variables vector class
-SET_TYPE_PROP(CCTpfaModel, GlobalVolumeVariables, CCGlobalVolumeVariables<TypeTag, GET_PROP_VALUE(TypeTag, EnableGlobalVolumeVariablesCache)>);
+SET_TYPE_PROP(CCTpfaModel, GridVolumeVariables, CCGridVolumeVariables<TypeTag, GET_PROP_VALUE(TypeTag, EnableGridVolumeVariablesCache)>);
 
 //! The sub control volume
 SET_PROP(CCTpfaModel, SubControlVolume)
diff --git a/dumux/discretization/fvgridvariables.hh b/dumux/discretization/fvgridvariables.hh
index 5de07b9aaef754a30f008995c98ad3c6245271ab..58e98b68f06932856d943f47ded9f4f21d2b7c5b 100644
--- a/dumux/discretization/fvgridvariables.hh
+++ b/dumux/discretization/fvgridvariables.hh
@@ -37,7 +37,7 @@ class FVGridVariables
 {
     using Problem = typename GET_PROP_TYPE(TypeTag, Problem);
     using FVGridGeometry = typename GET_PROP_TYPE(TypeTag, FVGridGeometry);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using GridFluxVariablesCache = typename GET_PROP_TYPE(TypeTag, GlobalFluxVariablesCache);
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
 
diff --git a/dumux/discretization/fvproperties.hh b/dumux/discretization/fvproperties.hh
index 5db3a642e2f094623910f95e53c1b962c2a5554f..3b2be681c94925d344e0b684261656ccc7f54e56 100644
--- a/dumux/discretization/fvproperties.hh
+++ b/dumux/discretization/fvproperties.hh
@@ -52,7 +52,7 @@ SET_TYPE_PROP(FiniteVolumeModel, ElementSolutionVector, Dune::BlockVector<typena
 SET_BOOL_PROP(FiniteVolumeModel, EnableFVGridGeometryCache, false);
 
 //! We do not store the volume variables by default
-SET_BOOL_PROP(FiniteVolumeModel, EnableGlobalVolumeVariablesCache, false);
+SET_BOOL_PROP(FiniteVolumeModel, EnableGridVolumeVariablesCache, false);
 
 //! disable flux variables data caching by default
 SET_BOOL_PROP(FiniteVolumeModel, EnableGlobalFluxVariablesCache, false);
diff --git a/dumux/discretization/staggered/elementvolumevariables.hh b/dumux/discretization/staggered/elementvolumevariables.hh
index 1bcb8e8976c0f8baf440baaa967fca3cf65253c6..26712c462b1aca7c83b14c29a3c85e8e07624f80 100644
--- a/dumux/discretization/staggered/elementvolumevariables.hh
+++ b/dumux/discretization/staggered/elementvolumevariables.hh
@@ -33,20 +33,20 @@ namespace Dumux
  * \ingroup ImplicitModel
  * \brief Base class for the volume variables vector
  */
-template<class TypeTag, bool enableGlobalVolVarsCache>
+template<class TypeTag, bool enableGridVolVarsCache>
 class StaggeredElementVolumeVariables
 {};
 
 // specialization in case of storing the volume variables globally
 template<class TypeTag>
-class StaggeredElementVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/true>
+class StaggeredElementVolumeVariables<TypeTag, /*enableGridVolVarsCache*/true>
 {
     using Problem = typename GET_PROP_TYPE(TypeTag, Problem);
     using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
     using FVElementGeometry = typename GET_PROP_TYPE(TypeTag, FVElementGeometry);
     using VolumeVariables = typename GET_PROP_TYPE(TypeTag, VolumeVariables);
-    using GlobalVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
     using IndexType = typename GridView::IndexSet::IndexType;
 
@@ -55,16 +55,16 @@ class StaggeredElementVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/true>
 
 public:
     //! Constructor
-    StaggeredElementVolumeVariables(const GlobalVolumeVariables& globalVolVars)
-    : globalVolVarsPtr_(&globalVolVars) {}
+    StaggeredElementVolumeVariables(const GridVolumeVariables& gridVolVars)
+    : gridVolVarsPtr_(&gridVolVars) {}
 
     const VolumeVariables& operator [](const SubControlVolume& scv) const
-    { return globalVolVars().volVars(scv.dofIndex()); }
+    { return gridVolVars().volVars(scv.dofIndex()); }
 
     // operator for the access with an index
     // needed for Staggered methods for the access to the boundary volume variables
     const VolumeVariables& operator [](const IndexType scvIdx) const
-    { return globalVolVars().volVars(scvIdx); }
+    { return gridVolVars().volVars(scvIdx); }
 
     // For compatibility reasons with the case of not storing the vol vars.
     // function to be called before assembling an element, preparing the vol vars within the stencil
@@ -80,17 +80,17 @@ public:
     {}
 
     //! The global volume variables object we are a restriction of
-    const GlobalVolumeVariables& globalVolVars() const
-    { return *globalVolVarsPtr_; }
+    const GridVolumeVariables& gridVolVars() const
+    { return *gridVolVarsPtr_; }
 
 private:
-    const GlobalVolumeVariables* globalVolVarsPtr_;
+    const GridVolumeVariables* gridVolVarsPtr_;
 };
 
 
 // Specialization when the current volume variables are not stored
 template<class TypeTag>
-class StaggeredElementVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/false>
+class StaggeredElementVolumeVariables<TypeTag, /*enableGridVolVarsCache*/false>
 {
     using Problem = typename GET_PROP_TYPE(TypeTag, Problem);
     using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
@@ -99,7 +99,7 @@ class StaggeredElementVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/false
     using ElementSolution = typename GET_PROP_TYPE(TypeTag, ElementSolutionVector);
     using VolumeVariables = typename GET_PROP_TYPE(TypeTag, VolumeVariables);
     using CellCenterPrimaryVariables = typename GET_PROP_TYPE(TypeTag, CellCenterPrimaryVariables);
-    using GlobalVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
     using FVElementGeometry = typename GET_PROP_TYPE(TypeTag, FVElementGeometry);
     using IndexType = typename GridView::IndexSet::IndexType;
@@ -116,8 +116,8 @@ class StaggeredElementVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/false
 public:
 
     //! Constructor
-    StaggeredElementVolumeVariables(const GlobalVolumeVariables& globalVolVars)
-    : globalVolVarsPtr_(&globalVolVars) {}
+    StaggeredElementVolumeVariables(const GridVolumeVariables& gridVolVars)
+    : gridVolVarsPtr_(&gridVolVars) {}
 
     // Binding of an element, prepares the volume variables within the element stencil
     // called by the local jacobian to prepare element assembly
@@ -127,7 +127,7 @@ public:
     {
         clear();
 
-        const auto& problem = globalVolVars().problem();
+        const auto& problem = gridVolVars().problem();
         const auto& fvGridGeometry = fvGeometry.fvGridGeometry();
         const auto globalI = fvGridGeometry.elementMapper().index(element);
         const auto map = fvGridGeometry.connectivityMap();
@@ -212,7 +212,7 @@ public:
         priVars = sol[cellCenterIdx][eIdx];
         ElementSolution elemSol{std::move(priVars)};
         volumeVariables_[0].update(elemSol,
-                                   globalVolVars().problem(),
+                                   gridVolVars().problem(),
                                    element,
                                    scv);
         volVarIndices_[0] = scv.dofIndex();
@@ -231,8 +231,8 @@ public:
     { return volumeVariables_[getLocalIdx_(scvIdx)]; }
 
     //! The global volume variables object we are a restriction of
-    const GlobalVolumeVariables& globalVolVars() const
-    { return *globalVolVarsPtr_; }
+    const GridVolumeVariables& gridVolVars() const
+    { return *gridVolVarsPtr_; }
 
     //! Clear all local storage
     void clear()
@@ -242,7 +242,7 @@ public:
     }
 
 private:
-    const GlobalVolumeVariables* globalVolVarsPtr_;
+    const GridVolumeVariables* gridVolVarsPtr_;
 
     const int getLocalIdx_(const int volVarIdx) const
     {
diff --git a/dumux/discretization/staggered/globalfluxvariablescache.hh b/dumux/discretization/staggered/globalfluxvariablescache.hh
index 5f5b305bc6af955341483e341eb7b61f51dfdb87..1374b427920afb7ae8129ac6ecd6194e0419df7d 100644
--- a/dumux/discretization/staggered/globalfluxvariablescache.hh
+++ b/dumux/discretization/staggered/globalfluxvariablescache.hh
@@ -49,7 +49,7 @@ class StaggeredGlobalFluxVariablesCache<TypeTag, true>
     using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
     using FVGridGeometry = typename GET_PROP_TYPE(TypeTag, FVGridGeometry);
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using IndexType = typename GridView::IndexSet::IndexType;
     using FluxVariablesCache = typename GET_PROP_TYPE(TypeTag, FluxVariablesCache);
     using ElementFluxVariablesCache = typename GET_PROP_TYPE(TypeTag, ElementFluxVariablesCache);
diff --git a/dumux/discretization/staggered/globalvolumevariables.hh b/dumux/discretization/staggered/globalvolumevariables.hh
index 83f66f9022bced724d10a3e786eff017d06caa99..82a751e741c11fca10964f43ebeb660ed765109e 100644
--- a/dumux/discretization/staggered/globalvolumevariables.hh
+++ b/dumux/discretization/staggered/globalvolumevariables.hh
@@ -30,13 +30,13 @@ namespace Dumux
  * \ingroup ImplicitModel
  * \brief Base class for the volume variables vector
  */
-template<class TypeTag, bool enableGlobalVolVarsCache>
-class StaggeredGlobalVolumeVariables
+template<class TypeTag, bool enableGridVolVarsCache>
+class StaggeredGridVolumeVariables
 {};
 
 //! specialization in case of storing the volume variables
 template<class TypeTag>
-class StaggeredGlobalVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/true>
+class StaggeredGridVolumeVariables<TypeTag, /*enableGridVolVarsCache*/true>
 {
     using Problem = typename GET_PROP_TYPE(TypeTag, Problem);
     using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
@@ -60,7 +60,7 @@ class StaggeredGlobalVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/true>
     enum { numEqCellCenter = GET_PROP_VALUE(TypeTag, NumEqCellCenter) };
 
 public:
-    StaggeredGlobalVolumeVariables(const Problem& problem) : problemPtr_(&problem) {}
+    StaggeredGridVolumeVariables(const Problem& problem) : problemPtr_(&problem) {}
 
     void update(const FVGridGeometry& fvGridGeometry, const SolutionVector& sol)
     {
@@ -117,7 +117,7 @@ public:
      *        The local object is only functional after calling its bind/bindElement method
      *        This is a free function that will be found by means of ADL
      */
-    friend inline ElementVolumeVariables localView(const StaggeredGlobalVolumeVariables& global)
+    friend inline ElementVolumeVariables localView(const StaggeredGridVolumeVariables& global)
     { return ElementVolumeVariables(global); }
 
     const VolumeVariables& volVars(const IndexType scvIdx) const
@@ -145,7 +145,7 @@ private:
 
 //! Specialization when the current volume variables are not stored globally
 template<class TypeTag>
-class StaggeredGlobalVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/false>
+class StaggeredGridVolumeVariables<TypeTag, /*enableGridVolVarsCache*/false>
 {
     using Problem = typename GET_PROP_TYPE(TypeTag, Problem);
     using FVGridGeometry = typename GET_PROP_TYPE(TypeTag, FVGridGeometry);
@@ -153,7 +153,7 @@ class StaggeredGlobalVolumeVariables<TypeTag, /*enableGlobalVolVarsCache*/false>
     using ElementVolumeVariables = typename GET_PROP_TYPE(TypeTag, ElementVolumeVariables);
 
 public:
-    StaggeredGlobalVolumeVariables(const Problem& problem) : problemPtr_(&problem) {}
+    StaggeredGridVolumeVariables(const Problem& problem) : problemPtr_(&problem) {}
 
     void update(const FVGridGeometry& fvGridGeometry, const SolutionVector& sol) {}
 
@@ -162,7 +162,7 @@ public:
      *        The local object is only functional after calling its bind/bindElement method
      *        This is a free function that will be found by means of ADL
      */
-    friend inline ElementVolumeVariables localView(const StaggeredGlobalVolumeVariables& global)
+    friend inline ElementVolumeVariables localView(const StaggeredGridVolumeVariables& global)
     { return ElementVolumeVariables(global); }
 
     const Problem& problem() const
diff --git a/dumux/discretization/staggered/gridvariables.hh b/dumux/discretization/staggered/gridvariables.hh
index b3630ec1eb308cd29028be3a52a86924d5c94a4b..d046306da961a768c4722d2e06647d0c985656a1 100644
--- a/dumux/discretization/staggered/gridvariables.hh
+++ b/dumux/discretization/staggered/gridvariables.hh
@@ -39,7 +39,7 @@ class StaggeredGridVariables : public FVGridVariables<TypeTag>
     using ParentType = FVGridVariables<TypeTag>;
     using Problem = typename GET_PROP_TYPE(TypeTag, Problem);
     using FVGridGeometry = typename GET_PROP_TYPE(TypeTag, FVGridGeometry);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using GridFaceVariables = typename GET_PROP_TYPE(TypeTag, GlobalFaceVars);
     using GridFluxVariablesCache = typename GET_PROP_TYPE(TypeTag, GlobalFluxVariablesCache);
     using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
diff --git a/dumux/discretization/staggered/properties.hh b/dumux/discretization/staggered/properties.hh
index cf53379c5094f4ee4bf710edbc77329a966ccf03..cdcb89e83bdec8a8a2c81dc6878a2c4a6fcec603 100644
--- a/dumux/discretization/staggered/properties.hh
+++ b/dumux/discretization/staggered/properties.hh
@@ -136,10 +136,10 @@ SET_TYPE_PROP(StaggeredModel, GlobalFaceVars, StaggeredGlobalFaceVariables<TypeT
 SET_TYPE_PROP(StaggeredModel, ElementBoundaryTypes, CCElementBoundaryTypes<TypeTag>);
 
 //! The global volume variables vector class
-SET_TYPE_PROP(StaggeredModel, GlobalVolumeVariables, StaggeredGlobalVolumeVariables<TypeTag, GET_PROP_VALUE(TypeTag, EnableGlobalVolumeVariablesCache)>);
+SET_TYPE_PROP(StaggeredModel, GridVolumeVariables, StaggeredGridVolumeVariables<TypeTag, GET_PROP_VALUE(TypeTag, EnableGridVolumeVariablesCache)>);
 
 //! The element volume variables vector class
-SET_TYPE_PROP(StaggeredModel, ElementVolumeVariables, StaggeredElementVolumeVariables<TypeTag, GET_PROP_VALUE(TypeTag, EnableGlobalVolumeVariablesCache)>);
+SET_TYPE_PROP(StaggeredModel, ElementVolumeVariables, StaggeredElementVolumeVariables<TypeTag, GET_PROP_VALUE(TypeTag, EnableGridVolumeVariablesCache)>);
 
 //! The global flux variables cache vector class
 SET_TYPE_PROP(StaggeredModel, GlobalFluxVariablesCache, StaggeredGlobalFluxVariablesCache<TypeTag, GET_PROP_VALUE(TypeTag, EnableGlobalFluxVariablesCache)>);
diff --git a/dumux/mixeddimension/facet/mpfa/couplingmanager.hh b/dumux/mixeddimension/facet/mpfa/couplingmanager.hh
index f5b8a66a648e64a5339ce367e4b21676f413fba6..bb2b25c283b9061f46f2c545020107b307e1bea0 100644
--- a/dumux/mixeddimension/facet/mpfa/couplingmanager.hh
+++ b/dumux/mixeddimension/facet/mpfa/couplingmanager.hh
@@ -154,7 +154,7 @@ public:
             return BulkPrimaryVariables(0.0);
 
         // calculate the local residual of the bulk element
-        auto prevElemVolVars = localView(bulkProblem().model().prevGlobalVolVars());
+        auto prevElemVolVars = localView(bulkProblem().model().prevGridVolVars());
         prevElemVolVars.bindElement(element, fvGeometry, bulkProblem().model().prevSol());
         bulkLocalResidual_.eval(element, fvGeometry, prevElemVolVars, curElemVolVars, elemBcTypes, elemFluxVarsCache);
         return bulkLocalResidual_.residual(0);
@@ -205,7 +205,7 @@ public:
         auto bulkFvGeometry = localView(bulkProblem().model().fvGridGeometry());
         bulkFvGeometry.bind(firstBulkElement);
 
-        auto bulkElemVolVars = localView(bulkProblem().model().curGlobalVolVars());
+        auto bulkElemVolVars = localView(bulkProblem().model().curGridVolVars());
         bulkElemVolVars.bind(firstBulkElement, bulkFvGeometry, bulkProblem().model().curSol());
 
         auto bulkElemFluxVarsCache = localView(bulkProblem().model().globalFluxVarsCache());
diff --git a/dumux/mixeddimension/subproblemlocaljacobian.hh b/dumux/mixeddimension/subproblemlocaljacobian.hh
index c284c6b40822a9c992c69670d0500583bc2d00bf..f0aae51640ec84100f48b49c384a26ba5d79d560 100644
--- a/dumux/mixeddimension/subproblemlocaljacobian.hh
+++ b/dumux/mixeddimension/subproblemlocaljacobian.hh
@@ -144,10 +144,10 @@ public:
         auto fvGeometry = localView(this->model_().fvGridGeometry());
         fvGeometry.bind(element);
 
-        auto curElemVolVars = localView(this->model_().curGlobalVolVars());
+        auto curElemVolVars = localView(this->model_().curGridVolVars());
         curElemVolVars.bind(element, fvGeometry, this->model_().curSol());
 
-        auto prevElemVolVars = localView(this->model_().prevGlobalVolVars());
+        auto prevElemVolVars = localView(this->model_().prevGridVolVars());
         prevElemVolVars.bindElement(element, fvGeometry, this->model_().prevSol());
 
         auto elemFluxVarsCache = localView(this->model_().globalFluxVarsCache());
diff --git a/dumux/porousmediumflow/compositional/primaryvariableswitch.hh b/dumux/porousmediumflow/compositional/primaryvariableswitch.hh
index 24bdb41d49ae114f5df3cd477f72f49fb341fdf3..188b1879dc1b65ece40a20ffecdd6e2bf411281e 100644
--- a/dumux/porousmediumflow/compositional/primaryvariableswitch.hh
+++ b/dumux/porousmediumflow/compositional/primaryvariableswitch.hh
@@ -73,7 +73,7 @@ class PrimaryVariableSwitch
     using ElementVolumeVariables = typename GET_PROP_TYPE(TypeTag, ElementVolumeVariables);
 
     using GridVariables = typename GET_PROP_TYPE(TypeTag, GridVariables);
-    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GlobalVolumeVariables);
+    using GridVolumeVariables = typename GET_PROP_TYPE(TypeTag, GridVolumeVariables);
     using FVGridGeometry = typename GET_PROP_TYPE(TypeTag, FVGridGeometry);
     using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
 
@@ -171,12 +171,12 @@ protected:
 
 private:
     template<class T = TypeTag>
-    static typename std::enable_if<!GET_PROP_VALUE(T, EnableGlobalVolumeVariablesCache), VolumeVariables&>::type
+    static typename std::enable_if<!GET_PROP_VALUE(T, EnableGridVolumeVariablesCache), VolumeVariables&>::type
     getVolVarAccess(GridVolumeVariables& gridVolVars, ElementVolumeVariables& elemVolVars, const SubControlVolume& scv)
     { return elemVolVars[scv]; }
 
     template<class T = TypeTag>
-    static typename std::enable_if<GET_PROP_VALUE(T, EnableGlobalVolumeVariablesCache), VolumeVariables&>::type
+    static typename std::enable_if<GET_PROP_VALUE(T, EnableGridVolumeVariablesCache), VolumeVariables&>::type
     getVolVarAccess(GridVolumeVariables& gridVolVars, ElementVolumeVariables& elemVolVars, const SubControlVolume& scv)
     { return gridVolVars.volVars(scv); }
 };
diff --git a/dumux/porousmediumflow/compositional/privarswitchnewtoncontroller.hh b/dumux/porousmediumflow/compositional/privarswitchnewtoncontroller.hh
index 76cb7d9a2688469f1a4334cfff9a293b1ab41431..42aeefc5d57978538e201bf849eef01bb67bc1e0 100644
--- a/dumux/porousmediumflow/compositional/privarswitchnewtoncontroller.hh
+++ b/dumux/porousmediumflow/compositional/privarswitchnewtoncontroller.hh
@@ -116,7 +116,7 @@ public:
         switchedInLastIteration_ = priVarSwitch_->update(uCurrentIter, gridVariables,
                                                          problem, fvGridGeometry);
 
-        Dune::Hybrid::ifElse(std::integral_constant<bool, GET_PROP_VALUE(TypeTag, EnableGlobalVolumeVariablesCache)>(),
+        Dune::Hybrid::ifElse(std::integral_constant<bool, GET_PROP_VALUE(TypeTag, EnableGridVolumeVariablesCache)>(),
         [&](auto IF) {
 
             std::cout << "blub";
@@ -139,7 +139,7 @@ public:
                         {
                             const auto eIdx = fvGridGeometry.elementMapper().index(element);
                             const ElementSolution elemSol(element, this->curSol(), fvGridGeometry);
-                            this->nonConstCurGlobalVolVars().volVars(eIdx, scv.indexInElement()).update(elemSol,
+                            this->nonConstCurGridVolVars().volVars(eIdx, scv.indexInElement()).update(elemSol,
                                                                                                         problem,
                                                                                                         element,
                                                                                                         scv);
@@ -164,7 +164,7 @@ public:
                             const auto& insideScv = fvGeometry.scv(insideScvIdx);
                             const ElementSolution elemSol(problem.dirichlet(element, scvf));
 
-                            this->nonConstCurGlobalVolVars().volVars(scvf.outsideScvIdx(), 0/*indexInElement*/).update(elemSol, problem, element, insideScv);
+                            this->nonConstCurGridVolVars().volVars(scvf.outsideScvIdx(), 0/*indexInElement*/).update(elemSol, problem, element, insideScv);
                         }
                     }
                 }
diff --git a/test/freeflow/staggered/angelitestproblem.hh b/test/freeflow/staggered/angelitestproblem.hh
index bc4b39e890bdadb3c0da3a9cd35521b9967be81a..9d0b1a1026a89a485a2c80145fdf48a89b18ef5f 100644
--- a/test/freeflow/staggered/angelitestproblem.hh
+++ b/test/freeflow/staggered/angelitestproblem.hh
@@ -66,7 +66,7 @@ SET_TYPE_PROP(AngeliTestProblem, Problem, Dumux::AngeliTestProblem<TypeTag> );
 SET_BOOL_PROP(AngeliTestProblem, EnableFVGridGeometryCache, true);
 
 SET_BOOL_PROP(AngeliTestProblem, EnableGlobalFluxVariablesCache, true);
-SET_BOOL_PROP(AngeliTestProblem, EnableGlobalVolumeVariablesCache, true);
+SET_BOOL_PROP(AngeliTestProblem, EnableGridVolumeVariablesCache, true);
 
 SET_BOOL_PROP(AngeliTestProblem, EnableInertiaTerms, true);
 }
diff --git a/test/freeflow/staggered/channeltestproblem.hh b/test/freeflow/staggered/channeltestproblem.hh
index 244cf54cce59218e2c2085dc1af97a83346ea372..b77cac324049186b6ee0a394283111ed06440b97 100644
--- a/test/freeflow/staggered/channeltestproblem.hh
+++ b/test/freeflow/staggered/channeltestproblem.hh
@@ -73,7 +73,7 @@ SET_TYPE_PROP(ChannelTestProblem, Problem, Dumux::ChannelTestProblem<TypeTag> );
 SET_BOOL_PROP(ChannelTestProblem, EnableFVGridGeometryCache, true);
 
 SET_BOOL_PROP(ChannelTestProblem, EnableGlobalFluxVariablesCache, true);
-SET_BOOL_PROP(ChannelTestProblem, EnableGlobalVolumeVariablesCache, true);
+SET_BOOL_PROP(ChannelTestProblem, EnableGridVolumeVariablesCache, true);
 
 
 #if ENABLE_NAVIERSTOKES
diff --git a/test/freeflow/staggered/closedsystemtestproblem.hh b/test/freeflow/staggered/closedsystemtestproblem.hh
index 7aff81ee799cd44f676b98090a4366e4fa744a40..1d73b7fa4d010ae4975f3ef65670a423b47da175 100644
--- a/test/freeflow/staggered/closedsystemtestproblem.hh
+++ b/test/freeflow/staggered/closedsystemtestproblem.hh
@@ -64,7 +64,7 @@ SET_TYPE_PROP(ClosedSystemTestProblem, Problem, Dumux::ClosedSystemTestProblem<T
 SET_BOOL_PROP(ClosedSystemTestProblem, EnableFVGridGeometryCache, true);
 
 SET_BOOL_PROP(ClosedSystemTestProblem, EnableGlobalFluxVariablesCache, true);
-SET_BOOL_PROP(ClosedSystemTestProblem, EnableGlobalVolumeVariablesCache, true);
+SET_BOOL_PROP(ClosedSystemTestProblem, EnableGridVolumeVariablesCache, true);
 
 }
 
diff --git a/test/freeflow/staggered/doneatestproblem.hh b/test/freeflow/staggered/doneatestproblem.hh
index a51bf0168a9306ff877e927c9d3f9e8bbc773ae3..1e1829204754e52d14891cbf38af361270e5a2f7 100644
--- a/test/freeflow/staggered/doneatestproblem.hh
+++ b/test/freeflow/staggered/doneatestproblem.hh
@@ -67,7 +67,7 @@ SET_TYPE_PROP(DoneaTestProblem, Problem, Dumux::DoneaTestProblem<TypeTag> );
 SET_BOOL_PROP(DoneaTestProblem, EnableFVGridGeometryCache, true);
 
 SET_BOOL_PROP(DoneaTestProblem, EnableGlobalFluxVariablesCache, true);
-SET_BOOL_PROP(DoneaTestProblem, EnableGlobalVolumeVariablesCache, true);
+SET_BOOL_PROP(DoneaTestProblem, EnableGridVolumeVariablesCache, true);
 
 #if ENABLE_NAVIERSTOKES
 SET_BOOL_PROP(DoneaTestProblem, EnableInertiaTerms, true);
diff --git a/test/freeflow/staggered/kovasznaytestproblem.hh b/test/freeflow/staggered/kovasznaytestproblem.hh
index 8f421f860119282f4182c20a52baa93e1fc80653..ddf4512c483b3ac429e8afbea5255d96cfe0f5cd 100644
--- a/test/freeflow/staggered/kovasznaytestproblem.hh
+++ b/test/freeflow/staggered/kovasznaytestproblem.hh
@@ -68,7 +68,7 @@ SET_TYPE_PROP(KovasznayTestProblem, Problem, Dumux::KovasznayTestProblem<TypeTag
 SET_BOOL_PROP(KovasznayTestProblem, EnableFVGridGeometryCache, true);
 
 SET_BOOL_PROP(KovasznayTestProblem, EnableGlobalFluxVariablesCache, true);
-SET_BOOL_PROP(KovasznayTestProblem, EnableGlobalVolumeVariablesCache, true);
+SET_BOOL_PROP(KovasznayTestProblem, EnableGridVolumeVariablesCache, true);
 
 #if ENABLE_NAVIERSTOKES
 SET_BOOL_PROP(KovasznayTestProblem, EnableInertiaTerms, true);
diff --git a/test/freeflow/staggerednc/channeltestproblem.hh b/test/freeflow/staggerednc/channeltestproblem.hh
index 126043eed2172f1216f2b856539a0dd223cebf47..f3541008ad1269f9fdd0d98284e68e94758852da 100644
--- a/test/freeflow/staggerednc/channeltestproblem.hh
+++ b/test/freeflow/staggerednc/channeltestproblem.hh
@@ -80,7 +80,7 @@ SET_TYPE_PROP(ChannelNCTestProblem, Problem, Dumux::ChannelNCTestProblem<TypeTag
 SET_BOOL_PROP(ChannelNCTestProblem, EnableFVGridGeometryCache, true);
 
 SET_BOOL_PROP(ChannelNCTestProblem, EnableGlobalFluxVariablesCache, true);
-SET_BOOL_PROP(ChannelNCTestProblem, EnableGlobalVolumeVariablesCache, true);
+SET_BOOL_PROP(ChannelNCTestProblem, EnableGridVolumeVariablesCache, true);
 
 // Enable gravity
 SET_BOOL_PROP(ChannelNCTestProblem, UseMoles, true);
diff --git a/test/freeflow/staggerednc/densityflowproblem.hh b/test/freeflow/staggerednc/densityflowproblem.hh
index 248e43863cc771884bf8382bd0ac33219d81e0a3..be3fe5215959a96b21536aece14c9a29c0d85e42 100644
--- a/test/freeflow/staggerednc/densityflowproblem.hh
+++ b/test/freeflow/staggerednc/densityflowproblem.hh
@@ -75,7 +75,7 @@ SET_TYPE_PROP(DensityDrivenFlowProblem, Problem, Dumux::DensityDrivenFlowProblem
 SET_BOOL_PROP(DensityDrivenFlowProblem, EnableFVGridGeometryCache, true);
 
 SET_BOOL_PROP(DensityDrivenFlowProblem, EnableGlobalFluxVariablesCache, true);
-SET_BOOL_PROP(DensityDrivenFlowProblem, EnableGlobalVolumeVariablesCache, true);
+SET_BOOL_PROP(DensityDrivenFlowProblem, EnableGridVolumeVariablesCache, true);
 
 SET_BOOL_PROP(DensityDrivenFlowProblem, UseMoles, true);
 
diff --git a/test/mixeddimension/embedded/1p2c_richards2c/richardstestproblem.hh b/test/mixeddimension/embedded/1p2c_richards2c/richardstestproblem.hh
index 4d5fa12ae428902577891194e1ecfeceb1b135e2..7b38a95db3f8467ece55d79ca604d95ef0e509b1 100644
--- a/test/mixeddimension/embedded/1p2c_richards2c/richardstestproblem.hh
+++ b/test/mixeddimension/embedded/1p2c_richards2c/richardstestproblem.hh
@@ -54,7 +54,7 @@ NEW_TYPE_TAG(RichardsTestCCProblem, INHERITS_FROM(CCTpfaModel, RichardsTestProbl
 SET_TYPE_PROP(RichardsTestProblem, Grid, Dune::UGGrid<3>);
 
 SET_BOOL_PROP(RichardsTestProblem, EnableFVGridGeometryCache, true);
-SET_BOOL_PROP(RichardsTestProblem, EnableGlobalVolumeVariablesCache, true);
+SET_BOOL_PROP(RichardsTestProblem, EnableGridVolumeVariablesCache, true);
 SET_BOOL_PROP(RichardsTestProblem, EnableGlobalFluxVariablesCache, true);
 SET_BOOL_PROP(RichardsTestProblem, SolutionDependentAdvection, false);
 SET_BOOL_PROP(RichardsTestProblem, SolutionDependentMolecularDiffusion, false);
@@ -269,7 +269,7 @@ public:
                 auto fvGeometry = localView(this->model().fvGridGeometry());
                 fvGeometry.bindElement(element);
 
-                auto elemVolVars = localView(this->model().curGlobalVolVars());
+                auto elemVolVars = localView(this->model().curGridVolVars());
                 elemVolVars.bindElement(element, fvGeometry, this->model().curSol());
 
                 for (auto&& scv : scvs(fvGeometry))
diff --git a/test/mixeddimension/embedded/1p2c_richards2c/rootsystemtestproblem.hh b/test/mixeddimension/embedded/1p2c_richards2c/rootsystemtestproblem.hh
index 6220d7e77644e8b806ed25258ee932600f75ef93..b8fefe6bbb4d19bd8d7d37b1166376df26743d66 100644
--- a/test/mixeddimension/embedded/1p2c_richards2c/rootsystemtestproblem.hh
+++ b/test/mixeddimension/embedded/1p2c_richards2c/rootsystemtestproblem.hh
@@ -61,7 +61,7 @@ SET_PROP(RootsystemTestProblem, FluidSystem)
 SET_TYPE_PROP(RootsystemTestProblem, Grid, Dune::FoamGrid<1, 3>);
 
 SET_BOOL_PROP(RootsystemTestProblem, EnableFVGridGeometryCache, true);
-SET_BOOL_PROP(RootsystemTestProblem, EnableGlobalVolumeVariablesCache, true);
+SET_BOOL_PROP(RootsystemTestProblem, EnableGridVolumeVariablesCache, true);
 SET_BOOL_PROP(RootsystemTestProblem, EnableGlobalFluxVariablesCache, true);
 SET_BOOL_PROP(RootsystemTestProblem, SolutionDependentAdvection, false);
 SET_BOOL_PROP(RootsystemTestProblem, SolutionDependentMolecularDiffusion, false);
@@ -351,7 +351,7 @@ public:
                 auto fvGeometry = localView(this->model().fvGridGeometry());
                 fvGeometry.bindElement(element);
 
-                auto elemVolVars = localView(this->model().curGlobalVolVars());
+                auto elemVolVars = localView(this->model().curGridVolVars());
                 elemVolVars.bindElement(element, fvGeometry, this->model().curSol());
 
                 for (auto&& scv : scvs(fvGeometry))
diff --git a/test/mixeddimension/embedded/1p2c_richards2c/rositestproblem.hh b/test/mixeddimension/embedded/1p2c_richards2c/rositestproblem.hh
index 602eed2c22ba9c085fdf354702b971f634b1b074..9af7478dbf81fa0a164ac75aebc92c697cc37d45 100644
--- a/test/mixeddimension/embedded/1p2c_richards2c/rositestproblem.hh
+++ b/test/mixeddimension/embedded/1p2c_richards2c/rositestproblem.hh
@@ -129,7 +129,7 @@ public:
             auto fvGeometry = localView(this->lowDimProblem().model().fvGridGeometry());
             fvGeometry.bindElement(element);
 
-            auto elemVolVars = localView(this->lowDimProblem().model().curGlobalVolVars());
+            auto elemVolVars = localView(this->lowDimProblem().model().curGridVolVars());
             elemVolVars.bindElement(element, fvGeometry, this->lowDimProblem().model().curSol());
 
             for (auto&& scv : scvs(fvGeometry))
@@ -146,7 +146,7 @@ public:
             auto fvGeometry = localView(this->bulkProblem().model().fvGridGeometry());
             fvGeometry.bindElement(element);
 
-            auto elemVolVars = localView(this->bulkProblem().model().curGlobalVolVars());
+            auto elemVolVars = localView(this->bulkProblem().model().curGridVolVars());
             elemVolVars.bindElement(element, fvGeometry, this->bulkProblem().model().curSol());
 
             for (auto&& scv : scvs(fvGeometry))
@@ -175,7 +175,7 @@ public:
             auto fvGeometry = localView(this->lowDimProblem().model().fvGridGeometry());
             fvGeometry.bindElement(element);
 
-            auto elemVolVars = localView(this->lowDimProblem().model().curGlobalVolVars());
+            auto elemVolVars = localView(this->lowDimProblem().model().curGridVolVars());
             elemVolVars.bindElement(element, fvGeometry, this->lowDimProblem().model().curSol());
 
             for (auto&& scv : scvs(fvGeometry))
@@ -200,7 +200,7 @@ public:
             auto fvGeometry = localView(this->bulkProblem().model().fvGridGeometry());
             fvGeometry.bindElement(element);
 
-            auto elemVolVars = localView(this->bulkProblem().model().curGlobalVolVars());
+            auto elemVolVars = localView(this->bulkProblem().model().curGridVolVars());
             elemVolVars.bindElement(element, fvGeometry, this->bulkProblem().model().curSol());
 
             for (auto&& scv : scvs(fvGeometry))
diff --git a/test/mixeddimension/embedded/1p_1p/bloodflowproblem.hh b/test/mixeddimension/embedded/1p_1p/bloodflowproblem.hh
index 84cdead243b5770f1a0ed02d54a02e0fff527d93..0553a667624fa25df4c2330a4d726f8736353ab1 100644
--- a/test/mixeddimension/embedded/1p_1p/bloodflowproblem.hh
+++ b/test/mixeddimension/embedded/1p_1p/bloodflowproblem.hh
@@ -307,7 +307,7 @@ public:
                 auto fvGeometry = localView(this->model().fvGridGeometry());
                 fvGeometry.bindElement(element);
 
-                auto elemVolVars = localView(this->model().curGlobalVolVars());
+                auto elemVolVars = localView(this->model().curGridVolVars());
                 elemVolVars.bindElement(element, fvGeometry, this->model().curSol());
 
                 for (auto&& scv : scvs(fvGeometry))
diff --git a/test/mixeddimension/embedded/1p_1p/tissueproblem.hh b/test/mixeddimension/embedded/1p_1p/tissueproblem.hh
index 235420d234f5e918555b343c4ff91223e6d9812e..0bd604b43bc2254b40638b175ae282eb65dffdc3 100644
--- a/test/mixeddimension/embedded/1p_1p/tissueproblem.hh
+++ b/test/mixeddimension/embedded/1p_1p/tissueproblem.hh
@@ -55,7 +55,7 @@ NEW_TYPE_TAG(TissueCCProblem, INHERITS_FROM(CCTpfaModel, TissueProblem));
 SET_TYPE_PROP(TissueProblem, Grid, Dune::YaspGrid<3, Dune::EquidistantOffsetCoordinates<typename GET_PROP_TYPE(TypeTag, Scalar), 3> >);
 
 SET_BOOL_PROP(TissueProblem, EnableFVGridGeometryCache, true);
-SET_BOOL_PROP(TissueProblem, EnableGlobalVolumeVariablesCache, true);
+SET_BOOL_PROP(TissueProblem, EnableGridVolumeVariablesCache, true);
 SET_BOOL_PROP(TissueProblem, EnableGlobalFluxVariablesCache, true);
 SET_BOOL_PROP(TissueProblem, SolutionDependentAdvection, false);
 SET_BOOL_PROP(TissueProblem, SolutionDependentMolecularDiffusion, false);
@@ -311,7 +311,7 @@ public:
                 auto fvGeometry = localView(this->model().fvGridGeometry());
                 fvGeometry.bindElement(element);
 
-                auto elemVolVars = localView(this->model().curGlobalVolVars());
+                auto elemVolVars = localView(this->model().curGridVolVars());
                 elemVolVars.bindElement(element, fvGeometry, this->model().curSol());
 
                 for (auto&& scv : scvs(fvGeometry))
diff --git a/test/mixeddimension/embedded/1p_richards/richardstestproblem.hh b/test/mixeddimension/embedded/1p_richards/richardstestproblem.hh
index 2b8ecb0cb291396dac8c2f9147f92828af3f1138..2b90036def18d3992d22b08438b702e2fdd657f0 100644
--- a/test/mixeddimension/embedded/1p_richards/richardstestproblem.hh
+++ b/test/mixeddimension/embedded/1p_richards/richardstestproblem.hh
@@ -54,7 +54,7 @@ SET_TYPE_PROP(RichardsTestProblem, Grid, Dune::YaspGrid<3, Dune::EquidistantOffs
 //SET_TYPE_PROP(RichardsTestProblem, Grid, Dune::ALUGrid<3, 3, Dune::cube, Dune::conforming>);
 
 SET_BOOL_PROP(RichardsTestProblem, EnableFVGridGeometryCache, true);
-SET_BOOL_PROP(RichardsTestProblem, EnableGlobalVolumeVariablesCache, true);
+SET_BOOL_PROP(RichardsTestProblem, EnableGridVolumeVariablesCache, true);
 SET_BOOL_PROP(RichardsTestProblem, EnableGlobalFluxVariablesCache, true);
 SET_BOOL_PROP(RichardsTestProblem, SolutionDependentAdvection, false);
 SET_BOOL_PROP(RichardsTestProblem, SolutionDependentMolecularDiffusion, false);
@@ -238,7 +238,7 @@ public:
                 auto fvGeometry = localView(this->model().fvGridGeometry());
                 fvGeometry.bindElement(element);
 
-                auto elemVolVars = localView(this->model().curGlobalVolVars());
+                auto elemVolVars = localView(this->model().curGridVolVars());
                 elemVolVars.bindElement(element, fvGeometry, this->model().curSol());
 
                 for (auto&& scv : scvs(fvGeometry))
diff --git a/test/mixeddimension/embedded/1p_richards/rootsystemtestproblem.hh b/test/mixeddimension/embedded/1p_richards/rootsystemtestproblem.hh
index df622ec8b0adf06d04fd7d4931a9b32d5f066c4c..d7557c652eea622597212b5b2b1c08da72d0fa9b 100644
--- a/test/mixeddimension/embedded/1p_richards/rootsystemtestproblem.hh
+++ b/test/mixeddimension/embedded/1p_richards/rootsystemtestproblem.hh
@@ -60,7 +60,7 @@ SET_PROP(RootsystemTestProblem, FluidSystem)
 SET_TYPE_PROP(RootsystemTestProblem, Grid, Dune::FoamGrid<1, 3>);
 
 SET_BOOL_PROP(RootsystemTestProblem, EnableFVGridGeometryCache, true);
-SET_BOOL_PROP(RootsystemTestProblem, EnableGlobalVolumeVariablesCache, true);
+SET_BOOL_PROP(RootsystemTestProblem, EnableGridVolumeVariablesCache, true);
 SET_BOOL_PROP(RootsystemTestProblem, EnableGlobalFluxVariablesCache, true);
 SET_BOOL_PROP(RootsystemTestProblem, SolutionDependentAdvection, false);
 SET_BOOL_PROP(RootsystemTestProblem, SolutionDependentMolecularDiffusion, false);
@@ -320,7 +320,7 @@ public:
                 auto fvGeometry = localView(this->model().fvGridGeometry());
                 fvGeometry.bindElement(element);
 
-                auto elemVolVars = localView(this->model().curGlobalVolVars());
+                auto elemVolVars = localView(this->model().curGridVolVars());
                 elemVolVars.bindElement(element, fvGeometry, this->model().curSol());
 
                 for (auto&& scv : scvs(fvGeometry))
diff --git a/test/porousmediumflow/1p/implicit/compressible/problem.hh b/test/porousmediumflow/1p/implicit/compressible/problem.hh
index c3b778d8a27f6509d8fe1c298fc43fe5a25fdb9a..8928258a6331d1b81f294451ff898888b74433a6 100644
--- a/test/porousmediumflow/1p/implicit/compressible/problem.hh
+++ b/test/porousmediumflow/1p/implicit/compressible/problem.hh
@@ -68,7 +68,7 @@ public:
 };
 
 // Disable caching (for testing purposes)
-SET_BOOL_PROP(OnePCompressible, EnableGlobalVolumeVariablesCache, false);
+SET_BOOL_PROP(OnePCompressible, EnableGridVolumeVariablesCache, false);
 SET_BOOL_PROP(OnePCompressible, EnableGlobalFluxVariablesCache, false);
 SET_BOOL_PROP(OnePCompressible, EnableFVGridGeometryCache, false);
 
diff --git a/test/porousmediumflow/1p/implicit/fractureproblem.hh b/test/porousmediumflow/1p/implicit/fractureproblem.hh
index 95ca89d51de1a207ae40126a8ca0e3853836d3b5..cd821cc30346b92d05169ed97a2d8db00ec96645 100644
--- a/test/porousmediumflow/1p/implicit/fractureproblem.hh
+++ b/test/porousmediumflow/1p/implicit/fractureproblem.hh
@@ -52,7 +52,7 @@ NEW_TYPE_TAG(FractureCCMpfaProblem, INHERITS_FROM(CCMpfaModel, FractureProblem))
 
 //! Enable caching (more memory, but faster runtime)
 SET_BOOL_PROP(FractureProblem, EnableFVGridGeometryCache, true);
-SET_BOOL_PROP(FractureProblem, EnableGlobalVolumeVariablesCache, true);
+SET_BOOL_PROP(FractureProblem, EnableGridVolumeVariablesCache, true);
 SET_BOOL_PROP(FractureProblem, EnableGlobalFluxVariablesCache, true);
 
 //! The grid type
diff --git a/test/porousmediumflow/1p/implicit/incompressible/problem.hh b/test/porousmediumflow/1p/implicit/incompressible/problem.hh
index 008c872ebef00726287fb36f3f8cf2420dbaeb3b..c9773bf74f9a7c9e070c6ea301b0cfa594566f21 100644
--- a/test/porousmediumflow/1p/implicit/incompressible/problem.hh
+++ b/test/porousmediumflow/1p/implicit/incompressible/problem.hh
@@ -70,7 +70,7 @@ SET_PROP(OnePIncompressible, FluidSystem)
 };
 
 // Enable caching
-SET_BOOL_PROP(OnePIncompressible, EnableGlobalVolumeVariablesCache, false);
+SET_BOOL_PROP(OnePIncompressible, EnableGridVolumeVariablesCache, false);
 SET_BOOL_PROP(OnePIncompressible, EnableGlobalFluxVariablesCache, false);
 SET_BOOL_PROP(OnePIncompressible, EnableFVGridGeometryCache, false);
 
diff --git a/test/porousmediumflow/2p/implicit/fracture/problem.hh b/test/porousmediumflow/2p/implicit/fracture/problem.hh
index 465f7b9266adf5e97d18c5db949f9ef1a99d5ff6..97815ec1027b705246367276189e7ab10f6947b4 100644
--- a/test/porousmediumflow/2p/implicit/fracture/problem.hh
+++ b/test/porousmediumflow/2p/implicit/fracture/problem.hh
@@ -69,7 +69,7 @@ SET_PROP(FractureProblem, FluidSystem)
 
 // Use global caching
 SET_BOOL_PROP(FractureProblem, EnableFVGridGeometryCache, true);
-SET_BOOL_PROP(FractureProblem, EnableGlobalVolumeVariablesCache, true);
+SET_BOOL_PROP(FractureProblem, EnableGridVolumeVariablesCache, true);
 SET_BOOL_PROP(FractureProblem, EnableGlobalFluxVariablesCache, true);
 
 // permeablility is solution-independent
diff --git a/test/porousmediumflow/2p/implicit/incompressible/problem.hh b/test/porousmediumflow/2p/implicit/incompressible/problem.hh
index 37e3b3f7c7f8fb0fdee5236814371f633a4d9225..61ed3af2c3e075c608459b4249ba9ebcce75b30a 100644
--- a/test/porousmediumflow/2p/implicit/incompressible/problem.hh
+++ b/test/porousmediumflow/2p/implicit/incompressible/problem.hh
@@ -69,7 +69,7 @@ SET_PROP(TwoPIncompressible, FluidSystem)
 };
 
 // Enable caching
-SET_BOOL_PROP(TwoPIncompressible, EnableGlobalVolumeVariablesCache, false);
+SET_BOOL_PROP(TwoPIncompressible, EnableGridVolumeVariablesCache, false);
 SET_BOOL_PROP(TwoPIncompressible, EnableGlobalFluxVariablesCache, false);
 SET_BOOL_PROP(TwoPIncompressible, EnableFVGridGeometryCache, false);
 } // end namespace Properties
diff --git a/test/porousmediumflow/tracer/1ptracer/1ptestproblem.hh b/test/porousmediumflow/tracer/1ptracer/1ptestproblem.hh
index cbbee4164bd6d167b001f361f8c5a73dd84e2239..1a4af3119cbb98e0681525a14ebf4931a1f612e3 100644
--- a/test/porousmediumflow/tracer/1ptracer/1ptestproblem.hh
+++ b/test/porousmediumflow/tracer/1ptracer/1ptestproblem.hh
@@ -59,7 +59,7 @@ SET_PROP(IncompressibleTestProblem, FluidSystem)
 };
 
 // Enable caching
-SET_BOOL_PROP(IncompressibleTestProblem, EnableGlobalVolumeVariablesCache, true);
+SET_BOOL_PROP(IncompressibleTestProblem, EnableGridVolumeVariablesCache, true);
 SET_BOOL_PROP(IncompressibleTestProblem, EnableGlobalFluxVariablesCache, true);
 SET_BOOL_PROP(IncompressibleTestProblem, EnableFVGridGeometryCache, true);
 
diff --git a/test/porousmediumflow/tracer/1ptracer/tracertestproblem.hh b/test/porousmediumflow/tracer/1ptracer/tracertestproblem.hh
index 26a59a2a1c2ad699ecdeb861396b838ff5a5bb82..ce515fc300cdabaa64d3e4aeebcc0464ebc79033 100644
--- a/test/porousmediumflow/tracer/1ptracer/tracertestproblem.hh
+++ b/test/porousmediumflow/tracer/1ptracer/tracertestproblem.hh
@@ -47,7 +47,7 @@ NEW_TYPE_TAG(TracerTestCCMpfaProblem, INHERITS_FROM(CCMpfaModel, TracerTestProbl
 NEW_TYPE_TAG(TracerTestBoxProblem, INHERITS_FROM(BoxModel, TracerTestProblem));
 
 // enable caching
-SET_BOOL_PROP(TracerTestProblem, EnableGlobalVolumeVariablesCache, true);
+SET_BOOL_PROP(TracerTestProblem, EnableGridVolumeVariablesCache, true);
 SET_BOOL_PROP(TracerTestProblem, EnableGlobalFluxVariablesCache, true);
 SET_BOOL_PROP(TracerTestProblem, EnableFVGridGeometryCache, true);
 
diff --git a/test/porousmediumflow/tracer/constvel/tracertestproblem.hh b/test/porousmediumflow/tracer/constvel/tracertestproblem.hh
index 73ed806f6f05b5cdf7a65aea29c7f48e0d5f7196..66ca5898f462f466f967ec8cff3da65d8e2167ee 100644
--- a/test/porousmediumflow/tracer/constvel/tracertestproblem.hh
+++ b/test/porousmediumflow/tracer/constvel/tracertestproblem.hh
@@ -47,7 +47,7 @@ NEW_TYPE_TAG(TracerTestMpfa, INHERITS_FROM(CCMpfaModel, TracerTest));
 NEW_TYPE_TAG(TracerTestBox, INHERITS_FROM(BoxModel, TracerTest));
 
 // enable caching
-SET_BOOL_PROP(TracerTest, EnableGlobalVolumeVariablesCache, true);
+SET_BOOL_PROP(TracerTest, EnableGridVolumeVariablesCache, true);
 SET_BOOL_PROP(TracerTest, EnableGlobalFluxVariablesCache, true);
 SET_BOOL_PROP(TracerTest, EnableFVGridGeometryCache, true);