diff --git a/dumux/discretization/cellcentered/mpfa/dualgridindexset.hh b/dumux/discretization/cellcentered/mpfa/dualgridindexset.hh
index 01c369b4ee47124678eb69f746a0f188ca70d73c..fcd012caafc51d75c8085b00967ddbe15a960d75 100644
--- a/dumux/discretization/cellcentered/mpfa/dualgridindexset.hh
+++ b/dumux/discretization/cellcentered/mpfa/dualgridindexset.hh
@@ -146,11 +146,11 @@ public:
     { return numBoundaryScvfs_; }
 
     //! returns the grid scv indices connected to this dual grid node
-    const NodalGridStencilType& globalScvIndices() const
+    const NodalGridStencilType& gridScvIndices() const
     { return scvIndices_; }
 
     //! returns the grid scvf indices connected to this dual grid node
-    const NodalGridScvfStencilType& globalScvfIndices() const
+    const NodalGridScvfStencilType& gridScvfIndices() const
     { return scvfIndices_; }
 
     //! returns whether or not the i-th scvf is on a domain boundary
@@ -161,21 +161,21 @@ public:
     }
 
     //! returns the grid scv idx of the i-th scv
-    GridIndexType scvIdxGlobal(unsigned int i) const
+    GridIndexType gridScvIndex(unsigned int i) const
     {
         assert(i < numScvs());
         return scvIndices_[i];
     }
 
     //! returns the index of the i-th scvf
-    GridIndexType scvfIdxGlobal(unsigned int i) const
+    GridIndexType gridScvfIndex(unsigned int i) const
     {
         assert(i < numScvfs());
         return scvfIndices_[i];
     }
 
     //! returns the grid index of the j-th scvf embedded in the i-th scv
-    GridIndexType scvfIdxGlobal(unsigned int i, unsigned int j) const
+    GridIndexType gridScvfIndex(unsigned int i, unsigned int j) const
     {
         assert(i < numScvs());
         assert(j < localScvfIndicesInScv_[i].size());
@@ -183,7 +183,7 @@ public:
     }
 
     //! returns the node-local index of the j-th scvf embedded in the i-th scv
-    LocalIndexType scvfIdxLocal(unsigned int i, unsigned int j) const
+    LocalIndexType localScvfIndex(unsigned int i, unsigned int j) const
     {
         assert(i < numScvs());
         assert(j < localScvfIndicesInScv_[i].size());
@@ -191,7 +191,7 @@ public:
     }
 
     //! returns the node-local index of the inside scv of the i-th scvf
-    LocalIndexType insideScvIdxLocal(unsigned int i) const
+    LocalIndexType insideScvLocalIndex(unsigned int i) const
     {
         assert(i < numScvfs());
         return scvfInsideScvIndices_[i];
diff --git a/dumux/discretization/cellcentered/mpfa/elementvolumevariables.hh b/dumux/discretization/cellcentered/mpfa/elementvolumevariables.hh
index 675980bf32850b70718c5f1f70b8803fb99f7284..7f8635d08aa24ea8cfe711daff5db1ed7adfbc17 100644
--- a/dumux/discretization/cellcentered/mpfa/elementvolumevariables.hh
+++ b/dumux/discretization/cellcentered/mpfa/elementvolumevariables.hh
@@ -317,7 +317,7 @@ private:
     void addBoundaryVolVars_(const Problem& problem, const FVElementGeometry& fvGeometry, const NodalIndexSet& nodalIndexSet)
     {
         // check each scvf in the index set for boundary presence
-        for (auto scvfIdx : nodalIndexSet.globalScvfIndices())
+        for (auto scvfIdx : nodalIndexSet.gridScvfIndices())
         {
             const auto& ivScvf = fvGeometry.scvf(scvfIdx);
 
diff --git a/dumux/discretization/cellcentered/mpfa/fluxvariablescachefiller.hh b/dumux/discretization/cellcentered/mpfa/fluxvariablescachefiller.hh
index 8d8b4968a906578f3dbfee41c7ee425f738c96c8..dfac3b1cb162b19163fc49ee9765017bc3efbde9 100644
--- a/dumux/discretization/cellcentered/mpfa/fluxvariablescachefiller.hh
+++ b/dumux/discretization/cellcentered/mpfa/fluxvariablescachefiller.hh
@@ -227,7 +227,7 @@ private:
         for (const auto& d : iv.localFaceData())
         {
             // obtain the scvf
-            const auto& scvfJ = fvGeometry().scvf(d.globalScvfIndex());
+            const auto& scvfJ = fvGeometry().scvf(d.gridScvfIndex());
             ivScvfs[i] = &scvfJ;
             ivFluxVarCaches[i] = &fluxVarsCacheContainer[scvfJ];
             ivFluxVarCaches[i]->setIvIndexInContainer(ivIndexInContainer);
diff --git a/dumux/discretization/cellcentered/mpfa/localfacedata.hh b/dumux/discretization/cellcentered/mpfa/localfacedata.hh
index 4fec383779ce834ccf76d3084350f28d9715da8c..8cc387d95b9afabbfd8b258e09fe138125a069df 100644
--- a/dumux/discretization/cellcentered/mpfa/localfacedata.hh
+++ b/dumux/discretization/cellcentered/mpfa/localfacedata.hh
@@ -43,7 +43,7 @@ class InteractionVolumeLocalFaceData
     LocalIndexType ivLocalScvfIndex_;          //!< the iv-local scvf index this scvf maps to
     LocalIndexType ivLocalInsideScvIndex_;     //!< the iv-local index of the scvfs' inside scv
     LocalIndexType scvfLocalOutsideScvfIndex_; //!< the index of this scvf in the scvf-local outside faces
-    GridIndexType globalScvfIndex_;            //!< the index of the corresponding global scvf
+    GridIndexType gridScvfIndex_;              //!< the index of the corresponding global scvf
     bool isOutside_;                           //!< indicates if this face is an "outside" face in the iv-local system
 
 public:
@@ -53,10 +53,10 @@ public:
     //! Constructor
     InteractionVolumeLocalFaceData(LocalIndexType faceIndex,
                                    LocalIndexType scvIndex,
-                                   GridIndexType globalScvfIndex)
+                                   GridIndexType gridScvfIndex)
     : ivLocalScvfIndex_(faceIndex)
     , ivLocalInsideScvIndex_(scvIndex)
-    , globalScvfIndex_(globalScvfIndex)
+    , gridScvfIndex_(gridScvfIndex)
     , isOutside_(false)
     {}
 
@@ -64,11 +64,11 @@ public:
     InteractionVolumeLocalFaceData(LocalIndexType faceIndex,
                                    LocalIndexType scvIndex,
                                    LocalIndexType indexInScvfOutsideFaces,
-                                   GridIndexType globalScvfIndex)
+                                   GridIndexType gridScvfIndex)
     : ivLocalScvfIndex_(faceIndex)
     , ivLocalInsideScvIndex_(scvIndex)
     , scvfLocalOutsideScvfIndex_(indexInScvfOutsideFaces)
-    , globalScvfIndex_(globalScvfIndex)
+    , gridScvfIndex_(gridScvfIndex)
     , isOutside_(true)
     {}
 
@@ -76,7 +76,7 @@ public:
     LocalIndexType ivLocalScvfIndex() const { return ivLocalScvfIndex_; }
     LocalIndexType ivLocalInsideScvIndex() const { return ivLocalInsideScvIndex_; }
     LocalIndexType scvfLocalOutsideScvfIndex() const { assert(isOutside_); return scvfLocalOutsideScvfIndex_; }
-    GridIndexType globalScvfIndex() const { return globalScvfIndex_; }
+    GridIndexType gridScvfIndex() const { return gridScvfIndex_; }
     bool isOutsideFace() const { return isOutside_; }
 };
 
diff --git a/dumux/discretization/cellcentered/mpfa/omethod/interactionvolume.hh b/dumux/discretization/cellcentered/mpfa/omethod/interactionvolume.hh
index 97c05b84b02d0a3a08a9015923f2909d25fc0ff1..4ed30d9eecfa847738524a60d144c00f1aad89de 100644
--- a/dumux/discretization/cellcentered/mpfa/omethod/interactionvolume.hh
+++ b/dumux/discretization/cellcentered/mpfa/omethod/interactionvolume.hh
@@ -158,7 +158,7 @@ public:
     {
         // for the o-scheme, the stencil is equal to the scv
         // index set of the dual grid's nodal index set
-        stencil_ = &indexSet.nodalIndexSet().globalScvIndices();
+        stencil_ = &indexSet.nodalIndexSet().gridScvIndices();
 
         // number of interaction-volume-local scvs(=node-local for o-scheme) and scvfs
         numFaces_ = indexSet.numFaces();
@@ -178,13 +178,12 @@ public:
         localFaceData_.reserve(numGlobalScvfs);
 
         // set up stuff related to sub-control volumes
-        const auto& scvIndices = indexSet.globalScvIndices();
         for (LocalIndexType scvIdxLocal = 0; scvIdxLocal < numLocalScvs; scvIdxLocal++)
         {
-            elements_.emplace_back(fvGeometry.fvGridGeometry().element( scvIndices[scvIdxLocal] ));
+            elements_.emplace_back(fvGeometry.fvGridGeometry().element( stencil()[scvIdxLocal] ));
             scvs_.emplace_back(fvGeometry.fvGridGeometry().mpfaHelper(),
                                fvGeometry,
-                               fvGeometry.scv( scvIndices[scvIdxLocal] ),
+                               fvGeometry.scv( stencil()[scvIdxLocal] ),
                                scvIdxLocal,
                                indexSet);
         }
@@ -197,7 +196,7 @@ public:
         wijk_.resize(numFaces_);
         for (LocalIndexType faceIdxLocal = 0; faceIdxLocal < numFaces_; ++faceIdxLocal)
         {
-            const auto& scvf = fvGeometry.scvf(indexSet.scvfIdxGlobal(faceIdxLocal));
+            const auto& scvf = fvGeometry.scvf(indexSet.gridScvfIndex(faceIdxLocal));
 
             // the neighboring scvs in local indices (order: 0 - inside scv, 1..n - outside scvs)
             const auto& neighborScvIndicesLocal = indexSet.neighboringLocalScvIndices(faceIdxLocal);
@@ -233,9 +232,9 @@ public:
                     const auto outsideLocalScvIdx = neighborScvIndicesLocal[i];
                     for (int coord = 0; coord < dim; ++coord)
                     {
-                        if (indexSet.scvfIdxLocal(outsideLocalScvIdx, coord) == faceIdxLocal)
+                        if (indexSet.localScvfIndex(outsideLocalScvIdx, coord) == faceIdxLocal)
                         {
-                            const auto globalScvfIdx = indexSet.nodalIndexSet().scvfIdxGlobal(outsideLocalScvIdx, coord);
+                            const auto globalScvfIdx = indexSet.nodalIndexSet().gridScvfIndex(outsideLocalScvIdx, coord);
                             const auto& flipScvf = fvGeometry.scvf(globalScvfIdx);
                             localFaceData_.emplace_back(faceIdxLocal,       // iv-local scvf idx
                                                         outsideLocalScvIdx, // iv-local scv index
@@ -335,7 +334,7 @@ public:
         ivIndexSetContainer.emplace_back(nodalIndexSet, flipScvfIndexSet);
 
         // store the index mapping
-        for (const auto scvfIdx : nodalIndexSet.globalScvfIndices())
+        for (const auto scvfIdx : nodalIndexSet.gridScvfIndices())
             scvfIndexMap[scvfIdx] = curGlobalIndex;
     }
 
diff --git a/dumux/discretization/cellcentered/mpfa/omethod/interactionvolumeindexset.hh b/dumux/discretization/cellcentered/mpfa/omethod/interactionvolumeindexset.hh
index 2ab9082e1da9bf531957191ab3eab76267a16830..ca930c1651df6e9cddf154d34eeb3e48f7fc0bcf 100644
--- a/dumux/discretization/cellcentered/mpfa/omethod/interactionvolumeindexset.hh
+++ b/dumux/discretization/cellcentered/mpfa/omethod/interactionvolumeindexset.hh
@@ -78,7 +78,7 @@ public:
             // for scvfs touching the boundary there are no "outside" scvfs
             if (nodalIndexSet.scvfIsOnBoundary(i))
             {
-                scvfNeighborScvLocalIndices_.push_back({nodalIndexSet.insideScvIdxLocal(i)});
+                scvfNeighborScvLocalIndices_.push_back({nodalIndexSet.insideScvLocalIndex(i)});
                 nodeToIvScvf_[i] = ivToNodeScvf_.size();
                 isHandled[i] = true;
                 ivToNodeScvf_.push_back(i);
@@ -92,12 +92,12 @@ public:
             isHandled[i] = true;
 
             // construct local index sets
-            const auto& flipScvfIndices = flipScvfIndexSet[nodalIndexSet.scvfIdxGlobal(i)];
+            const auto& flipScvfIndices = flipScvfIndexSet[nodalIndexSet.gridScvfIndex(i)];
             const auto numFlipIndices = flipScvfIndices.size();
 
             ScvfNeighborLocalIndexSet neighborsLocal;
             neighborsLocal.resize(numFlipIndices + 1);
-            neighborsLocal[0] = nodalIndexSet.insideScvIdxLocal(i);
+            neighborsLocal[0] = nodalIndexSet.insideScvLocalIndex(i);
 
             // mappings for all flip scvf
             for (unsigned int j = 0; j < numFlipIndices; ++j)
@@ -105,9 +105,9 @@ public:
                 const auto outsideScvfIdx = flipScvfIndices[j];
                 for (unsigned int nodeLocalIdx = 0; nodeLocalIdx < nodalIndexSet.numScvfs(); ++nodeLocalIdx)
                 {
-                    if (nodalIndexSet.scvfIdxGlobal(nodeLocalIdx) == outsideScvfIdx)
+                    if (nodalIndexSet.gridScvfIndex(nodeLocalIdx) == outsideScvfIdx)
                     {
-                        neighborsLocal[j+1] = nodalIndexSet.insideScvIdxLocal(nodeLocalIdx);
+                        neighborsLocal[j+1] = nodalIndexSet.insideScvLocalIndex(nodeLocalIdx);
                         nodeToIvScvf_[nodeLocalIdx] = curIvLocalScvfIdx;
                         isHandled[nodeLocalIdx] = true;
                         break; // go to next outside scvf
@@ -126,8 +126,8 @@ public:
     { return nodalIndexSet_; }
 
     //! returns the global scv indices connected to this dual grid node
-    const NodalGridStencilType& globalScvIndices() const
-    { return nodalIndexSet_.globalScvIndices(); }
+    const NodalGridStencilType& gridScvIndices() const
+    { return nodalIndexSet_.gridScvIndices(); }
 
     //! returns the number of faces in the interaction volume
     std::size_t numFaces() const
@@ -137,18 +137,18 @@ public:
     std::size_t numScvs() const
     { return nodalIndexSet_.numScvs(); }
 
-    //! returns a global scvf idx for a given iv-local scvf index
-    GridIndexType scvfIdxGlobal(LocalIndexType ivLocalScvfIdx) const
+    //! returns a grid scvf idx for a given iv-local scvf index
+    GridIndexType gridScvfIndex(LocalIndexType ivLocalScvfIdx) const
     {
         assert(ivLocalScvfIdx < numFaces());
-        return nodalIndexSet_.scvfIdxGlobal( ivToNodeScvf_[ivLocalScvfIdx] );
+        return nodalIndexSet_.gridScvfIndex( ivToNodeScvf_[ivLocalScvfIdx] );
     }
 
     //! returns the iv-local scvf idx of the i-th scvf embedded in a local scv
-    LocalIndexType scvfIdxLocal(LocalIndexType scvIdxLocal, unsigned int i) const
+    LocalIndexType localScvfIndex(LocalIndexType scvIdxLocal, unsigned int i) const
     {
-        assert(nodalIndexSet_.scvfIdxLocal(scvIdxLocal, i) < nodeToIvScvf_.size());
-        return nodeToIvScvf_[ nodalIndexSet_.scvfIdxLocal(scvIdxLocal, i) ];
+        assert(nodalIndexSet_.localScvfIndex(scvIdxLocal, i) < nodeToIvScvf_.size());
+        return nodeToIvScvf_[ nodalIndexSet_.localScvfIndex(scvIdxLocal, i) ];
     }
 
     //! returns the local indices of the neighboring scvs of an scvf
diff --git a/dumux/discretization/cellcentered/mpfa/omethod/localassembler.hh b/dumux/discretization/cellcentered/mpfa/omethod/localassembler.hh
index aeb4d2838f26383af3f7c787bef8403e7d4f7f6a..82aa7b82734b024eac19c550e5f92c6096d3ee25 100644
--- a/dumux/discretization/cellcentered/mpfa/omethod/localassembler.hh
+++ b/dumux/discretization/cellcentered/mpfa/omethod/localassembler.hh
@@ -133,7 +133,7 @@ public:
                 for (LocalIndexType localDir = 0; localDir < IV::Traits::GridView::dimension; localDir++)
                 {
                     // the scvf corresponding to this local direction in the scv
-                    const auto& curLocalScvf = iv.localScvf(posLocalScv.scvfIdxLocal(localDir));
+                    const auto& curLocalScvf = iv.localScvf(posLocalScv.localScvfIndex(localDir));
 
                     // on interior faces the coefficients of the AB matrix come into play
                     if (!curLocalScvf.isDirichlet())
@@ -262,7 +262,7 @@ public:
                 for (LocalIndexType localDir = 0; localDir < IV::Traits::GridView::dimension; localDir++)
                 {
                     // the scvf corresponding to this local direction in the scv
-                    const auto& curLocalScvf = iv.localScvf(posLocalScv.scvfIdxLocal(localDir));
+                    const auto& curLocalScvf = iv.localScvf(posLocalScv.localScvfIndex(localDir));
 
                     // on interior faces the coefficients of the AB matrix come into play
                     if (!curLocalScvf.isDirichlet())
@@ -300,7 +300,7 @@ public:
         // put the cell pressures first
         using LocalIndexType = typename IV::Traits::IndexSet::LocalIndexType;
         for (LocalIndexType i = 0; i < iv.numScvs(); ++i)
-            u[i] = getU( iv.localScv(i).globalScvIndex() );
+            u[i] = getU( iv.localScv(i).gridScvIndex() );
 
         // Dirichlet BCs come afterwards
         LocalIndexType i = iv.numScvs();
@@ -363,13 +363,13 @@ public:
         {
             // gravitational acceleration on this face
             const auto& curLocalScvf = iv.localScvf(faceIdx);
-            const auto& curGlobalScvf = this->fvGeometry().scvf(curLocalScvf.globalScvfIndex());
+            const auto& curGlobalScvf = this->fvGeometry().scvf(curLocalScvf.gridScvfIndex());
             const auto gravity = this->problem().gravityAtPos(curGlobalScvf.ipGlobal());
 
             // get permeability tensor in "positive" sub volume
             const auto& neighborScvIndices = curLocalScvf.neighboringLocalScvIndices();
             const auto& posLocalScv = iv.localScv(neighborScvIndices[0]);
-            const auto& posGlobalScv = this->fvGeometry().scv(posLocalScv.globalScvIndex());
+            const auto& posGlobalScv = this->fvGeometry().scv(posLocalScv.gridScvIndex());
             const auto& posVolVars = this->elemVolVars()[posGlobalScv];
             const auto& posElement = iv.element(neighborScvIndices[0]);
             const auto tensor = getT(this->problem(), posElement, posVolVars, this->fvGeometry(), posGlobalScv);
@@ -388,7 +388,7 @@ public:
                 {
                     // obtain outside tensor
                     const auto& negLocalScv = iv.localScv( neighborScvIndices[1] );
-                    const auto& negGlobalScv = this->fvGeometry().scv(negLocalScv.globalScvIndex());
+                    const auto& negGlobalScv = this->fvGeometry().scv(negLocalScv.gridScvIndex());
                     const auto& negVolVars = this->elemVolVars()[negGlobalScv];
                     const auto& negElement = iv.element( neighborScvIndices[1] );
                     const auto negTensor = getT(this->problem(), negElement, negVolVars, this->fvGeometry(), negGlobalScv);
@@ -497,13 +497,13 @@ public:
         {
             // gravitational acceleration on this face
             const auto& curLocalScvf = iv.localScvf(faceIdx);
-            const auto& curGlobalScvf = this->fvGeometry().scvf(curLocalScvf.globalScvfIndex());
+            const auto& curGlobalScvf = this->fvGeometry().scvf(curLocalScvf.gridScvfIndex());
             const auto gravity = this->problem().gravityAtPos(curGlobalScvf.ipGlobal());
 
             // get permeability tensor in "positive" sub volume
             const auto& neighborScvIndices = curLocalScvf.neighboringLocalScvIndices();
             const auto& posLocalScv = iv.localScv(neighborScvIndices[0]);
-            const auto& posGlobalScv = this->fvGeometry().scv(posLocalScv.globalScvIndex());
+            const auto& posGlobalScv = this->fvGeometry().scv(posLocalScv.gridScvIndex());
             const auto& posVolVars = this->elemVolVars()[posGlobalScv];
             const auto& posElement = iv.element(neighborScvIndices[0]);
             const auto tensor = getT(this->problem(), posElement, posVolVars, this->fvGeometry(), posGlobalScv);
@@ -526,7 +526,7 @@ public:
                     {
                         // obtain outside tensor
                         const auto& negLocalScv = iv.localScv( neighborScvIndices[idxInOutside] );
-                        const auto& negGlobalScv = this->fvGeometry().scv(negLocalScv.globalScvIndex());
+                        const auto& negGlobalScv = this->fvGeometry().scv(negLocalScv.gridScvIndex());
                         const auto& negVolVars = this->elemVolVars()[negGlobalScv];
                         const auto& negElement = iv.element( neighborScvIndices[idxInOutside] );
                         const auto negTensor = getT(this->problem(), negElement, negVolVars, this->fvGeometry(), negGlobalScv);
@@ -596,7 +596,7 @@ public:
                 for (LocalIndexType localDir = 0; localDir < IV::Traits::GridView::dimension; localDir++)
                 {
                     // the scvf corresponding to this local direction in the scv
-                    const auto& curLocalScvf = iv.localScvf(posLocalScv.scvfIdxLocal(localDir));
+                    const auto& curLocalScvf = iv.localScvf(posLocalScv.localScvfIndex(localDir));
 
                     // on interior faces the coefficients of the AB matrix come into play
                     if (!curLocalScvf.isDirichlet())
@@ -655,12 +655,12 @@ private:
             for (LocalIndexType faceIdx = 0; faceIdx < iv.numFaces(); ++faceIdx)
             {
                 const auto& curLocalScvf = iv.localScvf(faceIdx);
-                const auto& curGlobalScvf = this->fvGeometry().scvf(curLocalScvf.globalScvfIndex());
+                const auto& curGlobalScvf = this->fvGeometry().scvf(curLocalScvf.gridScvfIndex());
                 const auto& neighborScvIndices = curLocalScvf.neighboringLocalScvIndices();
 
                 // get tensor in "positive" sub volume
                 const auto& posLocalScv = iv.localScv(neighborScvIndices[0]);
-                const auto& posGlobalScv = this->fvGeometry().scv(posLocalScv.globalScvIndex());
+                const auto& posGlobalScv = this->fvGeometry().scv(posLocalScv.gridScvIndex());
                 const auto& posVolVars = this->elemVolVars()[posGlobalScv];
                 const auto& posElement = iv.element(neighborScvIndices[0]);
                 const auto tensor = getT(this->problem(), posElement, posVolVars, this->fvGeometry(), posGlobalScv);
@@ -671,7 +671,7 @@ private:
                 const auto posScvLocalDofIdx = posLocalScv.localDofIndex();
                 for (LocalIndexType localDir = 0; localDir < dim; localDir++)
                 {
-                    const auto& otherLocalScvf = iv.localScvf( posLocalScv.scvfIdxLocal(localDir) );
+                    const auto& otherLocalScvf = iv.localScvf( posLocalScv.localScvfIndex(localDir) );
                     const auto otherLocalDofIdx = otherLocalScvf.localDofIndex();
                     D[faceIdx][otherLocalDofIdx] -= wijk[localDir];
                     D[faceIdx][posScvLocalDofIdx] += wijk[localDir];
@@ -695,14 +695,14 @@ private:
             for (LocalIndexType faceIdx = 0; faceIdx < iv.numFaces(); ++faceIdx)
             {
                 const auto& curLocalScvf = iv.localScvf(faceIdx);
-                const auto& curGlobalScvf = this->fvGeometry().scvf(curLocalScvf.globalScvfIndex());
+                const auto& curGlobalScvf = this->fvGeometry().scvf(curLocalScvf.gridScvfIndex());
                 const auto curIsDirichlet = curLocalScvf.isDirichlet();
                 const auto curLocalDofIdx = curLocalScvf.localDofIndex();
 
                 // get tensor in "positive" sub volume
                 const auto& neighborScvIndices = curLocalScvf.neighboringLocalScvIndices();
                 const auto& posLocalScv = iv.localScv(neighborScvIndices[0]);
-                const auto& posGlobalScv = this->fvGeometry().scv(posLocalScv.globalScvIndex());
+                const auto& posGlobalScv = this->fvGeometry().scv(posLocalScv.gridScvIndex());
                 const auto& posVolVars = this->elemVolVars()[posGlobalScv];
                 const auto& posElement = iv.element(neighborScvIndices[0]);
                 const auto tensor = getT(this->problem(), posElement, posVolVars, this->fvGeometry(), posGlobalScv);
@@ -713,7 +713,7 @@ private:
                 // go over the coordinate directions in the positive sub volume
                 for (unsigned int localDir = 0; localDir < dim; localDir++)
                 {
-                    const auto& otherLocalScvf = iv.localScvf( posLocalScv.scvfIdxLocal(localDir) );
+                    const auto& otherLocalScvf = iv.localScvf( posLocalScv.localScvfIndex(localDir) );
                     const auto otherLocalDofIdx = otherLocalScvf.localDofIndex();
 
                     // if we are not on a Dirichlet face, add entries associated with unknown face pressures
@@ -748,7 +748,7 @@ private:
                     {
                         const auto idxOnScvf = idxInOutside+1;
                         const auto& negLocalScv = iv.localScv( neighborScvIndices[idxOnScvf] );
-                        const auto& negGlobalScv = this->fvGeometry().scv(negLocalScv.globalScvIndex());
+                        const auto& negGlobalScv = this->fvGeometry().scv(negLocalScv.gridScvIndex());
                         const auto& negVolVars = this->elemVolVars()[negGlobalScv];
                         const auto& negElement = iv.element( neighborScvIndices[idxOnScvf] );
                         const auto negTensor = getT(this->problem(), negElement, negVolVars, this->fvGeometry(), negGlobalScv);
@@ -762,10 +762,10 @@ private:
                         if (dim < dimWorld)
                             wijk[faceIdx][idxOnScvf] *= -1.0;
 
-                        // go over the coordinate directions in the positive sub volume
+                        // go over the coordinate directions in the negative sub volume
                         for (int localDir = 0; localDir < dim; localDir++)
                         {
-                            const auto otherLocalScvfIdx = negLocalScv.scvfIdxLocal(localDir);
+                            const auto otherLocalScvfIdx = negLocalScv.localScvfIndex(localDir);
                             const auto& otherLocalScvf = iv.localScvf(otherLocalScvfIdx);
                             const auto otherLocalDofIdx = otherLocalScvf.localDofIndex();
 
diff --git a/dumux/discretization/cellcentered/mpfa/omethod/localsubcontrolentities.hh b/dumux/discretization/cellcentered/mpfa/omethod/localsubcontrolentities.hh
index 32f2775f43c9ee69e5e298ece62bcfdcb7870716..6c492a60a4cf4b965d692274f24bb90f135182e1 100644
--- a/dumux/discretization/cellcentered/mpfa/omethod/localsubcontrolentities.hh
+++ b/dumux/discretization/cellcentered/mpfa/omethod/localsubcontrolentities.hh
@@ -82,7 +82,7 @@ public:
         LocalBasis localBasis;
         for (unsigned int coordIdx = 0; coordIdx < myDimension; ++coordIdx)
         {
-            const auto scvfIdx = indexSet.nodalIndexSet().scvfIdxGlobal(localDofIndex_, coordIdx);
+            const auto scvfIdx = indexSet.nodalIndexSet().gridScvfIndex(localDofIndex_, coordIdx);
             const auto& scvf = fvGeometry.scvf(scvfIdx);
             localBasis[coordIdx] = scvf.ipGlobal();
             localBasis[coordIdx] -= center;
@@ -96,8 +96,8 @@ public:
     ctype detX() const
     { return detX_; }
 
-    //! grid view-global index related to this scv
-    GridIndexType globalScvIndex() const
+    //! grid index related to this scv
+    GridIndexType gridScvIndex() const
     { return globalScvIndex_; }
 
     //! returns the index in the set of cell unknowns of the iv
@@ -105,10 +105,10 @@ public:
     { return localDofIndex_; }
 
     //! iv-local index of the coordir's scvf in this scv
-    LocalIndexType scvfIdxLocal(unsigned int coordDir) const
+    LocalIndexType localScvfIndex(unsigned int coordDir) const
     {
         assert(coordDir < myDimension);
-        return indexSet_->scvfIdxLocal(localDofIndex_, coordDir);
+        return indexSet_->localScvfIndex(localDofIndex_, coordDir);
     }
 
     //! the nu vectors are needed for setting up the omegas of the iv
@@ -170,7 +170,7 @@ public:
     LocalIndexType localDofIndex() const { return localDofIndex_; }
 
     //! returns the grid view-global index of this scvf
-    GridIndexType globalScvfIndex() const { return scvfIdxGlobal_; }
+    GridIndexType gridScvfIndex() const { return scvfIdxGlobal_; }
 
     //! Returns the local indices of the scvs neighboring this scvf
     const ScvfNeighborLocalIndexSet& neighboringLocalScvIndices() const { return *neighborScvIndicesLocal_; }
diff --git a/dumux/discretization/cellcentered/mpfa/omethod/staticinteractionvolume.hh b/dumux/discretization/cellcentered/mpfa/omethod/staticinteractionvolume.hh
index 04250ea70b06bd2082141b4fc8f4eb2de41c8442..c27a3f05985c28d20a33c686aa11890ef84176af 100644
--- a/dumux/discretization/cellcentered/mpfa/omethod/staticinteractionvolume.hh
+++ b/dumux/discretization/cellcentered/mpfa/omethod/staticinteractionvolume.hh
@@ -159,16 +159,15 @@ public:
         // for the o-scheme, the stencil is equal to the scv
         // index set of the dual grid's nodal index set
         assert(indexSet.numScvs() == numScv);
-        stencil_ = &indexSet.nodalIndexSet().globalScvIndices();
+        stencil_ = &indexSet.nodalIndexSet().gridScvIndices();
 
         // set up stuff related to sub-control volumes
-        const auto& scvIndices = indexSet.globalScvIndices();
         for (LocalIndexType scvIdxLocal = 0; scvIdxLocal < numScv; scvIdxLocal++)
         {
-            elements_[scvIdxLocal] = fvGeometry.fvGridGeometry().element( scvIndices[scvIdxLocal] );
+            elements_[scvIdxLocal] = fvGeometry.fvGridGeometry().element( stencil()[scvIdxLocal] );
             scvs_[scvIdxLocal] = LocalScvType(fvGeometry.fvGridGeometry().mpfaHelper(),
                                               fvGeometry,
-                                              fvGeometry.scv( scvIndices[scvIdxLocal] ),
+                                              fvGeometry.scv( stencil()[scvIdxLocal] ),
                                               scvIdxLocal,
                                               indexSet);
         }
@@ -176,7 +175,7 @@ public:
         // set up quantitites related to sub-control volume faces
         for (LocalIndexType faceIdxLocal = 0; faceIdxLocal < numScvf; ++faceIdxLocal)
         {
-            const auto& scvf = fvGeometry.scvf(indexSet.scvfIdxGlobal(faceIdxLocal));
+            const auto& scvf = fvGeometry.scvf(indexSet.gridScvfIndex(faceIdxLocal));
 
             // the neighboring scvs in local indices (order: 0 - inside scv, 1..n - outside scvs)
             const auto& neighborScvIndicesLocal = indexSet.neighboringLocalScvIndices(faceIdxLocal);
@@ -193,9 +192,9 @@ public:
             const auto outsideLocalScvIdx = neighborScvIndicesLocal[1];
             for (int coord = 0; coord < dim; ++coord)
             {
-                if (indexSet.scvfIdxLocal(outsideLocalScvIdx, coord) == faceIdxLocal)
+                if (indexSet.localScvfIndex(outsideLocalScvIdx, coord) == faceIdxLocal)
                 {
-                    const auto globalScvfIdx = indexSet.nodalIndexSet().scvfIdxGlobal(outsideLocalScvIdx, coord);
+                    const auto globalScvfIdx = indexSet.nodalIndexSet().gridScvfIndex(outsideLocalScvIdx, coord);
                     const auto& flipScvf = fvGeometry.scvf(globalScvfIdx);
                     localFaceData_[faceIdxLocal*2+1] = LocalFaceData(faceIdxLocal,       // iv-local scvf idx
                                                                      outsideLocalScvIdx, // iv-local scv index
@@ -295,7 +294,7 @@ public:
         ivIndexSetContainer.emplace_back(nodalIndexSet, flipScvfIndexSet);
 
         // store the index mapping
-        for (const auto scvfIdx : nodalIndexSet.globalScvfIndices())
+        for (const auto scvfIdx : nodalIndexSet.gridScvfIndices())
             scvfIndexMap[scvfIdx] = curGlobalIndex;
     }
 
diff --git a/dumux/discretization/fluxstencil.hh b/dumux/discretization/fluxstencil.hh
index fb3e859234172184a6eccd4608e361c135ddb99c..c601e6f1cc761e8d28ca9a70e2192255d8decad3 100644
--- a/dumux/discretization/fluxstencil.hh
+++ b/dumux/discretization/fluxstencil.hh
@@ -117,9 +117,9 @@ public:
 
         // return the scv (element) indices in the interaction region
         if (fvGridGeometry.vertexUsesSecondaryInteractionVolume(scvf.vertexIndex()))
-            return fvGridGeometry.gridInteractionVolumeIndexSets().secondaryIndexSet(scvf).globalScvIndices();
+            return fvGridGeometry.gridInteractionVolumeIndexSets().secondaryIndexSet(scvf).gridScvIndices();
         else
-            return fvGridGeometry.gridInteractionVolumeIndexSets().primaryIndexSet(scvf).globalScvIndices();
+            return fvGridGeometry.gridInteractionVolumeIndexSets().primaryIndexSet(scvf).gridScvIndices();
     }
 };