diff --git a/lecture/efm/1p2c_2p_2p2c/CMakeLists.txt b/lecture/efm/1p2c_2p_2p2c/CMakeLists.txt
index 246e7ef6d1df0aed5e11f3d2c387a67f5cbab863..4d09d31e9ab84d799025da6d80a1941a10ebb36b 100644
--- a/lecture/efm/1p2c_2p_2p2c/CMakeLists.txt
+++ b/lecture/efm/1p2c_2p_2p2c/CMakeLists.txt
@@ -14,7 +14,7 @@ dumux_add_test(NAME lens2p2cexercise3
               CMD_ARGS --script fuzzy
                        --files ${CMAKE_SOURCE_DIR}/lecture/references/lens-2p2c-exercise3-reference.vtu
                                ${CMAKE_CURRENT_BINARY_DIR}/lens-2p2c-00011.vtu
-                       --command "${CMAKE_CURRENT_BINARY_DIR}/lens2p2cexercise3 -ParameterFile ${CMAKE_CURRENT_SOURCE_DIR}/exercise3.input -Problem.Name lens-2p2c")
+                       --command "${CMAKE_CURRENT_BINARY_DIR}/lens2p2cexercise3 -ParameterFile ${CMAKE_CURRENT_SOURCE_DIR}/exercise3.input -Problem.Name lens-2p2c -SpatialParams.Temperature 313.15")
 
 dumux_add_test(NAME lens1p2cexercise3
               SOURCES lens1p2cexercise3.cc
diff --git a/lecture/efm/1p2c_2p_2p2c/exercise3.input b/lecture/efm/1p2c_2p_2p2c/exercise3.input
index 3cf360de721ca6259b69c1cd82c254c708183f81..85f4724779202971570fd194dade97f8f3c55617 100755
--- a/lecture/efm/1p2c_2p_2p2c/exercise3.input
+++ b/lecture/efm/1p2c_2p_2p2c/exercise3.input
@@ -24,6 +24,9 @@ BrooksCoreyPcEntry = 200     # entry pressure for the Brooks-Corey capillary pre
 Swr = 0.05                   # residual saturation of the wetting phase in the coarse soil [-]
 Snr = 0.1                    # residual saturation of the nonwetting phase in the coarse soil [-]
 
+[SpatialParams]
+Temperature = 283.15 	    # 10 degree Celcius for 2p problem and 1p2c problem, 40 degree Celcius for 2p2c problem
+
 [Boundary]
 LowerPressure = 2.0e5        # Dirichlet pressure value for the boundary condition at the lower boundary [Pa]
 UpperPressure = 4.0e5        # Dirichlet pressure value for the boundary condition at the upper boundary [Pa]
diff --git a/lecture/efm/1p2c_2p_2p2c/lens1p2cexercise3.cc b/lecture/efm/1p2c_2p_2p2c/lens1p2cexercise3.cc
index e8d3e8445d3312637ee73e9c2f2dd70106a772f5..0170fc0b725a6656c56b29dafd06f7d51db188fc 100755
--- a/lecture/efm/1p2c_2p_2p2c/lens1p2cexercise3.cc
+++ b/lecture/efm/1p2c_2p_2p2c/lens1p2cexercise3.cc
@@ -114,7 +114,6 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/efm/1p2c_2p_2p2c/lens1p2cproblem.hh b/lecture/efm/1p2c_2p_2p2c/lens1p2cproblem.hh
index aeb2e3b7760cd5153705883a9d38a19b3db7bf61..3bf7f0fefcc8c4130202f657254a5f4ef4cb3be9 100644
--- a/lecture/efm/1p2c_2p_2p2c/lens1p2cproblem.hh
+++ b/lecture/efm/1p2c_2p_2p2c/lens1p2cproblem.hh
@@ -91,21 +91,6 @@ public:
         upperPressure_ = getParam<Scalar>("Boundary.UpperPressure");
     }
 
-    /*!
-     * \name Problem parameters
-     */
-    // \{
-
-    /*!
-     * \brief Returns the temperature within the domain.
-     * This problem assumes a temperature of 10 degrees Celsius.
-     */
-    Scalar temperature() const
-    {
-        return 273.15 + 10; // -> 10 degrees Celsius
-    }
-
-    // \}
 
     /*!
      * \name Boundary conditions
diff --git a/lecture/efm/1p2c_2p_2p2c/lens1p2cspatialparams.hh b/lecture/efm/1p2c_2p_2p2c/lens1p2cspatialparams.hh
index 1d9b051b9dd386f3567b4815ab7da655e44105e8..4c6341c25db0fb9113dd0b9475ae7a6e3bce4a9f 100644
--- a/lecture/efm/1p2c_2p_2p2c/lens1p2cspatialparams.hh
+++ b/lecture/efm/1p2c_2p_2p2c/lens1p2cspatialparams.hh
@@ -25,7 +25,7 @@
 
 #include <dumux/common/properties.hh>
 
-#include <dumux/material/spatialparams/fv1p.hh>
+#include <dumux/porousmediumflow/fvspatialparams1p.hh>
 
 namespace Dumux {
 
@@ -56,10 +56,10 @@ public:
  * \brief Class for defining spatial parameters
  */
 template<class FVGridGeometry, class Scalar>
-class Lens1p2cSpatialParams : public FVSpatialParamsOneP<FVGridGeometry, Scalar,  Lens1p2cSpatialParams<FVGridGeometry, Scalar> >
+class Lens1p2cSpatialParams : public FVPorousMediumFlowSpatialParamsOneP<FVGridGeometry, Scalar,  Lens1p2cSpatialParams<FVGridGeometry, Scalar> >
 {
     using ThisType = Lens1p2cSpatialParams<FVGridGeometry, Scalar>;
-    using ParentType = FVSpatialParamsOneP<FVGridGeometry, Scalar, ThisType>;
+    using ParentType = FVPorousMediumFlowSpatialParamsOneP<FVGridGeometry, Scalar, ThisType>;
     using GridView = typename FVGridGeometry::GridView;
     using Element = typename GridView::template Codim<0>::Entity;
     using FVElementGeometry = typename FVGridGeometry::LocalView;
@@ -90,6 +90,7 @@ public:
 
         lensK_ = getParam<double>("SpatialParams.Fine.Permeability");
         outerK_ = getParam<double>("SpatialParams.Coarse.Permeability");
+        temperature_ = getParam<double>("SpatialParams.Temperature");
     }
 
     /*!
@@ -141,6 +142,15 @@ public:
         lensUpperRight_ = lensUpperRight;
     }
 
+    /*!
+     * \brief Returns the temperature at the domain at the given position
+     * \param globalPos The position in global coordinates where the temperature should be specified
+     */
+    Scalar temperatureAtPos(const GlobalPosition& globalPos) const
+    {
+        return temperature_;
+    }
+
 private:
     bool isInLens_(const GlobalPosition &pos) const
     {
@@ -160,6 +170,7 @@ private:
     Scalar outerK_;
     Scalar lensPorosity_;
     Scalar outerPorosity_;
+    Scalar temperature_;
 };
 
 } // end namespace Dumux
diff --git a/lecture/efm/1p2c_2p_2p2c/lens2p2cexercise3.cc b/lecture/efm/1p2c_2p_2p2c/lens2p2cexercise3.cc
index a2cafe1699077a3fc6d6576ada85b4a40305a470..5f8d0b2b49af247a973a31b2fd2a60d203709bdf 100644
--- a/lecture/efm/1p2c_2p_2p2c/lens2p2cexercise3.cc
+++ b/lecture/efm/1p2c_2p_2p2c/lens2p2cexercise3.cc
@@ -130,7 +130,7 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
+
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/efm/1p2c_2p_2p2c/lens2p2cproblem.hh b/lecture/efm/1p2c_2p_2p2c/lens2p2cproblem.hh
index c4718204a4bf2aff372e7c270429ae8ac9b50875..00275d2807370f044dfc1becb11176ba892b04dc 100644
--- a/lecture/efm/1p2c_2p_2p2c/lens2p2cproblem.hh
+++ b/lecture/efm/1p2c_2p_2p2c/lens2p2cproblem.hh
@@ -86,12 +86,11 @@ public:
     LensTwoPTwoCProblem(std::shared_ptr<const FVGridGeometry> fvGridGeometry )
         : ParentType(fvGridGeometry)
     {
-        temperature_ = 273.15 + 40; // [K]
         eps_ = 1e-6;
 
         // initialize the tables of the fluid system
-        FluidSystem::init(/*Tmin=*/temperature_ - 1.0,
-        /*Tmax=*/temperature_ + 1.0,
+        FluidSystem::init(/*Tmin=*/ 273.15 + getParam<Scalar>("SpatialParams.Temperature") - 1.0,
+        /*Tmax=*/ 273.15 + getParam<Scalar>("SpatialParams.Temperature") + 1.0,
         /*nT=*/3,
         /*pmin=*/1e5,
         /*pmax=*/3e7,
@@ -101,20 +100,6 @@ public:
         upperPressure_ = getParam<Scalar>("Boundary.UpperPressure");
     }
 
-    /*!
-     * \name Problem parameters
-     */
-    // \{
-
-    /*!
-     * \brief Returns the temperature within the domain.
-     */
-    Scalar temperature() const
-    {
-        return temperature_;
-    }
-
-    // \}
 
     /*!
      * \name Boundary conditions
@@ -220,7 +205,6 @@ public:
 private:
     Scalar eps_;
     Scalar episodeLength_; // [s]
-    Scalar temperature_; // [K]
     Scalar upperPressure_; // [Pa]
     Scalar lowerPressure_; // [Pa]
 
diff --git a/lecture/efm/1p2c_2p_2p2c/lens2pexercise3.cc b/lecture/efm/1p2c_2p_2p2c/lens2pexercise3.cc
index 2681a024e72b97ada8971a1723198a515ba999c0..24f073484d8515fde2e869a4f4fba61191fef456 100755
--- a/lecture/efm/1p2c_2p_2p2c/lens2pexercise3.cc
+++ b/lecture/efm/1p2c_2p_2p2c/lens2pexercise3.cc
@@ -132,7 +132,6 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/efm/1p2c_2p_2p2c/lens2pproblem.hh b/lecture/efm/1p2c_2p_2p2c/lens2pproblem.hh
index b070beaba60ea7c10277d24795bea37dd1860bfa..6ef1aa5846c7737144ecb962d531a771ae63d543 100644
--- a/lecture/efm/1p2c_2p_2p2c/lens2pproblem.hh
+++ b/lecture/efm/1p2c_2p_2p2c/lens2pproblem.hh
@@ -85,21 +85,6 @@ public:
         upperPressure_ = getParam<Scalar>("Boundary.UpperPressure");
     }
 
-    /*!
-     * \name Problem parameters
-     */
-    // \{
-
-    /*!
-     * \brief Returns the temperature within the domain.
-     * This problem assumes a uniform temperature of 10 degrees Celsius.
-     */
-    Scalar temperature() const
-    {
-        return 273.15 + 10; // -> 10°C
-    };
-
-    // \}
 
     /*!
      * \name Boundary conditions
diff --git a/lecture/efm/1p2c_2p_2p2c/lens2pspatialparams.hh b/lecture/efm/1p2c_2p_2p2c/lens2pspatialparams.hh
index 0921a384cf1dcd6df9e543f9a95d3ad516f04020..0f0b6e59d88855f47b21bdc32ba659f9b127c0c6 100644
--- a/lecture/efm/1p2c_2p_2p2c/lens2pspatialparams.hh
+++ b/lecture/efm/1p2c_2p_2p2c/lens2pspatialparams.hh
@@ -27,7 +27,7 @@
 #define DUMUX_LENS2P_SPATIALPARAMS_HH
 
 #include <dumux/material/fluidmatrixinteractions/2p/brookscorey.hh>
-#include <dumux/material/spatialparams/fv.hh>
+#include <dumux/porousmediumflow/fvspatialparamsmp.hh>
 
 namespace Dumux {
 
@@ -38,14 +38,14 @@ namespace Dumux {
  */
 template<class FVGridGeometry, class Scalar>
 class Lens2pSpatialParams
-: public FVSpatialParams<FVGridGeometry, Scalar, Lens2pSpatialParams<FVGridGeometry, Scalar>>
+: public FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar, Lens2pSpatialParams<FVGridGeometry, Scalar>>
 {
     using GridView = typename FVGridGeometry::GridView;
     using Element = typename GridView::template Codim<0>::Entity;
     using FVElementGeometry = typename FVGridGeometry::LocalView;
     using SubControlVolume = typename FVElementGeometry::SubControlVolume;
     using ThisType = Lens2pSpatialParams<FVGridGeometry, Scalar>;
-    using ParentType = FVSpatialParams<FVGridGeometry, Scalar, ThisType>;
+    using ParentType = FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar, ThisType>;
     static constexpr int dimWorld = GridView::dimensionworld;
     using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
 
@@ -70,8 +70,9 @@ public:
 
         lensK_ = getParam<Scalar>("SpatialParams.Fine.Permeability");
         outerK_ = getParam<Scalar>("SpatialParams.Coarse.Permeability");
-    }
 
+        temperature_ = getParam<Scalar>("SpatialParams.Temperature");
+    }
     /*!
      * \brief Function for defining the (intrinsic) permeability \f$[m^2]\f$
      *
@@ -137,6 +138,15 @@ public:
         return FluidSystem::phase0Idx;
     }
 
+    /*!
+     * \brief Returns the temperature at the domain at the given position
+     * \param globalPos The position in global coordinates where the temperature should be specified
+     */
+    Scalar temperatureAtPos(const GlobalPosition& globalPos) const
+    {
+        return temperature_;
+    }
+
     /*!
      * \brief Set the bounding box of the fine-sand lens
      * \param lensLowerLeft the lower left corner coordinates vector
@@ -166,6 +176,7 @@ private:
     Scalar outerK_;
     Scalar lensPorosity_;
     Scalar outerPorosity_;
+    Scalar temperature_;
     const PcKrSw pcKrSwFine_;
     const PcKrSw pcKrSwCoarse_;
     const Scalar eps_{1e-6};
diff --git a/lecture/efm/1p2cvs2p/exercise1.input b/lecture/efm/1p2cvs2p/exercise1.input
index b36f041e503aa473da20be5e00ebe8d7e41d25f6..50c9b6f2e4591bec4cc9fcb81706c77c91928f4e 100644
--- a/lecture/efm/1p2cvs2p/exercise1.input
+++ b/lecture/efm/1p2cvs2p/exercise1.input
@@ -12,6 +12,7 @@ UpperRight = 5 4                            # upper right corner coordinates (x,
 Cells = 40 64                               # grid resolution in (x,y) direction [-]
 
 [SpatialParams]
+Temperature = 283.15		     # Temperature for the entire domain [K]
 
 Fine.Permeability = 3.1e-11                  # intrinsic permeability of the fine porous medium [m^2]
 Coarse.Permeability = 3.1e-10                # intrinsic permeability of the coarse porous medium [m^2]
diff --git a/lecture/efm/1p2cvs2p/lens1p2cexercise1.cc b/lecture/efm/1p2cvs2p/lens1p2cexercise1.cc
index 3f1460614825ec682005139cae69762030de71e4..16dd4e60969b88f9a7eb1adeff055b2031a0fc26 100644
--- a/lecture/efm/1p2cvs2p/lens1p2cexercise1.cc
+++ b/lecture/efm/1p2cvs2p/lens1p2cexercise1.cc
@@ -116,7 +116,6 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/efm/1p2cvs2p/lens1p2cproblem.hh b/lecture/efm/1p2cvs2p/lens1p2cproblem.hh
index 601b44a02ac0fdb213fd8608d27c795414a05f03..051b7fe2cee61f50fea5bcef3072154376923e29 100644
--- a/lecture/efm/1p2cvs2p/lens1p2cproblem.hh
+++ b/lecture/efm/1p2cvs2p/lens1p2cproblem.hh
@@ -107,22 +107,7 @@ public:
         upperPressure_ = getParam<Scalar>("Boundary.UpperPressure");
     }
 
-    /*!
-     * \name Problem parameters
-     */
-    // \{
-
-    /*!
-     * \brief Returns the temperature within the domain.
-     * \param temperature DOC ME!
-     * This problem assumes a temperature of 10 degrees Celsius.
-     */
-    Scalar temperature() const
-    {
-        return 273.15 + 10; // -> 10 degrees Celsius
-    };
 
-    // \}
 
     /*!
      * \name Boundary conditions
diff --git a/lecture/efm/1p2cvs2p/lens2pexercise1.cc b/lecture/efm/1p2cvs2p/lens2pexercise1.cc
index 79d723b7a939234eec4683eccd8c03af1e1ff212..a160ff705a403f92a210a793e84d1af06f07a6a1 100644
--- a/lecture/efm/1p2cvs2p/lens2pexercise1.cc
+++ b/lecture/efm/1p2cvs2p/lens2pexercise1.cc
@@ -134,7 +134,6 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/efm/1p2cvs2p/lens2pproblem.hh b/lecture/efm/1p2cvs2p/lens2pproblem.hh
index 63158c7c8b9ab224df1e74b6ee91fd26132adf62..8f13223f672d133e10a0eecbbc726f005d288695 100644
--- a/lecture/efm/1p2cvs2p/lens2pproblem.hh
+++ b/lecture/efm/1p2cvs2p/lens2pproblem.hh
@@ -40,7 +40,7 @@ namespace Dumux {
  *        water saturated medium.
  *
  * DOC ME! The domain is sized 5m times 4m and features a rectangular lens
- * with low permeablility which spans from (1 m , 2 m) to (4 m, 3 m)
+ * with low permeablility which spans from (0.8 m , 2 m) to (4 m, 3 m)
  * and is surrounded by a medium with higher permability. Note that
  * this problem is discretized using only two dimensions, so from the
  * point of view of the two-phase model, the depth of the domain
@@ -116,21 +116,6 @@ public:
         infiltrationEndTime_= getParam<Scalar>("Boundary.InfiltrationEndTime");
     }
 
-    /*!
-     * \name Problem parameters
-     */
-    // \{
-
-    /*!
-     * \brief Returns the temperature within the domain.
-     * This problem assumes a uniform temperature of 10 degrees Celsius.
-     */
-    Scalar temperature() const
-    {
-        return 273.15 + 10; // -> 10°C
-    };
-
-    // \}
 
     /*!
      * \name Boundary conditions
diff --git a/lecture/efm/2p/lens2pexercise2.cc b/lecture/efm/2p/lens2pexercise2.cc
index 70afb5cd17988ac973edff1b3c54bcb0f6ca466b..5e5879fec2768c8d9be4019339e066055e7297d7 100644
--- a/lecture/efm/2p/lens2pexercise2.cc
+++ b/lecture/efm/2p/lens2pexercise2.cc
@@ -134,7 +134,6 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/efm/2p/lens2pexercise2.input b/lecture/efm/2p/lens2pexercise2.input
index 3c7503222c123e3c459f01703aba4cb62ae89001..0e262798531ba71235f8f4822eb3770c0274712d 100644
--- a/lecture/efm/2p/lens2pexercise2.input
+++ b/lecture/efm/2p/lens2pexercise2.input
@@ -25,6 +25,9 @@ BrooksCoreyPcEntry = 200    # entry pressure for the Brooks-Corey capillary pres
 Swr = 0.05                  # residual saturation of the wetting phase in the coarse soil [-]
 Snr = 0.0                   # residual saturation of the nonwetting phase in the coarse soil [-]
 
+[SpatialParams]
+Temperature = 10.0 	   # temperature in the entire domain [°C]	
+
 [Boundary]
 LowerPressure = 1.19612e5                   # Dirichlet pressure value for the boundary condition at the lower boundary [Pa]
 UpperPressure = 1.0e5                       # Dirichlet pressure value for the boundary condition at the upper boundary [Pa]
diff --git a/lecture/efm/2p/lens2pproblem.hh b/lecture/efm/2p/lens2pproblem.hh
index c2761f12283644fdeeef6113e0d261af57758358..93c796668f9651686d3dd15b2cde41c7a21b8bec 100644
--- a/lecture/efm/2p/lens2pproblem.hh
+++ b/lecture/efm/2p/lens2pproblem.hh
@@ -130,22 +130,6 @@ public:
         }
     }
 
-    /*!
-     * \name Problem parameters
-     */
-    // \{
-
-    /*!
-     * \brief Returns the temperature within the domain.
-     *
-     * This problem assumes a uniform temperature of 10 degrees Celsius.
-     */
-    Scalar temperature() const
-    {
-        return 273.15 + 10; // -> 10°C
-    };
-
-    // \}
 
     /*!
      * \name Boundary conditions
@@ -184,7 +168,7 @@ public:
     {
         PrimaryVariables values(0.0);
         FluidState fluidState;
-        fluidState.setTemperature(this->temperature());
+        fluidState.setTemperature(this->spatialParams().temperatureAtPos(globalPos));
         fluidState.setPressure(FluidSystem::phase0Idx, /*pressure=*/1e5);
         fluidState.setPressure(FluidSystem::phase1Idx, /*pressure=*/1e5);
 
@@ -260,7 +244,7 @@ public:
     {
         PrimaryVariables values;
         FluidState fluidState;
-        fluidState.setTemperature(this->temperature());
+        fluidState.setTemperature(this->spatialParams().temperatureAtPos(globalPos));
         fluidState.setPressure(FluidSystem::phase0Idx, /*pressure=*/1e5);
         fluidState.setPressure(FluidSystem::phase1Idx, /*pressure=*/1e5);
 
diff --git a/lecture/mm/co2plume/co2plumeshapeexercise.cc b/lecture/mm/co2plume/co2plumeshapeexercise.cc
index 12162f20d3e211b862530ba92e4fd52236cb60f9..7b4097a96296c438a5ba7681c164f9d5bafcdc6f 100644
--- a/lecture/mm/co2plume/co2plumeshapeexercise.cc
+++ b/lecture/mm/co2plume/co2plumeshapeexercise.cc
@@ -79,7 +79,6 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/mm/co2plume/co2plumeshapespatialparameters.hh b/lecture/mm/co2plume/co2plumeshapespatialparameters.hh
index 509bafbc7e24cc2a41ec6480aac305db8abfd2fc..ab6371da3b2845af65a3b7c4ebd17f91aeb4c06f 100644
--- a/lecture/mm/co2plume/co2plumeshapespatialparameters.hh
+++ b/lecture/mm/co2plume/co2plumeshapespatialparameters.hh
@@ -27,7 +27,7 @@
 #define DUMUX_PLUMESHAPE_SPATIAL_PARAMS_HH
 
 #include <dumux/io/grid/griddata.hh>
-#include <dumux/material/spatialparams/fv.hh>
+#include <dumux/porousmediumflow/fvspatialparamsmp.hh>
 #include <dumux/material/fluidmatrixinteractions/2p/brookscorey.hh>
 
 #include <dumux/porousmediumflow/co2/model.hh>
@@ -41,7 +41,7 @@ namespace Dumux {
  */
 template<class FVGridGeometry, class Scalar>
 class PlumeShapeSpatialParams
-: public FVSpatialParams<FVGridGeometry,
+: public FVPorousMediumFlowSpatialParamsMP<FVGridGeometry,
                          Scalar,
                          PlumeShapeSpatialParams<FVGridGeometry, Scalar>>
 {
@@ -50,7 +50,7 @@ class PlumeShapeSpatialParams
     using FVElementGeometry = typename FVGridGeometry::LocalView;
     using SubControlVolume = typename FVElementGeometry::SubControlVolume;
     using Element = typename GridView::template Codim<0>::Entity;
-    using ParentType = FVSpatialParams<FVGridGeometry, Scalar,
+    using ParentType = FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar,
                                        PlumeShapeSpatialParams<FVGridGeometry, Scalar>>;
     using GlobalPosition = typename SubControlVolume::GlobalPosition;
     using PcKrSwCurve = FluidMatrix::BrooksCoreyDefault<Scalar>;
diff --git a/lecture/mm/columnxylene/columnxyleneexercise.cc b/lecture/mm/columnxylene/columnxyleneexercise.cc
index 09cc76c28084970b0b00884036587b883d10a70d..01fcb54cc589ed69568be67d4a9d17f0c7730d74 100644
--- a/lecture/mm/columnxylene/columnxyleneexercise.cc
+++ b/lecture/mm/columnxylene/columnxyleneexercise.cc
@@ -102,7 +102,7 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
+
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/mm/columnxylene/columnxylenespatialparams.hh b/lecture/mm/columnxylene/columnxylenespatialparams.hh
index b4b6eb1d5793090c2c1b56a09ae13c06aa1223a4..1246233f5ad07d500635e9cced951e59d473e34b 100644
--- a/lecture/mm/columnxylene/columnxylenespatialparams.hh
+++ b/lecture/mm/columnxylene/columnxylenespatialparams.hh
@@ -26,7 +26,7 @@
 
 #include <dumux/porousmediumflow/3p3c/indices.hh>
 #include <dumux/common/properties.hh>
-#include <dumux/material/spatialparams/fv.hh>
+#include <dumux/porousmediumflow/fvspatialparamsmp.hh>
 #include <dumux/material/fluidmatrixinteractions/3p/parkervangenuchten.hh>
 #include <dumux/material/fluidmatrixinteractions/3p/napladsorption.hh>
 
@@ -37,7 +37,7 @@ namespace Dumux {
  */
 template<class FVGridGeometry, class Scalar>
 class ColumnSpatialParams
-: public FVSpatialParams<FVGridGeometry, Scalar,
+: public FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar,
                          ColumnSpatialParams<FVGridGeometry, Scalar>>
 {
     using GridView = typename FVGridGeometry::GridView;
@@ -45,7 +45,7 @@ class ColumnSpatialParams
     using SubControlVolume = typename FVElementGeometry::SubControlVolume;
 
     using Element = typename GridView::template Codim<0>::Entity;
-    using ParentType = FVSpatialParams<FVGridGeometry, Scalar,
+    using ParentType = FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar,
                                        ColumnSpatialParams<FVGridGeometry, Scalar>>;
 
     using GlobalPosition = typename SubControlVolume::GlobalPosition;
diff --git a/lecture/mm/convectivemixing/convmixexercise.cc b/lecture/mm/convectivemixing/convmixexercise.cc
index 3cfabe4bc7c9c86983eb3220fdf9a0d539551a01..77197227fac0a2044d73b2d1449a774993226530 100644
--- a/lecture/mm/convectivemixing/convmixexercise.cc
+++ b/lecture/mm/convectivemixing/convmixexercise.cc
@@ -84,7 +84,6 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/mm/convectivemixing/convmixexercise.input b/lecture/mm/convectivemixing/convmixexercise.input
index 0f005f7cdfb30f73380ca6f198140fee250fede5..3c0e4f94b84d247f6e7910802d988f8f2c23a424 100644
--- a/lecture/mm/convectivemixing/convmixexercise.input
+++ b/lecture/mm/convectivemixing/convmixexercise.input
@@ -11,11 +11,12 @@ Cells = 30 30
 [SpatialParams]
 Tortuosity = 0.706
 Permeability = 3e-13
+DepthBOR = 1400 # [m] depth below ground surface
 
 [Problem]
 Name = convmix # name passed to the output routines
 EnableGravity = 1 # enable gravity
-DepthBOR = 1400 # [m] depth below ground surface
+
 
 [Brine]
 Salinity = 0.05 # brine salinity
diff --git a/lecture/mm/convectivemixing/convmixproblem.hh b/lecture/mm/convectivemixing/convmixproblem.hh
index 07c72d8a4d3fe1dfdbf0cc11732f14e40c10febc..abbae292783513b807aed0a82b5a6f773abb9b7b 100644
--- a/lecture/mm/convectivemixing/convmixproblem.hh
+++ b/lecture/mm/convectivemixing/convmixproblem.hh
@@ -90,7 +90,6 @@ public:
     ConvmixProblem(std::shared_ptr<const FVGridGeometry> fvGridGeometry)
     : ParentType(fvGridGeometry)
     {
-        depthBOR_ = getParam<Scalar>("Problem.DepthBOR");
         name_ = getParam<std::string>("Problem.Name");
 
         //initialize fluid system
@@ -108,17 +107,6 @@ public:
      */
     // \{
 
-    /*!
-     * \brief Returns the temperature within the domain [K].
-     *
-     * This problem assumes a temperature of 20 degrees Celsius.
-     */
-    Scalar temperatureAtPos(const GlobalPosition &globalPos) const
-    {
-        return (283.15 + (depthBOR_ - globalPos[1])*0.032); // geothermal temperatur in [K]
-                                                            // assuming 10°C at surface and a
-                                                            // geothermal gradient of 0.032 K/m
-    };
 
     // \}
 
@@ -232,10 +220,10 @@ private:
     {
         PrimaryVariables priVars;
 
-        const Scalar temp = temperatureAtPos(globalPos);
+        const Scalar temp = this->spatialParams().temperatureAtPos(globalPos);
         const Scalar salinity = getParam<Scalar>("Brine.Salinity");
 
-        priVars[pressureIdx] = 1.013e5 + (depthBOR_ - globalPos[1]) * 1100 * 9.81;  // hydrostatic pressure distribution
+        priVars[pressureIdx] = 1.013e5 + (this->spatialParams().depthBorAtPos(globalPos) - globalPos[1]) * 1100 * 9.81;  // hydrostatic pressure distribution
         priVars[CO2Idx] = 0.;  // initial condition for the CO2 massfraction
 
         Scalar moleFracCO2, xgH2O;
@@ -254,8 +242,6 @@ private:
         return priVars;
     }
         static constexpr Scalar eps_ = 1e-6;
-
-        Scalar depthBOR_; // bottom of reservoir [m]
         std::string name_ ;
     };
 
diff --git a/lecture/mm/convectivemixing/convmixspatialparams.hh b/lecture/mm/convectivemixing/convmixspatialparams.hh
index fc6a76c6d95d300c461c311cac4095fb0171c133..114b993e268272006d19ec63475ae31818254335 100644
--- a/lecture/mm/convectivemixing/convmixspatialparams.hh
+++ b/lecture/mm/convectivemixing/convmixspatialparams.hh
@@ -25,7 +25,7 @@
 #define DUMUX_CONVMIX_SPATIAL_PARAMS_HH
 
 #include <dumux/porousmediumflow/properties.hh>
-#include <dumux/material/spatialparams/fv1p.hh>
+#include <dumux/porousmediumflow/fvspatialparams1p.hh>
 
 namespace Dumux {
 
@@ -35,14 +35,14 @@ namespace Dumux {
  */
 template<class FVGridGeometry, class Scalar>
 class ConvmixSpatialParams
-: public FVSpatialParamsOneP<FVGridGeometry, Scalar,
+: public FVPorousMediumFlowSpatialParamsOneP<FVGridGeometry, Scalar,
                              ConvmixSpatialParams<FVGridGeometry, Scalar>>
 {
     using GridView = typename FVGridGeometry::GridView;
     using FVElementGeometry = typename FVGridGeometry::LocalView;
     using SubControlVolume = typename FVElementGeometry::SubControlVolume;
     using Element = typename GridView::template Codim<0>::Entity;
-    using ParentType = FVSpatialParamsOneP<FVGridGeometry, Scalar,
+    using ParentType = FVPorousMediumFlowSpatialParamsOneP<FVGridGeometry, Scalar,
                                            ConvmixSpatialParams<FVGridGeometry, Scalar>>;
 
     static const int dimWorld = GridView::dimensionworld;
@@ -57,6 +57,7 @@ public:
     {
         permeability_ = getParam<Scalar>("SpatialParams.Permeability", 3e-13);
         porosity_ = 0.2;
+        depthBOR_ =  getParam<Scalar>("SpatialParams.DepthBOR");
     }
 
     /*!
@@ -88,9 +89,30 @@ public:
                         const ElementSolution& elemSol) const
     { return 0; }
 
+    /*!
+     * \brief Returns the temperature at the domain at the given position
+     * \param globalPos The position in global coordinates where the temperature should be specified
+     *        // geothermal temperatur in [K]
+             // assuming 10°C at surface and a
+            // geothermal gradient of 0.032 K/m
+     */
+    Scalar temperatureAtPos(const GlobalPosition& globalPos) const
+    {
+        return 283.15 + (depthBOR_ - globalPos[1])*0.032;
+    }
+
+    /*!
+     * \brief Define bottom of reservoir \f$\mathrm{[m]}\f$.
+     *
+     * \param globalPos The global position
+     */
+    Scalar depthBorAtPos(const GlobalPosition& globalPos) const
+    { return depthBOR_; }
+
 private:
     Scalar permeability_;
     Scalar porosity_;
+    Scalar depthBOR_;
 };
 
 } // end namespace Dumux
diff --git a/lecture/mm/fractures/fracture_exercise.input b/lecture/mm/fractures/fracture_exercise.input
index 9fe6a9cc427a1526516dbecb75855f2915194443..bf1d0e3736f8c6354e5554c28070a726864e3190 100644
--- a/lecture/mm/fractures/fracture_exercise.input
+++ b/lecture/mm/fractures/fracture_exercise.input
@@ -22,6 +22,7 @@ Problem.Name = matrix
 Problem.Name = fractures
 
 [SpatialParams]
+Temperature = 283.15 #[K]
 Aperture = 1e-1
 Permeability = 1e-14
 Porosity = 0.1
diff --git a/lecture/mm/fractures/fractureproblem.hh b/lecture/mm/fractures/fractureproblem.hh
index 7f32eacfea1ad8d3685f88816e8808d03d50957c..34e49b651ef10ebad7a0d8463e188bdce55ffa9f 100644
--- a/lecture/mm/fractures/fractureproblem.hh
+++ b/lecture/mm/fractures/fractureproblem.hh
@@ -111,14 +111,6 @@ public:
         return source;
     }
 
-    //! Set the aperture as extrusion factor.
-    Scalar extrusionFactorAtPos(const GlobalPosition& globalPos) const
-    {
-        // We treat the fractures as lower-dimensional in the grid,
-        // but we have to give it the aperture as extrusion factor
-        // such that the dimensions are correct in the end.
-        return aperture_;
-    }
 
     //! evaluates the Dirichlet boundary condition for a given position
     PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const
@@ -167,16 +159,12 @@ public:
                 if (scvf.boundary())
                     flux -= neumannAtPos(scvf.ipGlobal())[contiH2OEqIdx]
                             *scvf.area()
-                            *extrusionFactorAtPos(scvf.ipGlobal());
+                            *this->spatialParams().extrusionFactorAtPos(scvf.ipGlobal());
         }
 
         return flux;
     }
 
-    //! returns the temperature in \f$\mathrm{[K]}\f$ in the domain
-    Scalar temperature() const
-    { return 283.15; /*10°*/ }
-
     //! sets the pointer to the coupling manager.
     void setCouplingManager(std::shared_ptr<CouplingManager> cm)
     { couplingManagerPtr_ = cm; }
diff --git a/lecture/mm/fractures/fractures.cc b/lecture/mm/fractures/fractures.cc
index 739de2748b674dd7cb366917baf450c90fdf90af..c4f05e1dfa0984293892642ba1502bc8e6791471 100644
--- a/lecture/mm/fractures/fractures.cc
+++ b/lecture/mm/fractures/fractures.cc
@@ -99,8 +99,7 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometries
     auto matrixFvGridGeometry = std::make_shared<MatrixFVGridGeometry>(matrixGridView);
     auto fractureFvGridGeometry = std::make_shared<FractureFVGridGeometry>(fractureGridView);
-    matrixFvGridGeometry->update();
-    fractureFvGridGeometry->update();
+
 
     // the problems (boundary/initial conditions etc)
     using MatrixProblem = GetPropType<MatrixTypeTag, Properties::Problem>;
diff --git a/lecture/mm/fractures/fracturespatialparams.hh b/lecture/mm/fractures/fracturespatialparams.hh
index 8f6277bace3dabfe3a65d6ba5750f88156397f53..38ff9d3b3bdbe8d172721524842e7e2d1bcaffaa 100644
--- a/lecture/mm/fractures/fracturespatialparams.hh
+++ b/lecture/mm/fractures/fracturespatialparams.hh
@@ -24,7 +24,7 @@
 #ifndef DUMUX_COURSE_FRACTURESEXERCISE_FRACTURE_SPATIALPARAMS_HH
 #define DUMUX_COURSE_FRACTURESEXERCISE_FRACTURE_SPATIALPARAMS_HH
 
-#include <dumux/material/spatialparams/fv.hh>
+#include <dumux/porousmediumflow/fvspatialparamsmp.hh>
 #include <dumux/material/fluidmatrixinteractions/2p/vangenuchten.hh>
 
 namespace Dumux {
@@ -34,10 +34,10 @@ namespace Dumux {
  */
 template< class FVGridGeometry, class Scalar >
 class FractureSpatialParams
-: public FVSpatialParams< FVGridGeometry, Scalar, FractureSpatialParams<FVGridGeometry, Scalar> >
+: public FVPorousMediumFlowSpatialParamsMP< FVGridGeometry, Scalar, FractureSpatialParams<FVGridGeometry, Scalar> >
 {
     using ThisType = FractureSpatialParams< FVGridGeometry, Scalar >;
-    using ParentType = FVSpatialParams< FVGridGeometry, Scalar, ThisType >;
+    using ParentType = FVPorousMediumFlowSpatialParamsMP< FVGridGeometry, Scalar, ThisType >;
 
     using SubControlVolume = typename FVGridGeometry::SubControlVolume;
     using GridView = typename FVGridGeometry::GridView;
@@ -64,6 +64,8 @@ public:
     {
         porosity_ = getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Fracture.Porosity");
         permeability_ = getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Fracture.Permeability");
+        temperature_ = getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Temperature");
+        aperture_ = getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Aperture");
     }
 
     //! Function for defining the (intrinsic) permeability \f$[m^2]\f$.
@@ -93,8 +95,28 @@ public:
         return FluidSystem::phase0Idx;
     }
 
+        /*!
+     * \brief Returns the temperature at the domain at the given position
+     * \param globalPos The position in global coordinates where the temperature should be specified
+     */
+    Scalar temperatureAtPos(const GlobalPosition& globalPos) const
+    {
+        return temperature_;
+    }
+
+        //! Set the aperture as extrusion factor.
+    Scalar extrusionFactorAtPos(const GlobalPosition& globalPos) const
+    {
+        // We treat the fractures as lower-dimensional in the grid,
+        // but we have to give it the aperture as extrusion factor
+        // such that the dimensions are correct in the end.
+        return aperture_;
+    }
+
 private:
     Scalar porosity_;
+    Scalar temperature_;
+    Scalar aperture_;
     PermeabilityType permeability_;
     const PcKrSw pcKrSwFracture_;
 };
diff --git a/lecture/mm/fractures/matrixproblem.hh b/lecture/mm/fractures/matrixproblem.hh
index bb556bfb69ad625fc38c067f43d0eb70e0c76bdf..bb20ee1d2a28c8a5adadacb780a55f2719ce021f 100644
--- a/lecture/mm/fractures/matrixproblem.hh
+++ b/lecture/mm/fractures/matrixproblem.hh
@@ -244,10 +244,6 @@ public:
         return flux;
     }
 
-    //! returns the temperature in \f$\mathrm{[K]}\f$ in the domain
-    Scalar temperature() const
-    { return 283.15; /*10°*/ }
-
     //! sets the pointer to the coupling manager.
     void setCouplingManager(std::shared_ptr<CouplingManager> cm)
     { couplingManagerPtr_ = cm; }
diff --git a/lecture/mm/fractures/matrixspatialparams.hh b/lecture/mm/fractures/matrixspatialparams.hh
index 29c37e202429baf08ce84c2e4e0a53ef957b6d9c..d1cc419114e68762793e1ee814ac05501bbdec8c 100644
--- a/lecture/mm/fractures/matrixspatialparams.hh
+++ b/lecture/mm/fractures/matrixspatialparams.hh
@@ -24,7 +24,8 @@
 #ifndef DUMUX_COURSE_FRACTURESEXERCISE_MATRIX_SPATIALPARAMS_HH
 #define DUMUX_COURSE_FRACTURESEXERCISE_MATRIX_SPATIALPARAMS_HH
 
-#include <dumux/material/spatialparams/fv.hh>
+
+#include <dumux/porousmediumflow/fvspatialparamsmp.hh>
 #include <dumux/material/fluidmatrixinteractions/2p/vangenuchten.hh>
 
 namespace Dumux {
@@ -34,10 +35,10 @@ namespace Dumux {
  */
 template< class FVGridGeometry, class Scalar >
 class MatrixSpatialParams
-: public FVSpatialParams< FVGridGeometry, Scalar, MatrixSpatialParams<FVGridGeometry, Scalar> >
+: public FVPorousMediumFlowSpatialParamsMP< FVGridGeometry, Scalar, MatrixSpatialParams<FVGridGeometry, Scalar> >
 {
     using ThisType = MatrixSpatialParams< FVGridGeometry, Scalar >;
-    using ParentType = FVSpatialParams< FVGridGeometry, Scalar, ThisType >;
+    using ParentType = FVPorousMediumFlowSpatialParamsMP< FVGridGeometry, Scalar, ThisType >;
 
     using GridView = typename FVGridGeometry::GridView;
     using Grid = typename GridView::Grid;
@@ -60,6 +61,7 @@ public:
     {
         porosity_ = getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Porosity");
         permeability_ = getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Permeability");
+        temperature_ = getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Temperature");
         porosityOverburden_ = getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Overburden.Porosity");
         permeabilityOverburden_ = getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Overburden.Permeability");
     }
@@ -97,6 +99,15 @@ public:
         return FluidSystem::phase0Idx;
     }
 
+    /*!
+     * \brief Returns the temperature at the domain at the given position
+     * \param globalPos The position in global coordinates where the temperature should be specified
+     */
+    Scalar temperatureAtPos(const GlobalPosition& globalPos) const
+    {
+        return temperature_;
+    }
+
 private:
     Scalar porosity_;
     Scalar porosityOverburden_;
@@ -104,6 +115,7 @@ private:
     PermeabilityType permeabilityOverburden_;
     const PcKrSw pcKrSw_;
     const PcKrSw pcKrSwOverburden_;
+    Scalar temperature_;
 };
 
 } // end namespace Dumux
diff --git a/lecture/mm/fuelcell/fuelcell.cc b/lecture/mm/fuelcell/fuelcell.cc
index 2ca67fa3b3522becbd4998cb414590accfc4148a..19599b3ddb2c9a6f797768234fd97c7ea0acbb1a 100644
--- a/lecture/mm/fuelcell/fuelcell.cc
+++ b/lecture/mm/fuelcell/fuelcell.cc
@@ -116,7 +116,7 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
+
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/mm/fuelcell/fuelcell.input b/lecture/mm/fuelcell/fuelcell.input
index 464cb9dd4796cebd7d9552948c010e4f0ed66066..49cac53e207a2ee4d5b56012c4725c102e03798c 100644
--- a/lecture/mm/fuelcell/fuelcell.input
+++ b/lecture/mm/fuelcell/fuelcell.input
@@ -45,6 +45,7 @@ MaxRelativeShift = 1e-5
 [OperationalConditions]
 GasPressureInlet1 = 2.013e5 # [Pa] pressure at the upper inlet
 GasPressureInlet2 = 2.013e5 # [Pa] pressure at the lower inlet # 2.013e5
+# for interdigitated conditions, GasPressureInlet1 may be set, e.g. to 2.015e5
 LiquidWaterSaturationInlet = 0.055
 #LiquidWaterSaturationInlet = 0.41 # drainage
 
diff --git a/lecture/mm/fuelcell/fuelcellspatialparams.hh b/lecture/mm/fuelcell/fuelcellspatialparams.hh
index 44e0f652037c41c920aed12d4248aea1bb92bafb..2ec4f0217adac15be2804fbaa46a2635caedd00b 100644
--- a/lecture/mm/fuelcell/fuelcellspatialparams.hh
+++ b/lecture/mm/fuelcell/fuelcellspatialparams.hh
@@ -27,7 +27,7 @@
 
 #include <dumux/common/properties.hh>
 
-#include <dumux/material/spatialparams/fv.hh>
+#include <dumux/porousmediumflow/fvspatialparamsmp.hh>
 #include "./material/acosta.hh"
 #include "./material/thermalconductivityconstant.hh"
 
@@ -61,14 +61,14 @@ struct ThermalConductivityModel<TypeTag, TTag::FuelCellLectureSpatialParams> { u
  *        problem which uses the (non-)isothermal 2pnc box model
  */
 template<class TypeTag>
-class FuelCellLectureSpatialParams: public FVSpatialParams<GetPropType<TypeTag, Properties::GridGeometry>,
+class FuelCellLectureSpatialParams: public FVPorousMediumFlowSpatialParamsMP<GetPropType<TypeTag, Properties::GridGeometry>,
                                     GetPropType<TypeTag, Properties::Scalar>,
                                     FuelCellLectureSpatialParams<TypeTag>>
 {
     using ThisType = FuelCellLectureSpatialParams<TypeTag>;
     using Scalar = GetPropType<TypeTag, Properties::Scalar>;
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
-    using ParentType = FVSpatialParams<FVGridGeometry, Scalar, ThisType>;
+    using ParentType = FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar, ThisType>;
     using GridView = typename FVGridGeometry::GridView;
     using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
     using Element = typename GridView::template Codim<0>::Entity;
diff --git a/lecture/mm/heatpipe/heatpipe.cc b/lecture/mm/heatpipe/heatpipe.cc
index bc47cb037250fb05ebf8a0811525d049144ea9eb..d78b26b4574d0da92908b17366411acbb732cc2a 100644
--- a/lecture/mm/heatpipe/heatpipe.cc
+++ b/lecture/mm/heatpipe/heatpipe.cc
@@ -81,7 +81,6 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/mm/heatpipe/heatpipespatialparams.hh b/lecture/mm/heatpipe/heatpipespatialparams.hh
index e05d26d5078b61c7782d75494054f77e511a95a9..e6a525975634b3302a0b4bdd43a3f0b30b3aa55c 100644
--- a/lecture/mm/heatpipe/heatpipespatialparams.hh
+++ b/lecture/mm/heatpipe/heatpipespatialparams.hh
@@ -19,7 +19,7 @@
 #ifndef DUMUX_HEATPIPE_SPATIAL_PARAMS_HH
 #define DUMUX_HEATPIPE_SPATIAL_PARAMS_HH
 
-#include <dumux/material/spatialparams/fv.hh>
+#include <dumux/porousmediumflow/fvspatialparamsmp.hh>
 
 #include "krpcheatpipe.hh"
 
@@ -28,11 +28,11 @@ namespace Dumux
 
 template<class FVGridGeometry, class Scalar>
 class HeatPipeSpatialParams
-: public FVSpatialParams<FVGridGeometry, Scalar, HeatPipeSpatialParams<FVGridGeometry, Scalar>>
+: public FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar, HeatPipeSpatialParams<FVGridGeometry, Scalar>>
 
 {
     using ThisType = HeatPipeSpatialParams<FVGridGeometry, Scalar>;
-    using ParentType = FVSpatialParams<FVGridGeometry, Scalar, ThisType>;
+    using ParentType = FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar, ThisType>;
 
     using GridView = typename FVGridGeometry::GridView;
     using Element = typename GridView::template Codim<0>::Entity;
diff --git a/lecture/mm/heavyoil/sagd/sagd.cc b/lecture/mm/heavyoil/sagd/sagd.cc
index d1b6da09a7491415e985185ca988d42f080ec65f..1260cbf8fa8bc54c75da3dd3b00f8d4e9b649ef2 100644
--- a/lecture/mm/heavyoil/sagd/sagd.cc
+++ b/lecture/mm/heavyoil/sagd/sagd.cc
@@ -106,7 +106,6 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/mm/heavyoil/sagd/spatialparams.hh b/lecture/mm/heavyoil/sagd/spatialparams.hh
index a1185077e944fefe7ca3f85cf544132fd398be60..b98c0afcfa56a48b11f31ba31e1bf215f2a9366e 100644
--- a/lecture/mm/heavyoil/sagd/spatialparams.hh
+++ b/lecture/mm/heavyoil/sagd/spatialparams.hh
@@ -26,7 +26,7 @@
 
 #include <dumux/porousmediumflow/properties.hh>
 #include <dumux/porousmediumflow/3pwateroil/indices.hh>
-#include <dumux/material/spatialparams/fv.hh>
+#include <dumux/porousmediumflow/fvspatialparamsmp.hh>
 #include <dumux/material/fluidmatrixinteractions/3p/parkervangenuchten.hh>
 
 namespace Dumux {
@@ -37,7 +37,7 @@ namespace Dumux {
  */
 template<class FVGridGeometry, class Scalar>
 class SagdSpatialParams
-: public FVSpatialParams<FVGridGeometry, Scalar,
+: public FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar,
                          SagdSpatialParams<FVGridGeometry, Scalar>>
 {
     using GridView = typename FVGridGeometry::GridView;
@@ -49,7 +49,7 @@ class SagdSpatialParams
     using GlobalPosition = typename SubControlVolume::GlobalPosition;
 
     using Element = typename GridView::template Codim<0>::Entity;
-    using ParentType = FVSpatialParams<FVGridGeometry, Scalar,
+    using ParentType = FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar,
                                        SagdSpatialParams<FVGridGeometry, Scalar>>;
     using ThreePhasePcKrSw = FluidMatrix::ParkerVanGenuchten3PDefault<Scalar>;
 
diff --git a/lecture/mm/heavyoil/sagdcyclic/sagd_cyclic.cc b/lecture/mm/heavyoil/sagdcyclic/sagd_cyclic.cc
index d36dda2daff3794143eded07180b5575fde82f1c..ff10528cb42e2f94902ab196e27ca1f3ed3e625d 100644
--- a/lecture/mm/heavyoil/sagdcyclic/sagd_cyclic.cc
+++ b/lecture/mm/heavyoil/sagdcyclic/sagd_cyclic.cc
@@ -106,7 +106,6 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/mm/heavyoil/sagdcyclic/spatialparams.hh b/lecture/mm/heavyoil/sagdcyclic/spatialparams.hh
index 0fc1bd1e6f63666bda8b3978f8a45415592a7929..fe7545686ec770f70f7b71fcac83e0bf19f2a3b7 100644
--- a/lecture/mm/heavyoil/sagdcyclic/spatialparams.hh
+++ b/lecture/mm/heavyoil/sagdcyclic/spatialparams.hh
@@ -26,7 +26,7 @@
 
 #include <dumux/porousmediumflow/properties.hh>
 #include <dumux/porousmediumflow/3pwateroil/indices.hh>
-#include <dumux/material/spatialparams/fv.hh>
+#include <dumux/porousmediumflow/fvspatialparamsmp.hh>
 #include <dumux/material/fluidmatrixinteractions/3p/parkervangenuchten.hh>
 
 namespace Dumux {
@@ -36,7 +36,7 @@ namespace Dumux {
  */
 template<class FVGridGeometry, class Scalar>
 class SagdSpatialParams
-: public FVSpatialParams<FVGridGeometry, Scalar,
+: public FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar,
                          SagdSpatialParams<FVGridGeometry, Scalar>>
 {
     using GridView = typename FVGridGeometry::GridView;
@@ -48,7 +48,7 @@ class SagdSpatialParams
     using GlobalPosition = typename SubControlVolume::GlobalPosition;
 
     using Element = typename GridView::template Codim<0>::Entity;
-    using ParentType = FVSpatialParams<FVGridGeometry, Scalar,
+    using ParentType = FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar,
                                        SagdSpatialParams<FVGridGeometry, Scalar>>;
     using ThreePhasePcKrSw = FluidMatrix::ParkerVanGenuchten3PDefault<Scalar>;
 
diff --git a/lecture/mm/heavyoil/sagdcyclichyst/sagd_cyclic_hyst.cc b/lecture/mm/heavyoil/sagdcyclichyst/sagd_cyclic_hyst.cc
index 52f9b326ee35efb55a71d1ce8cce4f0a9a7028fe..54a49221d2fedd5b403ed3a8c719fec0d0f7fd3b 100644
--- a/lecture/mm/heavyoil/sagdcyclichyst/sagd_cyclic_hyst.cc
+++ b/lecture/mm/heavyoil/sagdcyclichyst/sagd_cyclic_hyst.cc
@@ -106,7 +106,6 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/mm/heavyoil/sagdcyclichyst/spatialparams.hh b/lecture/mm/heavyoil/sagdcyclichyst/spatialparams.hh
index acae9de6ad4e8bb65d1fa51905b97d0c2df4acfc..135b718c413c347932c1a90f8d4f65944cf5cd2d 100644
--- a/lecture/mm/heavyoil/sagdcyclichyst/spatialparams.hh
+++ b/lecture/mm/heavyoil/sagdcyclichyst/spatialparams.hh
@@ -25,7 +25,7 @@
 #define DUMUX_SAGD_SPATIAL_PARAMS_HH
 
 #include <dumux/porousmediumflow/properties.hh>
-#include <dumux/material/spatialparams/fv.hh>
+#include <dumux/porousmediumflow/fvspatialparamsmp.hh>
 
 #include <dumux/porousmediumflow/3pwateroil/indices.hh>
 
@@ -38,7 +38,7 @@ namespace Dumux {
  */
 template<class FVGridGeometry, class Scalar>
 class SagdSpatialParams
-: public FVSpatialParams<FVGridGeometry, Scalar,
+: public FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar,
                          SagdSpatialParams<FVGridGeometry, Scalar>>
 {
     using GridView = typename FVGridGeometry::GridView;
@@ -50,7 +50,7 @@ class SagdSpatialParams
     using GlobalPosition = typename SubControlVolume::GlobalPosition;
 
     using Element = typename GridView::template Codim<0>::Entity;
-    using ParentType = FVSpatialParams<FVGridGeometry, Scalar,
+    using ParentType = FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar,
                                        SagdSpatialParams<FVGridGeometry, Scalar>>;
 
     static constexpr bool isBox = FVGridGeometry::discMethod == DiscretizationMethod::box;
diff --git a/lecture/mm/henryproblem/henry1p2c/henry1p2c.cc b/lecture/mm/henryproblem/henry1p2c/henry1p2c.cc
index 918dc03af54792c0beabb3ab7fa32137202a751e..8118c802c83072126693d34298ff584303c5343e 100644
--- a/lecture/mm/henryproblem/henry1p2c/henry1p2c.cc
+++ b/lecture/mm/henryproblem/henry1p2c/henry1p2c.cc
@@ -109,7 +109,6 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/mm/henryproblem/henry1p2c/henry1p2c.input b/lecture/mm/henryproblem/henry1p2c/henry1p2c.input
index 0517f7ee771f3ebc57a78bb7bf71dc32b4e2e698..d9e32d1082ae723a054d20f25f3d057e3dc14591 100644
--- a/lecture/mm/henryproblem/henry1p2c/henry1p2c.input
+++ b/lecture/mm/henryproblem/henry1p2c/henry1p2c.input
@@ -7,7 +7,7 @@ File = ./grids/henry.dgf
 
 [Problem]
 freshWaterFluxRate = 6.6E-2 #  [kg/sm^2] fresh water flux rate at the left boundary
-diffusionCoefficient = 6.6e-6 # 1.2e-9 #[m2/s] Diffusion coefficient
+diffusionCoefficient = 0.12e-9 #[m2/s] Diffusion coefficient
 Name = Henry1p2c
 AlphaL = 0.1 # longitual dispersivity
 AlphaT = 0.01 # transversal dispersivity
diff --git a/lecture/mm/henryproblem/henry1p2c/henry1p2cproblem.hh b/lecture/mm/henryproblem/henry1p2c/henry1p2cproblem.hh
index 2c0a22ba377f7d72eba1a9cd510296fb6fda5e95..d6a449fd5ba896c3219849cac0033f6f6f9c5f28 100644
--- a/lecture/mm/henryproblem/henry1p2c/henry1p2cproblem.hh
+++ b/lecture/mm/henryproblem/henry1p2c/henry1p2cproblem.hh
@@ -70,23 +70,6 @@ public:
       freshWaterFluxRate_= getParam<Scalar>("Problem.freshWaterFluxRate");
     }
 
-    /*!
-     * \name Problem parameters
-     */
-    // \{
-
-    /*!
-     * \brief Returns the temperature within the domain.
-     *
-     * This problem assumes a temperature of 36 degrees Celsius.
-     */
-    Scalar temperature() const
-    {
-        return 273.15 + 20; // in [K]
-    };
-
-    // \}
-
     /*!
      * \name Boundary conditions
      */
diff --git a/lecture/mm/henryproblem/henry1p2c/henry1p2cspatialparameters.hh b/lecture/mm/henryproblem/henry1p2c/henry1p2cspatialparameters.hh
index d4fc7f5b1dbb5851a4a6b0e003ae6eb1fe70922e..d39cf35baa88b0612b44f949060b95e5d57e7bf8 100644
--- a/lecture/mm/henryproblem/henry1p2c/henry1p2cspatialparameters.hh
+++ b/lecture/mm/henryproblem/henry1p2c/henry1p2cspatialparameters.hh
@@ -25,8 +25,7 @@
 #ifndef DUMUX_HENRY1P2C_SPATIAL_PARAMETERS_HH
 #define DUMUX_HENRY1P2C_SPATIAL_PARAMETERS_HH
 
-#include <dumux/material/spatialparams/fv.hh>
-#include <dumux/material/fluidmatrixinteractions/2p/linearmaterial.hh>
+#include <dumux/porousmediumflow/fvspatialparams1p.hh>
 
 namespace Dumux {
 
@@ -37,7 +36,7 @@ namespace Dumux {
  */
 template<class FVGridGeometry, class Scalar>
 class Henry1p2cSpatialParams :
-public FVSpatialParams<FVGridGeometry, Scalar,
+public FVPorousMediumFlowSpatialParamsOneP<FVGridGeometry, Scalar,
                        Henry1p2cSpatialParams<FVGridGeometry, Scalar>>
 {
     using GridView = typename FVGridGeometry::GridView;
@@ -45,7 +44,7 @@ public FVSpatialParams<FVGridGeometry, Scalar,
     using SubControlVolume = typename FVElementGeometry::SubControlVolume;
 
     using Element = typename GridView::template Codim<0>::Entity;
-    using ParentType = FVSpatialParams<FVGridGeometry, Scalar,
+    using ParentType = FVPorousMediumFlowSpatialParamsOneP<FVGridGeometry, Scalar,
                                        Henry1p2cSpatialParams<FVGridGeometry, Scalar>>;
 
     using GlobalPosition = typename SubControlVolume::GlobalPosition;
@@ -59,6 +58,7 @@ public:
         // intrinsic permeabilities
         perm_ = 1.019368e-9;
         porosity_ = 0.35;
+        temperature_ = 293.15;
     }
 
     /*!
@@ -91,9 +91,21 @@ public:
         return std::array<Scalar, 2> {alphaL, alphaT};
     }
 
+    /*!
+     * \brief Returns the temperature within the domain.
+     *
+     * This problem assumes a temperature of 20 degrees Celsius.
+     */
+    Scalar temperatureAtPos(const GlobalPosition& globalPos) const
+    {
+        return temperature_; // in [K]
+    };
+
+
 private:
-    Scalar perm_;
+    PermeabilityType perm_;
     Scalar porosity_;
+    Scalar temperature_;
 };
 
 } // end namespace Dumux
diff --git a/lecture/mm/henryproblem/henry2p/henry2p.cc b/lecture/mm/henryproblem/henry2p/henry2p.cc
index 1ee74a01885417a13d24d78973aecdfd583608f9..050d33f78fcdc56bb19387735a26c1705165df5e 100644
--- a/lecture/mm/henryproblem/henry2p/henry2p.cc
+++ b/lecture/mm/henryproblem/henry2p/henry2p.cc
@@ -111,7 +111,7 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
+
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/mm/henryproblem/henry2p/henry2pproblem.hh b/lecture/mm/henryproblem/henry2p/henry2pproblem.hh
index ecaebbac76b402bcb8eaca4e8c9c8df810e905cd..5a733fea73fa67afd62abc2baa861011ffa6233d 100644
--- a/lecture/mm/henryproblem/henry2p/henry2pproblem.hh
+++ b/lecture/mm/henryproblem/henry2p/henry2pproblem.hh
@@ -67,7 +67,6 @@ public:
     {
         FluidSystem::init();
         eps_ = 3e-6;
-        temperature_ = 273.15 + 20; // -> 20°C
         freshWaterFluxRate_= getParam<Scalar>("Problem.freshWaterFluxRate");
     }
 
@@ -76,17 +75,6 @@ public:
      */
     // \{
 
-    /*!
-     * \brief Returns the temperature within the domain.
-     *
-     * This problem assumes a uniform temperature of 10 degrees Celsius.
-     */
-    Scalar temperature() const
-    {
-        return temperature_;
-    }
-
-
     NumEqVector sourceAtPos( const GlobalPosition &globalPos) const
     {
         return NumEqVector(0.0);
@@ -235,7 +223,6 @@ private:
     }
 
     static constexpr  Scalar depthBOR_ = 1.0;
-    Scalar temperature_;
     Scalar eps_;
     Scalar freshWaterFluxRate_;
 };
diff --git a/lecture/mm/henryproblem/henry2p/henry2pspatialparams.hh b/lecture/mm/henryproblem/henry2p/henry2pspatialparams.hh
index f55a5a522f3591d68fdbbca606702c9d9212614f..29aa4f19f8b0e188aed163af7e100378139c3a65 100644
--- a/lecture/mm/henryproblem/henry2p/henry2pspatialparams.hh
+++ b/lecture/mm/henryproblem/henry2p/henry2pspatialparams.hh
@@ -25,7 +25,7 @@
 #ifndef DUMUX_HENRY2P_SPATIAL_PARAMS_HH
 #define DUMUX_HENRY2P_SPATIAL_PARAMS_HH
 
-#include <dumux/material/spatialparams/fv.hh>
+#include <dumux/porousmediumflow/fvspatialparamsmp.hh>
 #include <dumux/material/fluidmatrixinteractions/2p/linearmaterial.hh>
 #include <dumux/porousmediumflow/2p/model.hh>
 
@@ -38,14 +38,14 @@ namespace Dumux {
 
 template<class FVGridGeometry, class Scalar>
 class Henry2pSpatialParams :
-public FVSpatialParams<FVGridGeometry, Scalar, Henry2pSpatialParams<FVGridGeometry, Scalar>>
+public FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar, Henry2pSpatialParams<FVGridGeometry, Scalar>>
 {
     using ThisType = Henry2pSpatialParams<FVGridGeometry, Scalar>;
     using GridView = typename FVGridGeometry::GridView;
     using Element = typename GridView::template Codim<0>::Entity;
     using FVElementGeometry = typename FVGridGeometry::LocalView;
     using SubControlVolume = typename FVElementGeometry::SubControlVolume;
-    using ParentType = FVSpatialParams<FVGridGeometry, Scalar, ThisType>;
+    using ParentType = FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar, ThisType>;
     static constexpr int dimWorld = GridView::dimensionworld;
     using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
 
@@ -71,8 +71,9 @@ public:
         typename PcKrSwCurve::BasicParams params(0.0/*pcEntry*/, 0.0/*pcMax*/);
         pcKrSwCurve_ = std::make_unique<PcKrSwCurve>(params);
 
-        K_ = 1.019368e-9;
+        k_ = 1.019368e-9;
         porosity_=0.35;
+        temperature_ = 293.15;
     }
 
     /*!
@@ -81,14 +82,14 @@ public:
      * \param globalPos The global position
      */
     PermeabilityType permeabilityAtPos(const GlobalPosition& globalPos) const
-    { return K_; }
+    { return k_; }
 
     /*!
      * \brief Define the porosity \f$\mathrm{[-]}\f$.
      *
      * \param globalPos The global position
      */
-    double porosityAtPos(const GlobalPosition& globalPos) const
+    Scalar porosityAtPos(const GlobalPosition& globalPos) const
     { return porosity_; }
 
     /*!
@@ -111,9 +112,20 @@ public:
     int wettingPhaseAtPos(const GlobalPosition& globalPos) const
     { return FluidSystem::phase0Idx; }
 
+        /*!
+     * \brief Returns the temperature within the domain.
+     *
+     * This problem assumes a temperature of 20 degrees Celsius.
+     */
+    Scalar temperatureAtPos(const GlobalPosition& globalPos) const
+    {
+        return temperature_; // in [K]
+    };
+
 private:
-    Scalar K_;
+    PermeabilityType k_;
     Scalar porosity_;
+    Scalar temperature_;
     std::unique_ptr<PcKrSwCurve> pcKrSwCurve_;
 
 
diff --git a/lecture/mm/naplinfiltration/3p/naplinfiltration3p.cc b/lecture/mm/naplinfiltration/3p/naplinfiltration3p.cc
index 09c200f2f0d9814dd95a49e1feae615798bbbb81..b6ccfb425d4687b6638070730e7525f5b9c90878 100644
--- a/lecture/mm/naplinfiltration/3p/naplinfiltration3p.cc
+++ b/lecture/mm/naplinfiltration/3p/naplinfiltration3p.cc
@@ -112,7 +112,6 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/mm/naplinfiltration/3p/naplinfiltration3p.input b/lecture/mm/naplinfiltration/3p/naplinfiltration3p.input
index 770afb7a82c4da72efc54fb081c7104eb84a672f..d4353182b7f674cdfa3ff2160cfd9d9bbbaf3b91 100644
--- a/lecture/mm/naplinfiltration/3p/naplinfiltration3p.input
+++ b/lecture/mm/naplinfiltration/3p/naplinfiltration3p.input
@@ -9,6 +9,7 @@ UpperRight = 500 10  # coordinates of upper right grid corner [m]
 Cells = 250 10       # number of cells in (x, y) direction [-]
 
 [SpatialParams]
+temperature = 283.15 # [K] 
 permeability = 1.e-11        # [m^2]
 porosity = 0.40              # [-]
 Swr = 0.12
diff --git a/lecture/mm/naplinfiltration/3p/problem.hh b/lecture/mm/naplinfiltration/3p/problem.hh
index 6bc6273e2573a481fd270fe8988bc4f8707fad2b..954445562aa73afffe0adacffed86001d1f62472 100644
--- a/lecture/mm/naplinfiltration/3p/problem.hh
+++ b/lecture/mm/naplinfiltration/3p/problem.hh
@@ -95,7 +95,6 @@ public:
     InfiltrationThreePProblem(std::shared_ptr<const FVGridGeometry> fvGridGeometry)
     : ParentType(fvGridGeometry)
     {
-        temperature_ = 273.15 + 10.0; // -> 10 degrees Celsius
         FluidSystem::init(282.15, 284.15, 3, 8e4, 3e5, 200);
 
         name_ = getParam<std::string>("Problem.Name");
@@ -119,18 +118,6 @@ public:
     const std::string& name() const
     { return name_; }
 
-    /*!
-     * \brief Returns the temperature within the domain.
-     *
-     * \param globalPos The position
-     *
-     * This problem assumes a temperature of 10 degrees Celsius.
-     */
-    Scalar temperatureAtPos(const GlobalPosition &globalPos) const
-    {
-        return temperature_;
-    }
-
     // \}
 
     /*!
@@ -217,16 +204,6 @@ public:
         return initial_(globalPos);
     }
 
-    /*!
-     * \brief Returns the temperature within the domain.
-     *
-     * This problem assumes a uniform temperature of 10 degrees Celsius.
-     */
-    Scalar temperature() const
-    { return temperature_; }
-
-
-
 private:
     // internal method for the initial condition (reused for the
     // dirichlet conditions!)
@@ -289,7 +266,6 @@ private:
         return sw;
     }
 
-    Scalar temperature_;
     static constexpr Scalar eps_ = 1e-6;
     std::string name_;
     Scalar time_;
diff --git a/lecture/mm/naplinfiltration/3p3c/naplinfiltration3p3c.cc b/lecture/mm/naplinfiltration/3p3c/naplinfiltration3p3c.cc
index 0a8816fba49c2dd2b6a4225517d595019084df61..9c6722e70890030dd136b355569c10134805956d 100644
--- a/lecture/mm/naplinfiltration/3p3c/naplinfiltration3p3c.cc
+++ b/lecture/mm/naplinfiltration/3p3c/naplinfiltration3p3c.cc
@@ -109,7 +109,6 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/mm/naplinfiltration/3p3c/naplinfiltration3p3c.input b/lecture/mm/naplinfiltration/3p3c/naplinfiltration3p3c.input
index b5500a54546065bb1dfe228f4077ee2ec461420c..b5fede1bdb21ea708acf6c7ad17e0877d72d686a 100644
--- a/lecture/mm/naplinfiltration/3p3c/naplinfiltration3p3c.input
+++ b/lecture/mm/naplinfiltration/3p3c/naplinfiltration3p3c.input
@@ -9,6 +9,7 @@ UpperRight = 500 10  # coordinates of upper right grid corner [m]
 Cells = 250 10       # number of cells in (x, y) direction [-]
 
 [SpatialParams]
+temperature = 283.15 	     #[K]
 permeability = 1.e-11        # [m^2]
 porosity = 0.40              # [-]
 Swr = 0.12
diff --git a/lecture/mm/naplinfiltration/3p3c/problem.hh b/lecture/mm/naplinfiltration/3p3c/problem.hh
index 3139c392e9708478662726235db211ad8faeb065..e2eb41786b95a48e1180d6e4669f2d3fb8147aae 100644
--- a/lecture/mm/naplinfiltration/3p3c/problem.hh
+++ b/lecture/mm/naplinfiltration/3p3c/problem.hh
@@ -107,7 +107,6 @@ public:
     InfiltrationThreePThreeCProblem(std::shared_ptr<const FVGridGeometry> fvGridGeometry)
     : ParentType(fvGridGeometry)
     {
-        temperature_ = 273.15 + 10.0; // -> 10 degrees Celsius
         FluidSystem::init(282.15, 284.15, 3, 8e4, 3e5, 200);
 
         name_ = getParam<std::string>("Problem.Name");
@@ -125,18 +124,6 @@ public:
     const std::string& name() const
     { return name_; }
 
-    /*!
-     * \brief Returns the temperature within the domain.
-     *
-     * \param globalPos The position
-     *
-     * This problem assumes a temperature of 10 degrees Celsius.
-     */
-    Scalar temperatureAtPos(const GlobalPosition &globalPos) const
-    {
-        return temperature_;
-    }
-
     // \}
 
     /*!
@@ -283,7 +270,6 @@ private:
         return sw;
     }
 
-    Scalar temperature_;
     static constexpr Scalar eps_ = 1e-6;
     std::string name_;
     Scalar time_;
diff --git a/lecture/mm/naplinfiltration/spatialparams.hh b/lecture/mm/naplinfiltration/spatialparams.hh
index 7722719d7d6fd496e8bf243e22e2b079fcef394e..44e54fb5bca5d8e3217f0df329fc42f96779a3f0 100644
--- a/lecture/mm/naplinfiltration/spatialparams.hh
+++ b/lecture/mm/naplinfiltration/spatialparams.hh
@@ -25,7 +25,7 @@
 #define DUMUX_NAPLINFILTRATION_SPATIAL_PARAMS_HH
 
 #include <dumux/porousmediumflow/properties.hh>
-#include <dumux/material/spatialparams/fv.hh>
+#include <dumux/porousmediumflow/fvspatialparamsmp.hh>
 #include <dumux/material/fluidmatrixinteractions/3p/parkervangenuchten.hh>
 #include <dumux/material/fluidmatrixinteractions/3p/napladsorption.hh>
 #include <dumux/io/gnuplotinterface.hh>
@@ -37,14 +37,14 @@ namespace Dumux {
  */
 template<class FVGridGeometry, class Scalar>
 class InfiltrationSpatialParams
-: public FVSpatialParams<FVGridGeometry, Scalar,
+: public FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar,
                          InfiltrationSpatialParams<FVGridGeometry, Scalar>>
 {
     using GridView = typename FVGridGeometry::GridView;
     using FVElementGeometry = typename FVGridGeometry::LocalView;
     using SubControlVolume = typename FVElementGeometry::SubControlVolume;
     using Element = typename GridView::template Codim<0>::Entity;
-    using ParentType = FVSpatialParams<FVGridGeometry, Scalar,
+    using ParentType = FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar,
                                        InfiltrationSpatialParams<FVGridGeometry, Scalar>>;
     using GlobalPosition = typename SubControlVolume::GlobalPosition;
     using ThreePhasePcKrSw = FluidMatrix::ParkerVanGenuchten3PDefault<Scalar>;
@@ -70,6 +70,9 @@ public:
         // porosities
         porosity_ = getParam<Scalar>("SpatialParams.porosity");
 
+        // temperature
+        temperature_ = getParam<Scalar>("SpatialParams.temperature");
+
         plotFluidMatrixInteractions_ =  getParam<bool>("Output.PlotFluidMatrixInteractions");
     }
 
@@ -147,6 +150,16 @@ public:
      */
     auto fluidMatrixInteractionAtPos(const GlobalPosition& globalPos) const
     { return makeFluidMatrixInteraction(threePhasePcKrSw_, adsorption_); }
+
+        /*!
+     * \brief Returns the temperature at the domain at the given position
+     * \param globalPos The position in global coordinates where the temperature should be specified
+     */
+    Scalar temperatureAtPos(const GlobalPosition& globalPos) const
+    {
+        return temperature_;
+    }
+
 private:
 /*
     bool isFineMaterial_(const GlobalPosition &globalPos) const
@@ -158,6 +171,7 @@ private:
 
     Scalar permeability_;
     Scalar porosity_;
+    Scalar temperature_;
 
     const ThreePhasePcKrSw threePhasePcKrSw_;
     const AdsorptionModel adsorption_;
diff --git a/lecture/mm/remediationscenarios/remediationscenariosexercise.cc b/lecture/mm/remediationscenarios/remediationscenariosexercise.cc
index e6c91f142dbc4d9b74fedb00cc3e711204ed0eb9..c53ffd77421d202acd029d259c765a52a8045ff1 100644
--- a/lecture/mm/remediationscenarios/remediationscenariosexercise.cc
+++ b/lecture/mm/remediationscenarios/remediationscenariosexercise.cc
@@ -111,7 +111,7 @@ int main(int argc, char** argv) try
     // create the finite volume grid geometry
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
     auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
-    fvGridGeometry->update();
+
 
     // the problem (initial and boundary conditions)
     using Problem = GetPropType<TypeTag, Properties::Problem>;
diff --git a/lecture/mm/remediationscenarios/remediationscenariosspatialparams.hh b/lecture/mm/remediationscenarios/remediationscenariosspatialparams.hh
index 1eaabaa221861fd7682884e9005a39b21a772257..bdebd20fe7ce45afd1525c022dc352d136fb6a02 100644
--- a/lecture/mm/remediationscenarios/remediationscenariosspatialparams.hh
+++ b/lecture/mm/remediationscenarios/remediationscenariosspatialparams.hh
@@ -26,7 +26,7 @@
 #include <dune/common/float_cmp.hh>
 
 #include <dumux/porousmediumflow/properties.hh>
-#include <dumux/material/spatialparams/fv.hh>
+#include <dumux/porousmediumflow/fvspatialparamsmp.hh>
 #include <dumux/material/fluidmatrixinteractions/3p/parkervangenuchten.hh>
 
 namespace Dumux {
@@ -36,7 +36,7 @@ namespace Dumux {
  */
 template<class TypeTag>
 class KuevetteSpatialParams
-: public FVSpatialParams<GetPropType<TypeTag, Properties::GridGeometry>, GetPropType<TypeTag, Properties::Scalar>, KuevetteSpatialParams<TypeTag>>
+: public FVPorousMediumFlowSpatialParamsMP<GetPropType<TypeTag, Properties::GridGeometry>, GetPropType<TypeTag, Properties::Scalar>, KuevetteSpatialParams<TypeTag>>
 {
     using Scalar = GetPropType<TypeTag, Properties::Scalar>;
     using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
@@ -45,7 +45,7 @@ class KuevetteSpatialParams
     using FVElementGeometry = typename FVGridGeometry::LocalView;
     using SubControlVolume = typename FVElementGeometry::SubControlVolume;
     using GlobalPosition = typename SubControlVolume::GlobalPosition;
-    using ParentType = FVSpatialParams<FVGridGeometry, Scalar, KuevetteSpatialParams<TypeTag>>;
+    using ParentType = FVPorousMediumFlowSpatialParamsMP<FVGridGeometry, Scalar, KuevetteSpatialParams<TypeTag>>;
 
     using ThreePhasePcKrSw = FluidMatrix::ParkerVanGenuchten3PDefault<Scalar>;
 
diff --git a/lecture/references/Henry1p2c-reference.vtu b/lecture/references/Henry1p2c-reference.vtu
index 728dc6d62858e0d61a796ee6310a627493150083..bdfebab5ae2e74832d0bbaac62b0335a86a511bc 100644
--- a/lecture/references/Henry1p2c-reference.vtu
+++ b/lecture/references/Henry1p2c-reference.vtu
@@ -2,524 +2,154 @@
 <VTKFile type="UnstructuredGrid" version="0.1" byte_order="LittleEndian">
   <UnstructuredGrid>
     <Piece NumberOfCells="800" NumberOfPoints="861">
-      <PointData Scalars="P">
+      <PointData Scalars="p">
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