diff --git a/tutorials/modules/incompressibleFluid/pitzDailyMapped/0/U b/tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/0/U
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailyMapped/0/U
rename to tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/0/U
diff --git a/tutorials/modules/incompressibleFluid/pitzDailyMapped/0/k b/tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/0/k
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailyMapped/0/k
rename to tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/0/k
diff --git a/tutorials/modules/incompressibleFluid/pitzDailyMapped/0/nuTilda b/tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/0/nuTilda
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailyMapped/0/nuTilda
rename to tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/0/nuTilda
diff --git a/tutorials/modules/incompressibleFluid/pitzDailyMapped/0/nut b/tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/0/nut
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailyMapped/0/nut
rename to tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/0/nut
diff --git a/tutorials/modules/incompressibleFluid/pitzDailyMapped/0/p b/tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/0/p
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailyMapped/0/p
rename to tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/0/p
diff --git a/tutorials/modules/incompressibleFluid/pitzDailyMapped/constant/momentumTransport b/tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/constant/momentumTransport
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailyMapped/constant/momentumTransport
rename to tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/constant/momentumTransport
diff --git a/tutorials/modules/incompressibleFluid/pitzDailyMapped/constant/physicalProperties b/tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/constant/physicalProperties
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailyMapped/constant/physicalProperties
rename to tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/constant/physicalProperties
diff --git a/tutorials/modules/incompressibleFluid/pitzDailyMapped/system/blockMeshDict b/tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/system/blockMeshDict
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailyMapped/system/blockMeshDict
rename to tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/system/blockMeshDict
diff --git a/tutorials/modules/incompressibleFluid/pitzDailyMapped/system/controlDict b/tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/system/controlDict
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailyMapped/system/controlDict
rename to tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/system/controlDict
diff --git a/tutorials/modules/incompressibleFluid/pitzDailyMapped/system/decomposeParDict b/tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/system/decomposeParDict
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailyMapped/system/decomposeParDict
rename to tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/system/decomposeParDict
diff --git a/tutorials/modules/incompressibleFluid/pitzDailyMapped/system/fvSchemes b/tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/system/fvSchemes
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailyMapped/system/fvSchemes
rename to tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/system/fvSchemes
diff --git a/tutorials/modules/incompressibleFluid/pitzDailyMapped/system/fvSolution b/tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/system/fvSolution
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailyMapped/system/fvSolution
rename to tutorials/modules/incompressibleFluid/pitzDailyLESDevelopedInlet/system/fvSolution
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/0/U b/tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/0/U
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/0/U
rename to tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/0/U
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/0/epsilon b/tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/0/epsilon
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/0/epsilon
rename to tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/0/epsilon
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/0/k b/tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/0/k
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/0/k
rename to tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/0/k
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/0/nuTilda b/tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/0/nuTilda
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/0/nuTilda
rename to tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/0/nuTilda
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/0/nut b/tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/0/nut
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/0/nut
rename to tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/0/nut
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/0/p b/tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/0/p
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/0/p
rename to tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/0/p
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/Allrun b/tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/Allrun
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/Allrun
rename to tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/Allrun
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/constant/boundaryData/inlet/0/U b/tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/constant/boundaryData/inlet/0/U
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/constant/boundaryData/inlet/0/U
rename to tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/constant/boundaryData/inlet/0/U
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/constant/boundaryData/inlet/0/epsilon b/tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/constant/boundaryData/inlet/0/epsilon
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/constant/boundaryData/inlet/0/epsilon
rename to tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/constant/boundaryData/inlet/0/epsilon
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/constant/boundaryData/inlet/0/k b/tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/constant/boundaryData/inlet/0/k
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/constant/boundaryData/inlet/0/k
rename to tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/constant/boundaryData/inlet/0/k
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/constant/boundaryData/inlet/points b/tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/constant/boundaryData/inlet/points
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/constant/boundaryData/inlet/points
rename to tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/constant/boundaryData/inlet/points
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/constant/momentumTransport b/tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/constant/momentumTransport
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/constant/momentumTransport
rename to tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/constant/momentumTransport
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/constant/physicalProperties b/tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/constant/physicalProperties
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/constant/physicalProperties
rename to tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/constant/physicalProperties
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/system/controlDict b/tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/system/controlDict
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/system/controlDict
rename to tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/system/controlDict
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/system/decomposeParDict b/tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/system/decomposeParDict
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/system/decomposeParDict
rename to tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/system/decomposeParDict
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/system/fvSchemes b/tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/system/fvSchemes
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/system/fvSchemes
rename to tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/system/fvSchemes
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/system/fvSolution b/tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/system/fvSolution
similarity index 100%
rename from tutorials/modules/incompressibleFluid/pitzDailySteadyExptInlet/system/fvSolution
rename to tutorials/modules/incompressibleFluid/pitzDailySteadyExperimentalInlet/system/fvSolution
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/0/U.orig b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/0/U.orig
new file mode 100644
index 0000000000..13ce46a6d7
--- /dev/null
+++ b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/0/U.orig
@@ -0,0 +1,43 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       volVectorField;
+    location    "0";
+    object      U;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions      [0 1 -1 0 0 0 0];
+
+internalField   uniform (0 0 0);
+
+boundaryField
+{
+    cutIn
+    {
+        type            fixedValue;
+        value           $internalField;
+    }
+    cutOut
+    {
+        type            pressureInletOutletVelocity;
+        value           $internalField;
+    }
+    lowerWall
+    {
+        type            noSlip;
+    }
+    frontAndBack
+    {
+        type            empty;
+    }
+}
+
+// ************************************************************************* //
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/0/epsilon.orig b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/0/epsilon.orig
new file mode 100644
index 0000000000..9f60e89ca6
--- /dev/null
+++ b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/0/epsilon.orig
@@ -0,0 +1,46 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       volScalarField;
+    location    "0";
+    object      epsilon;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions      [0 2 -3 0 0 0 0];
+
+internalField   uniform 14.855;
+
+boundaryField
+{
+    cutIn
+    {
+        type            fixedValue;
+        value           $internalField;
+    }
+    cutOut
+    {
+        type            inletOutlet;
+        inletValue      $internalField;
+        value           $internalField;
+    }
+    lowerWall
+    {
+        type            epsilonWallFunction;
+        value           $internalField;
+    }
+    frontAndBack
+    {
+        type            empty;
+    }
+}
+
+
+// ************************************************************************* //
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/0/k.orig b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/0/k.orig
new file mode 100644
index 0000000000..54bff1fc53
--- /dev/null
+++ b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/0/k.orig
@@ -0,0 +1,46 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       volScalarField;
+    location    "0";
+    object      k;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions      [0 2 -2 0 0 0 0];
+
+internalField   uniform 0.375;
+
+boundaryField
+{
+    cutIn
+    {
+        type            fixedValue;
+        value           $internalField;
+    }
+    cutOut
+    {
+        type            inletOutlet;
+        inletValue      $internalField;
+        value           $internalField;
+    }
+    lowerWall
+    {
+        type            kqRWallFunction;
+        value           $internalField;
+    }
+    frontAndBack
+    {
+        type            empty;
+    }
+}
+
+
+// ************************************************************************* //
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/0/nut.orig b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/0/nut.orig
new file mode 100644
index 0000000000..5a5bb56915
--- /dev/null
+++ b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/0/nut.orig
@@ -0,0 +1,45 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       volScalarField;
+    location    "0";
+    object      nut;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions      [0 2 -1 0 0 0 0];
+
+internalField   uniform 0;
+
+boundaryField
+{
+    cutIn
+    {
+        type            calculated;
+        value           $internalField;
+    }
+    cutOut
+    {
+        type            calculated;
+        value           $internalField;
+    }
+    lowerWall
+    {
+        type            nutkWallFunction;
+        value           $internalField;
+    }
+    frontAndBack
+    {
+        type            empty;
+    }
+}
+
+
+// ************************************************************************* //
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/0/p.orig b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/0/p.orig
new file mode 100644
index 0000000000..9c6acaf4f5
--- /dev/null
+++ b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/0/p.orig
@@ -0,0 +1,43 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       volScalarField;
+    location    "0";
+    object      p;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions      [0 2 -2 0 0 0 0];
+
+internalField   uniform 0;
+
+boundaryField
+{
+    cutIn
+    {
+        type            zeroGradient;
+    }
+    cutOut
+    {
+        type            entrainmentPressure;
+        p0              $internalField;
+        value           $internalField;
+    }
+    lowerWall
+    {
+        type            zeroGradient;
+    }
+    frontAndBack
+    {
+        type            empty;
+    }
+}
+
+// ************************************************************************* //
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/Allclean b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/Allclean
new file mode 100755
index 0000000000..204f58f154
--- /dev/null
+++ b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/Allclean
@@ -0,0 +1,9 @@
+#!/bin/sh
+cd ${0%/*} || exit 1    # Run from this directory
+
+# Source tutorial run functions
+. $WM_PROJECT_DIR/bin/tools/CleanFunctions
+
+cleanCase && rm -rf pitzDailySteady constant system/controlDict system/fv*
+
+#------------------------------------------------------------------------------
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/Allrun b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/Allrun
new file mode 120000
index 0000000000..f8f6fb5227
--- /dev/null
+++ b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/Allrun
@@ -0,0 +1 @@
+Allrun-parallel
\ No newline at end of file
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/Allrun-parallel b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/Allrun-parallel
new file mode 100755
index 0000000000..baf5dae9c9
--- /dev/null
+++ b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/Allrun-parallel
@@ -0,0 +1,46 @@
+#!/bin/sh
+cd ${0%/*} || exit 1    # Run from this directory
+
+# Source tutorial run and clean functions
+. $WM_PROJECT_DIR/bin/tools/RunFunctions
+. $WM_PROJECT_DIR/bin/tools/CleanFunctions
+
+# Copy the source case
+isTest "$@" && path=.. || path=$FOAM_TUTORIALS/modules/incompressibleFluid
+cp -r $path/pitzDailySteady/constant .
+cp -r $path/pitzDailySteady/system/controlDict system
+cp -r $path/pitzDailySteady/system/fv* system
+cp -r $path/pitzDailySteady .
+
+# Run the source case in parallel
+(
+    cd pitzDailySteady
+    isTest "$@" && cleanCase
+    cp ../system/decomposeParDict system
+    runApplication blockMesh -dict $FOAM_TUTORIALS/resources/blockMesh/pitzDaily
+    runApplication decomposePar
+    runParallel foamRun
+)
+
+# Mesh
+runApplication blockMesh
+runApplication decomposePar
+
+# Map from the source case into this case and run in parallel
+#
+# !!! Smooth interpolative mapping from a coarse to a fine case is not
+# available within mapFieldsPar. All current options create fields with step
+# changes at the boundaries between coarse source cells. This poor
+# initialisation results in a large transient at the start of the part
+# simulation. We need a lot of under-relaxation to overcome this. In future, it
+# is desired to introduce smooth interpolative mapping, which should resolve
+# this issue and the need for additional under-relaxation.
+#
+runParallel mapFieldsPar pitzDailySteady -sourceTime latestTime -fields "(epsilon k nut p U)"
+runApplication foamDictionary system/fvSolution -entry relaxationFactors/equations -set '{ ".*" 0.1; }'
+runParallel foamRun
+
+# Reconstruct, including the values mapped to the zero directory
+runApplication reconstructPar -withZero
+
+#------------------------------------------------------------------------------
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/Allrun-serial b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/Allrun-serial
new file mode 100755
index 0000000000..d2ef23cf99
--- /dev/null
+++ b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/Allrun-serial
@@ -0,0 +1,39 @@
+#!/bin/sh
+cd ${0%/*} || exit 1    # Run from this directory
+
+# Source tutorial run and clean functions
+. $WM_PROJECT_DIR/bin/tools/RunFunctions
+. $WM_PROJECT_DIR/bin/tools/CleanFunctions
+
+# Copy the source case
+isTest "$@" && path=.. || path=$FOAM_TUTORIALS/modules/incompressibleFluid
+cp -r $path/pitzDailySteady/constant .
+cp -r $path/pitzDailySteady/system/controlDict system
+cp -r $path/pitzDailySteady/system/fv* system
+cp -r $path/pitzDailySteady .
+
+# Run the source case
+(
+    cd pitzDailySteady
+    isTest "$@" && cleanCase
+    ./Allrun
+)
+
+# Mesh
+runApplication blockMesh
+
+# Map from the source case into this case and run
+#
+# !!! Smooth interpolative mapping from a coarse to a fine case is not
+# available within mapFieldsPar. All current options create fields with step
+# changes at the boundaries between coarse source cells. This poor
+# initialisation results in a large transient at the start of the part
+# simulation. We need a lot of under-relaxation to overcome this. In future, it
+# is desired to introduce smooth interpolative mapping, which should resolve
+# this issue and the need for additional under-relaxation.
+#
+runApplication mapFieldsPar pitzDailySteady -sourceTime latestTime -fields "(epsilon k nut p U)"
+runApplication foamDictionary system/fvSolution -entry relaxationFactors/equations -set '{ ".*" 0.1; }'
+runApplication foamRun
+
+#------------------------------------------------------------------------------
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/system/blockMeshDict b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/system/blockMeshDict
new file mode 100644
index 0000000000..ca3ce122d1
--- /dev/null
+++ b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/system/blockMeshDict
@@ -0,0 +1,85 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       dictionary;
+    object      blockMeshDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+convertToMeters 0.001;
+
+vertices
+(
+    (-2 0 -0.5)
+    (-2 1 -0.5)
+    (0 -1 -0.5)
+    (0 0 -0.5)
+    (0 1 -0.5)
+    (2 -1 -0.5)
+    (2 0 -0.5)
+    (2 1 -0.5)
+
+    (-2 0 0.5)
+    (-2 1 0.5)
+    (0 -1 0.5)
+    (0 0 0.5)
+    (0 1 0.5)
+    (2 -1 0.5)
+    (2 0 0.5)
+    (2 1 0.5)
+);
+
+blocks
+(
+    hex (0 3 4 1 8 11 12 9) (30 40 1) simpleGrading (0.2 5 1)
+    hex (2 5 6 3 10 13 14 11) (30 40 1) simpleGrading (5 0.2 1)
+    hex (3 6 7 4 11 14 15 12) (30 40 1) simpleGrading (5 5 1)
+);
+
+defaultPatch
+{
+    name frontAndBack;
+    type empty;
+}
+
+boundary
+(
+    lowerWall
+    {
+        type wall;
+        faces
+        (
+            (0 3 11 8)
+            (3 2 10 11)
+        );
+    }
+    cutIn
+    {
+        type patch;
+        faces
+        (
+            (0 1 9 8)
+            (2 5 13 10)
+        );
+    }
+    cutOut
+    {
+        type patch;
+        faces
+        (
+            (1 4 12 9)
+            (4 7 15 12)
+            (5 6 14 13)
+            (6 7 15 14)
+        );
+    }
+);
+
+// ************************************************************************* //
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/system/decomposeParDict b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/system/decomposeParDict
new file mode 100644
index 0000000000..f963d34548
--- /dev/null
+++ b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/system/decomposeParDict
@@ -0,0 +1,20 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       dictionary;
+    object      decomposeParDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+numberOfSubdomains  4;
+
+method              scotch;
+
+// ************************************************************************* //
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/system/mapFieldsDict b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/system/mapFieldsDict
new file mode 100644
index 0000000000..c84ed818df
--- /dev/null
+++ b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToPart/system/mapFieldsDict
@@ -0,0 +1,20 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       dictionary;
+    object      mapFieldsDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+patchMap        (lowerWall lowerWall);
+
+cuttingPatches  (cutIn);
+
+// ************************************************************************* //
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToRefined/Allclean b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToRefined/Allclean
new file mode 100755
index 0000000000..f8b27ed740
--- /dev/null
+++ b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToRefined/Allclean
@@ -0,0 +1,11 @@
+#!/bin/sh
+cd ${0%/*} || exit 1    # Run from this directory
+
+# Source tutorial run functions
+. $WM_PROJECT_DIR/bin/tools/CleanFunctions
+
+cleanCase && rm -rf pitzDailySteady 0 constant
+
+find system -type f -not -name decomposeParDict -delete
+
+#------------------------------------------------------------------------------
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToRefined/Allmesh b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToRefined/Allmesh
new file mode 100755
index 0000000000..c833d9cec9
--- /dev/null
+++ b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToRefined/Allmesh
@@ -0,0 +1,30 @@
+#!/bin/sh
+cd ${0%/*} || exit 1    # Run from this directory
+
+# Source tutorial run functions
+. $WM_PROJECT_DIR/bin/tools/RunFunctions
+
+# Get the standard mesh dictionary
+cp -f $FOAM_TUTORIALS/resources/blockMesh/pitzDaily system
+
+# Decrease the mesh spacings by a factor
+factor=5/4
+for nX in 18 180 25
+do
+    for nY in 27 30
+    do
+        nXYZ0="($nX $nY 1)"
+        nXYZ1="($(echo $nX*$factor | bc) $(echo $nY*$factor | bc) 1)"
+        sed -i "s/$nXYZ0/$nXYZ1/g" system/blockMeshDict
+    done
+done
+
+# Create a slightly inconsistent geometry, with some cells and patch faces
+# falling outside the source case. This tests the stabilisation of the
+# mesh-to-mesh interpolations.
+sed -i 's/(0 0 \(.*\))/(-1.2 0 \1)/g' system/blockMeshDict
+
+# Mesh
+runApplication blockMesh
+
+#------------------------------------------------------------------------------
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToRefined/Allrun b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToRefined/Allrun
new file mode 120000
index 0000000000..f8f6fb5227
--- /dev/null
+++ b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToRefined/Allrun
@@ -0,0 +1 @@
+Allrun-parallel
\ No newline at end of file
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToRefined/Allrun-parallel b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToRefined/Allrun-parallel
new file mode 100755
index 0000000000..bbbb2b70c9
--- /dev/null
+++ b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToRefined/Allrun-parallel
@@ -0,0 +1,35 @@
+#!/bin/sh
+cd ${0%/*} || exit 1    # Run from this directory
+
+# Source tutorial run and clean functions
+. $WM_PROJECT_DIR/bin/tools/RunFunctions
+. $WM_PROJECT_DIR/bin/tools/CleanFunctions
+
+# Copy the source case
+isTest "$@" && path=.. || path=$FOAM_TUTORIALS/modules/incompressibleFluid
+cp -r $path/pitzDailySteady/constant .
+cp -r $path/pitzDailySteady/system/* system
+cp -r $path/pitzDailySteady .
+
+# Run the source case in parallel
+(
+    cd pitzDailySteady
+    isTest "$@" && cleanCase
+    cp ../system/decomposeParDict system
+    runApplication blockMesh -dict $FOAM_TUTORIALS/resources/blockMesh/pitzDaily
+    runApplication decomposePar
+    runParallel foamRun
+)
+
+# Mesh
+./Allmesh
+runApplication decomposePar
+
+# Map from the source case into this case and run
+runParallel mapFieldsPar pitzDailySteady -consistent -sourceTime latestTime
+runParallel foamRun
+
+# Reconstruct, including the values mapped to the zero directory
+runApplication reconstructPar -withZero
+
+#------------------------------------------------------------------------------
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToRefined/Allrun-serial b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToRefined/Allrun-serial
new file mode 100755
index 0000000000..57c8136216
--- /dev/null
+++ b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToRefined/Allrun-serial
@@ -0,0 +1,28 @@
+#!/bin/sh
+cd ${0%/*} || exit 1    # Run from this directory
+
+# Source tutorial run and clean functions
+. $WM_PROJECT_DIR/bin/tools/RunFunctions
+. $WM_PROJECT_DIR/bin/tools/CleanFunctions
+
+# Copy the source case
+isTest "$@" && path=.. || path=$FOAM_TUTORIALS/modules/incompressibleFluid
+cp -r $path/pitzDailySteady/constant .
+cp -r $path/pitzDailySteady/system/* system
+cp -r $path/pitzDailySteady .
+
+# Run the source case
+(
+    cd pitzDailySteady
+    isTest "$@" && cleanCase
+    ./Allrun
+)
+
+# Mesh
+./Allmesh
+
+# Map from the source case into this case and run
+runApplication mapFieldsPar pitzDailySteady -consistent -sourceTime latestTime
+runApplication foamRun
+
+#------------------------------------------------------------------------------
diff --git a/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToRefined/system/decomposeParDict b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToRefined/system/decomposeParDict
new file mode 100644
index 0000000000..f963d34548
--- /dev/null
+++ b/tutorials/modules/incompressibleFluid/pitzDailySteadyMappedToRefined/system/decomposeParDict
@@ -0,0 +1,20 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       dictionary;
+    object      decomposeParDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+numberOfSubdomains  4;
+
+method              scotch;
+
+// ************************************************************************* //