diff --git a/tutorials/verificationAndValidation/schemes/weightedFluxExample/0.orig/DT b/tutorials/verificationAndValidation/schemes/weightedFluxExample/0.orig/DT
new file mode 100644
index 0000000000..e9e255e0b5
--- /dev/null
+++ b/tutorials/verificationAndValidation/schemes/weightedFluxExample/0.orig/DT
@@ -0,0 +1,30 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v1912                                 |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       volScalarField;
+    object      DT;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions      [0 2 -1 0 0 0 0];
+
+internalField   uniform 0;
+
+boundaryField
+{
+    "(top|bottom|sideWalls)"
+    {
+        type            fixedGradient;
+        gradient        uniform 0;
+    }
+}
+
+// ************************************************************************* //
diff --git a/tutorials/verificationAndValidation/schemes/weightedFluxExample/0.orig/T b/tutorials/verificationAndValidation/schemes/weightedFluxExample/0.orig/T
new file mode 100644
index 0000000000..43e145270b
--- /dev/null
+++ b/tutorials/verificationAndValidation/schemes/weightedFluxExample/0.orig/T
@@ -0,0 +1,39 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v1912                                 |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       volScalarField;
+    object      T;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions      [0 0 0 1 0 0 0];
+
+internalField   uniform 273;
+
+boundaryField
+{
+    top
+    {
+        type            fixedValue;
+        value           uniform 1;
+    }
+    bottom
+    {
+        type            fixedValue;
+        value           uniform 0;
+    }
+    sideWalls
+    {
+        type            zeroGradient;
+    }
+}
+
+// ************************************************************************* //
diff --git a/tutorials/verificationAndValidation/schemes/weightedFluxExample/Allclean b/tutorials/verificationAndValidation/schemes/weightedFluxExample/Allclean
new file mode 100755
index 0000000000..10503f97cb
--- /dev/null
+++ b/tutorials/verificationAndValidation/schemes/weightedFluxExample/Allclean
@@ -0,0 +1,12 @@
+#!/bin/sh
+cd "${0%/*}" || exit                                # Run from this directory
+. ${WM_PROJECT_DIR:?}/bin/tools/CleanFunctions      # Tutorial clean functions
+#------------------------------------------------------------------------------
+
+cleanCase0
+
+rm -f *.png
+
+rm -f system/controlDict system/fvSchemes
+
+#------------------------------------------------------------------------------
diff --git a/tutorials/verificationAndValidation/schemes/weightedFluxExample/Allrun b/tutorials/verificationAndValidation/schemes/weightedFluxExample/Allrun
new file mode 100755
index 0000000000..5bcc22315a
--- /dev/null
+++ b/tutorials/verificationAndValidation/schemes/weightedFluxExample/Allrun
@@ -0,0 +1,42 @@
+#!/bin/sh
+cd "${0%/*}" || exit                                # Run from this directory
+. ${WM_PROJECT_DIR:?}/bin/tools/RunFunctions        # Tutorial run functions
+#------------------------------------------------------------------------------
+
+restore0Dir
+
+cp -f system/controlDict.template system/controlDict
+cp -f system/fvSchemes.template system/fvSchemes
+
+runApplication blockMesh
+runApplication setFields
+
+# ----
+echo "Run base-line (1)"
+foamDictionary -entry endTime -set 1 system/controlDict >/dev/null
+sed -i '/^ *laplacian/s/Gauss.*;/Gauss linear corrected;/' system/fvSchemes
+
+runApplication -s 1 $(getApplication)
+
+# ----
+echo "Run harmonic corrected (2)"
+
+foamDictionary -entry endTime -set 2 system/controlDict >/dev/null
+sed -i '/^ *laplacian/s/Gauss.*;/Gauss harmonic corrected;/' system/fvSchemes
+
+runApplication -s 2 $(getApplication)
+
+# ----
+echo "Run weightedFlux (3)"
+foamDictionary -entry endTime -set 3 system/controlDict >/dev/null
+sed -i '/^ *grad/s/Gauss.*;/Gauss weightedFlux "DT";/' system/fvSchemes
+
+runApplication -s 3 $(getApplication)
+
+# ----
+
+runApplication -s singleGraph  postProcess -func singleGraph
+
+./plot $@
+
+#------------------------------------------------------------------------------
diff --git a/tutorials/verificationAndValidation/schemes/weightedFluxExample/constant/transportProperties b/tutorials/verificationAndValidation/schemes/weightedFluxExample/constant/transportProperties
new file mode 100644
index 0000000000..63ccdb4eca
--- /dev/null
+++ b/tutorials/verificationAndValidation/schemes/weightedFluxExample/constant/transportProperties
@@ -0,0 +1,20 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v1912                                 |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    location    "constant";
+    object      transportProperties;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+DT              0; //Not used
+
+// ************************************************************************* //
diff --git a/tutorials/verificationAndValidation/schemes/weightedFluxExample/plot b/tutorials/verificationAndValidation/schemes/weightedFluxExample/plot
new file mode 100755
index 0000000000..3d4164670b
--- /dev/null
+++ b/tutorials/verificationAndValidation/schemes/weightedFluxExample/plot
@@ -0,0 +1,88 @@
+#!/bin/bash
+cd "${0%/*}" || exit                                # Run from this directory
+. ${WM_PROJECT_DIR:?}/bin/tools/RunFunctions        # Tutorial run functions
+#------------------------------------------------------------------------------
+
+# Plot temperature, heat flux vs analytical
+
+graphDir="postProcessing/singleGraph"
+
+#------------------------------------------------------------------------------
+
+plotTemperature() {
+    graphName="Tprofile.png"
+    echo "Creating temperature profile graph to $graphName"
+    gnuplot<<GNUPLOT
+    set terminal pngcairo font "Helvetica,12" size 800,600
+    set title "Temperature profile" font "Helvetica,12"
+
+    set key bottom right
+    set xlabel "z" font "Helvetica,12"
+    set ylabel "Temperature" font "Helvetica,16"
+    set output "$graphName"
+
+    set logscale y
+    set format y "10^{%L}"
+    set key font ",12"
+
+    set lmargin 10
+    set rmargin 1.5
+    set bmargin 3.2
+
+    s1=1
+    s2=1e6
+
+    fo(x)=s1/(s1+s2)+s2*x/(s1+s2)
+    fu(x)=s1/(s1+s2)+s1*x/(s1+s2)
+
+    plot \
+    (x<=0)?fu(x):fo(x) w l lc 0 t 'analytical solution', \
+    "$graphDir/1/line_T.xy" u 1:2 w p pt 2 ps 2 lt rgb "red" t 'linear interpolation', \
+    "$graphDir/2/line_T.xy" u 1:2 w p pt 6 ps 2 lt rgb "green" t 'harmonic interpolation'
+
+GNUPLOT
+}
+
+
+plotHeatFlux() {
+    graphName="heatFlux.png"
+    echo "Creating heat-flux graph to $graphName"
+    gnuplot<<GNUPLOT
+    set terminal pngcairo font "Helvetica,12" size 800,600
+    set title "Heat Flux" font "Helvetica,16"
+
+    set key top right
+    set xlabel "z" font "Helvetica,12"
+    set output "$graphName"
+
+    set logscale y
+    set format y "10^{%L}"
+    set key font ",12"
+
+    set lmargin 10
+    set rmargin 1.5
+    set bmargin 3.2
+
+    plot \
+    "$graphDir/1/line_flux.xy" u 1:4 w p pt 6 ps 2 lt rgb "red" t 'laplacian: linear, grad: linear', \
+    "$graphDir/2/line_flux.xy" u 1:4 w p pt 2 ps 2 lt rgb "blue" t 'laplacian: harmonic, grad: linear', \
+    "$graphDir/3/line_flux.xy" u 1:4 w l lt rgb "green" t 'laplacian: harmonic, grad: weightedFlux'
+GNUPLOT
+}
+
+
+if notTest $@
+then
+    # Create validation plots
+
+    # Require gnuplot
+    command -v gnuplot >/dev/null || {
+        echo "gnuplot not found - skipping graph creation" 1>&2
+        exit 1
+    }
+
+    plotTemperature
+    plotHeatFlux
+fi
+
+# ------------------------------------------------------------------------------
diff --git a/tutorials/verificationAndValidation/schemes/weightedFluxExample/system/blockMeshDict b/tutorials/verificationAndValidation/schemes/weightedFluxExample/system/blockMeshDict
new file mode 100644
index 0000000000..6f60948134
--- /dev/null
+++ b/tutorials/verificationAndValidation/schemes/weightedFluxExample/system/blockMeshDict
@@ -0,0 +1,68 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v1912                                 |
+|   \\  /    A nd           | Website:  www.OpenFOAM.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      blockMeshDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+a  0.5;
+b -0.5;
+h1  -1;
+h2   1;
+
+vertices
+(
+    ($a $a $h1)
+    ($b $a $h1)
+    ($b $b $h1)
+    ($a $b $h1)
+
+    ($a $a $h2)
+    ($b $a $h2)
+    ($b $b $h2)
+    ($a $b $h2)
+);
+
+blocks
+(
+    hex (0 1 2 3 4 5 6 7) (1 1 100) simpleGrading (1 1 1)
+);
+
+edges
+(
+);
+
+boundary
+(
+    bottom
+    {
+        type wall;
+        faces
+        (
+            (0 1 2 3)
+        );
+    }
+    top
+    {
+        type wall;
+        faces
+        (
+            (4 5 6 7)
+        );
+    }
+);
+
+mergePatchPairs
+(
+);
+
+// ************************************************************************* //
diff --git a/tutorials/verificationAndValidation/schemes/weightedFluxExample/system/controlDict.template b/tutorials/verificationAndValidation/schemes/weightedFluxExample/system/controlDict.template
new file mode 100644
index 0000000000..8076b8e8a9
--- /dev/null
+++ b/tutorials/verificationAndValidation/schemes/weightedFluxExample/system/controlDict.template
@@ -0,0 +1,49 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v1912                                 |
+|   \\  /    A nd           | Website:  www.OpenFOAM.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    location    "system";
+    object      controlDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+application     laplacianFoam;
+
+startFrom       latestTime;
+
+startTime       0;
+
+stopAt          endTime;
+
+endTime         1;
+
+deltaT          0.005;
+
+writeControl    runTime;
+
+writeInterval   1;
+
+purgeWrite      0;
+
+writeFormat     ascii;
+
+writePrecision  6;
+
+writeCompression off;
+
+timeFormat      general;
+
+timePrecision   6;
+
+runTimeModifiable true;
+
+
+// ************************************************************************* //
diff --git a/tutorials/verificationAndValidation/schemes/weightedFluxExample/system/fvSchemes.template b/tutorials/verificationAndValidation/schemes/weightedFluxExample/system/fvSchemes.template
new file mode 100644
index 0000000000..3cfbac54f5
--- /dev/null
+++ b/tutorials/verificationAndValidation/schemes/weightedFluxExample/system/fvSchemes.template
@@ -0,0 +1,49 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v1912                                 |
+|   \\  /    A nd           | Website:  www.OpenFOAM.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    location    "system";
+    object      fvSchemes;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+ddtSchemes
+{
+    default         steadyState;
+}
+
+gradSchemes
+{
+    grad(T)         Gauss linear;
+}
+
+divSchemes
+{
+    default         none;
+}
+
+laplacianSchemes
+{
+    laplacian(DT,T) Gauss linear corrected;
+}
+
+interpolationSchemes
+{
+    default         linear;
+}
+
+snGradSchemes
+{
+    default         corrected;
+}
+
+
+// ************************************************************************* //
diff --git a/tutorials/verificationAndValidation/schemes/weightedFluxExample/system/fvSolution b/tutorials/verificationAndValidation/schemes/weightedFluxExample/system/fvSolution
new file mode 100644
index 0000000000..e9b4e33f1a
--- /dev/null
+++ b/tutorials/verificationAndValidation/schemes/weightedFluxExample/system/fvSolution
@@ -0,0 +1,35 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v1912                                 |
+|   \\  /    A nd           | Website:  www.OpenFOAM.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    location    "system";
+    object      fvSolution;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+solvers
+{
+    T
+    {
+        solver          PCG;
+        preconditioner  DIC;
+        tolerance       1e-15;
+        relTol          0;
+    }
+}
+
+SIMPLE
+{
+    nNonOrthogonalCorrectors 2;
+}
+
+
+// ************************************************************************* //
diff --git a/tutorials/verificationAndValidation/schemes/weightedFluxExample/system/setFieldsDict b/tutorials/verificationAndValidation/schemes/weightedFluxExample/system/setFieldsDict
new file mode 100644
index 0000000000..f4dbb22c4d
--- /dev/null
+++ b/tutorials/verificationAndValidation/schemes/weightedFluxExample/system/setFieldsDict
@@ -0,0 +1,38 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v1912                                 |
+|   \\  /    A nd           | Website:  www.OpenFOAM.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    location    "system";
+    object      setFieldsDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+defaultFieldValues
+(
+    volScalarFieldValue DT 1
+);
+
+regions
+(
+    cylinderToCell
+    {
+        p1 (0 0 -5);
+        p2 (0 0 .000);
+        radius 1;
+        fieldValues
+        (
+            volScalarFieldValue DT 1e6
+        );
+    }
+);
+
+
+// ************************************************************************* //
diff --git a/tutorials/verificationAndValidation/schemes/weightedFluxExample/system/singleGraph b/tutorials/verificationAndValidation/schemes/weightedFluxExample/system/singleGraph
new file mode 100644
index 0000000000..6139c9e90f
--- /dev/null
+++ b/tutorials/verificationAndValidation/schemes/weightedFluxExample/system/singleGraph
@@ -0,0 +1,26 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v1912                                 |
+|   \\  /    A nd           | Website:  www.OpenFOAM.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+
+singleGraph
+{
+    start   (0 0 -1);
+    end     (0 0  1);
+    fields  (T flux);
+
+    #includeEtc "caseDicts/postProcessing/graphs/sampleDict.cfg"
+
+    setConfig
+    {
+        axis    z;
+    }
+
+    // Must be last entry
+    #includeEtc "caseDicts/postProcessing/graphs/graph.cfg"
+}
+
+// ************************************************************************* //