diff --git a/src/meshTools/Make/files b/src/meshTools/Make/files
index 13a2ccf684..bc16f3a4eb 100644
--- a/src/meshTools/Make/files
+++ b/src/meshTools/Make/files
@@ -71,6 +71,7 @@ $(crot)/axisAngleRotation.C
 $(crot)/coordinateRotation.C
 $(crot)/cylindricalRotation.C
 $(crot)/identityRotation.C
+$(crot)/specifiedRotation.C
 $(crot)/EulerCoordinateRotation.C
 $(crot)/STARCDCoordinateRotation.C
 
diff --git a/src/meshTools/coordinate/rotation/specifiedRotation.C b/src/meshTools/coordinate/rotation/specifiedRotation.C
new file mode 100644
index 0000000000..06117a99f1
--- /dev/null
+++ b/src/meshTools/coordinate/rotation/specifiedRotation.C
@@ -0,0 +1,104 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2021 OpenCFD Ltd.
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+\*---------------------------------------------------------------------------*/
+
+#include "specifiedRotation.H"
+#include "dictionary.H"
+#include "addToRunTimeSelectionTable.H"
+
+// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
+
+namespace Foam
+{
+namespace coordinateRotations
+{
+
+defineTypeName(specified);
+//FUTURE addToRunTimeSelectionTable(coordinateRotation, specified, dictionary);
+
+}
+}
+
+
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+Foam::coordinateRotations::specified::specified()
+:
+    coordinateRotation(),
+    Rmatrix_(sphericalTensor::I)
+{}
+
+
+Foam::coordinateRotations::specified::specified(const tensor& rot)
+:
+    coordinateRotation(),
+    Rmatrix_(rot)
+{}
+
+
+Foam::coordinateRotations::specified::specified(const dictionary& dict)
+:
+    specified()
+{
+    // Not yet implemented, pending definition
+}
+
+
+// * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * * //
+
+void Foam::coordinateRotations::specified::clear()
+{
+    Rmatrix_ = sphericalTensor::I;
+}
+
+
+Foam::tensor Foam::coordinateRotations::specified::R() const
+{
+    return Rmatrix_;
+}
+
+
+void Foam::coordinateRotations::specified::write(Ostream& os) const
+{
+    os << "specified rotation";
+}
+
+
+void Foam::coordinateRotations::specified::writeEntry
+(
+    const word& keyword,
+    Ostream& os
+) const
+{
+    os.beginBlock(keyword);
+
+    os.writeEntry("type", type());
+
+    os.endBlock();
+}
+
+
+// ************************************************************************* //
diff --git a/src/meshTools/coordinate/rotation/specifiedRotation.H b/src/meshTools/coordinate/rotation/specifiedRotation.H
new file mode 100644
index 0000000000..8c27a65330
--- /dev/null
+++ b/src/meshTools/coordinate/rotation/specifiedRotation.H
@@ -0,0 +1,127 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2021 OpenCFD Ltd.
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+Class
+    Foam::coordinateRotations::specified
+
+Description
+    An user-specified coordinateRotation, primarily to be used internally
+    within coding when the rotation matrix is already known but
+    needs to be wrapped as a coordinateRotation for use in a coordinate
+    system.
+
+Note
+    Currently no runtime selection mechanism, since specifying a
+    rotation matrix via a dictionary can be fragile due to rounding
+    factors and uncertainty if a forward or reverse rotation matrix
+    is intended.
+
+SourceFiles
+    specifiedRotation.C
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef coordinateRotations_specified_H
+#define coordinateRotations_specified_H
+
+#include "coordinateRotation.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+namespace coordinateRotations
+{
+
+/*---------------------------------------------------------------------------*\
+               Class coordinateRotations::specified Declaration
+\*---------------------------------------------------------------------------*/
+
+class specified
+:
+    public coordinateRotation
+{
+    // Private Data
+
+        //- The rotation matrix
+        tensor Rmatrix_;
+
+
+public:
+
+    //- Runtime type information
+    TypeNameNoDebug("specified");
+
+
+    // Constructors
+
+        //- Default construct - an identity matrix
+        specified();
+
+        //- Construct from transformation matrix
+        explicit specified(const tensor& rot);
+
+        //- Construct from dictionary
+        explicit specified(const dictionary& unused);
+
+        //- Return clone
+        autoPtr<coordinateRotation> clone() const
+        {
+            return
+                autoPtr<coordinateRotation>::NewFrom
+                <coordinateRotations::specified>(*this);
+        }
+
+
+    //- Destructor
+    virtual ~specified() = default;
+
+
+    // Member Functions
+
+        //- Reset specification
+        virtual void clear();
+
+        //- Return the rotation tensor
+        virtual tensor R() const;
+
+        //- Write information
+        virtual void write(Ostream& os) const;
+
+        //- Write dictionary entry
+        virtual void writeEntry(const word& keyword, Ostream& os) const;
+};
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace coordinateRotations
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //
diff --git a/src/meshTools/coordinate/systems/cartesianCS.C b/src/meshTools/coordinate/systems/cartesianCS.C
index 3e7a74e3cb..46574df247 100644
--- a/src/meshTools/coordinate/systems/cartesianCS.C
+++ b/src/meshTools/coordinate/systems/cartesianCS.C
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2014 OpenFOAM Foundation
-    Copyright (C) 2018-2019 OpenCFD Ltd.
+    Copyright (C) 2018-2021 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -70,6 +70,12 @@ Foam::coordSystem::cartesian::cartesian(autoPtr<coordinateSystem>&& csys)
 {}
 
 
+Foam::coordSystem::cartesian::cartesian(const coordinateRotation& crot)
+:
+    coordinateSystem(crot)
+{}
+
+
 Foam::coordSystem::cartesian::cartesian
 (
     const point& origin,
diff --git a/src/meshTools/coordinate/systems/cartesianCS.H b/src/meshTools/coordinate/systems/cartesianCS.H
index 2837da76e5..2b326e5909 100644
--- a/src/meshTools/coordinate/systems/cartesianCS.H
+++ b/src/meshTools/coordinate/systems/cartesianCS.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2013 OpenFOAM Foundation
-    Copyright (C) 2018-2019 OpenCFD Ltd.
+    Copyright (C) 2018-2021 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -75,7 +75,7 @@ public:
 
     // Constructors
 
-        //- Construct null. This is an identity coordinateSystem.
+        //- Default construct. This is an identity coordinate system
         cartesian();
 
         //- Copy construct
@@ -93,6 +93,12 @@ public:
         //- Move construct from autoPtr of another coordinateSystem type
         explicit cartesian(autoPtr<coordinateSystem>&& csys);
 
+        //- Copy construct from rotation with origin=0
+        explicit cartesian(const coordinateRotation& crot);
+
+        //- Move construct from rotation with origin=0
+        explicit cartesian(coordinateRotation&& crot);
+
         //- Construct from origin and rotation
         cartesian(const point& origin, const coordinateRotation& crot);
 
diff --git a/src/meshTools/coordinate/systems/coordinateSystem.H b/src/meshTools/coordinate/systems/coordinateSystem.H
index 9048c7c3c3..21083ceb8f 100644
--- a/src/meshTools/coordinate/systems/coordinateSystem.H
+++ b/src/meshTools/coordinate/systems/coordinateSystem.H
@@ -260,7 +260,7 @@ public:
 
     // Constructors
 
-        //- Construct null. This is an identity coordinateSystem.
+        //- Default construct. This is an identity coordinate system
         coordinateSystem();
 
         //- Copy construct from rotation with origin=0
diff --git a/src/meshTools/coordinate/systems/cylindricalCS.C b/src/meshTools/coordinate/systems/cylindricalCS.C
index 89a766bab2..a4884af3e1 100644
--- a/src/meshTools/coordinate/systems/cylindricalCS.C
+++ b/src/meshTools/coordinate/systems/cylindricalCS.C
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2018-2020 OpenCFD Ltd.
+    Copyright (C) 2018-2021 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -108,6 +108,12 @@ Foam::coordSystem::cylindrical::cylindrical(autoPtr<coordinateSystem>&& csys)
 {}
 
 
+Foam::coordSystem::cylindrical::cylindrical(const coordinateRotation& crot)
+:
+    coordinateSystem(crot)
+{}
+
+
 Foam::coordSystem::cylindrical::cylindrical
 (
     const point& origin,
diff --git a/src/meshTools/coordinate/systems/cylindricalCS.H b/src/meshTools/coordinate/systems/cylindricalCS.H
index b05846ff1d..6441b1ccd2 100644
--- a/src/meshTools/coordinate/systems/cylindricalCS.H
+++ b/src/meshTools/coordinate/systems/cylindricalCS.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2014 OpenFOAM Foundation
-    Copyright (C) 2018 OpenCFD Ltd.
+    Copyright (C) 2018-2021 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -114,7 +114,7 @@ public:
 
     // Constructors
 
-        //- Construct null (identity coordinateSystem)
+        //- Default construct. This is an identity coordinate system
         cylindrical();
 
         //- Copy construct
@@ -132,6 +132,9 @@ public:
         //- Move construct from autoPtr of another coordinateSystem type
         explicit cylindrical(autoPtr<coordinateSystem>&& csys);
 
+        //- Copy construct from rotation with origin=0
+        explicit cylindrical(const coordinateRotation& crot);
+
         //- Construct from origin and rotation
         cylindrical(const point& origin, const coordinateRotation& crot);
 
diff --git a/src/parallel/decompose/decompositionMethods/geomDecomp/geomDecomp.C b/src/parallel/decompose/decompositionMethods/geomDecomp/geomDecomp.C
index 049fc2a494..11aacf9109 100644
--- a/src/parallel/decompose/decompositionMethods/geomDecomp/geomDecomp.C
+++ b/src/parallel/decompose/decompositionMethods/geomDecomp/geomDecomp.C
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2017 OpenFOAM Foundation
-    Copyright (C) 2018 OpenCFD Ltd.
+    Copyright (C) 2018-2021 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -27,36 +27,103 @@ License
 \*---------------------------------------------------------------------------*/
 
 #include "geomDecomp.H"
+#include "specifiedRotation.H"
 
 // * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
 
+void Foam::geomDecomp::setOrder()
+{
+    const word order(coeffsDict_.getOrDefault<word>("order", ""));
+
+    if (order.empty())
+    {
+        return;
+    }
+    else if (order.size() != 3)
+    {
+        FatalIOErrorInFunction(decompDict_)
+            << "Number of characters in order (" << order << ") != 3"
+            << exit(FatalIOError);
+    }
+
+    for (int i = 0; i < 3; ++i)
+    {
+        // Change [x-z] -> [0-2]
+
+        switch (order[i])
+        {
+            case 'x': order_[i] = 0; break;
+            case 'y': order_[i] = 1; break;
+            case 'z': order_[i] = 2; break;
+
+            default:
+                FatalIOErrorInFunction(decompDict_)
+                    << "Illegal decomposition order " << order << nl
+                    << "It should only contain x, y or z"
+                    << exit(FatalError);
+                break;
+        }
+    }
+}
+
+
 void Foam::geomDecomp::readCoeffs()
 {
     coeffsDict_.readIfPresent("delta", delta_);
+
     coeffsDict_.readEntry("n", n_);
 
-    // Verify that the input makes sense
     if (nDomains_ != n_.x()*n_.y()*n_.z())
     {
+        // Verify that the input makes sense
         FatalErrorInFunction
             << "Wrong number of domain divisions in geomDecomp:" << nl
             << "Number of domains    : " << nDomains_ << nl
             << "Wanted decomposition : " << n_
             << exit(FatalError);
     }
+    setOrder();
 
-    const scalar d = 1 - 0.5*delta_*delta_;
-    const scalar d2 = sqr(d);
+    const dictionary* transformDict =
+        coeffsDict_.findDict("transform", keyType::LITERAL);
 
-    const scalar a = delta_;
-    const scalar a2 = sqr(a);
+    if (transformDict)
+    {
+        csys_ = coordinateSystem(*transformDict);
+    }
+    else if (equal(delta_, 0))
+    {
+        csys_.clear();  // Reset to identity
+    }
+    else
+    {
+        const scalar d = 1 - 0.5*delta_*delta_;
+        const scalar d2 = sqr(d);
 
-    rotDelta_ = tensor
-    (
-        d2,         -a*d,         a,
-        a*d - a2*d,  a*a2 + d2,  -2*a*d,
-        a*d2 + a2,   a*d - a2*d,  d2 - a2
-    );
+        const scalar a = delta_;
+        const scalar a2 = sqr(a);
+
+        // Direction (forward/reverse) doesn't matter much
+        tensor rot
+        (
+            d2,         -a*d,         a,
+            a*d - a2*d,  a*a2 + d2,  -2*a*d,
+            a*d2 + a2,   a*d - a2*d,  d2 - a2
+        );
+
+        // origin=0
+        csys_ = coordinateSystem(coordinateRotations::specified(rot));
+    }
+}
+
+// * * * * * * * * * * * * Protected Member Functions  * * * * * * * * * * * //
+
+Foam::tmp<Foam::pointField> Foam::geomDecomp::adjustPoints
+(
+    const pointField& points
+) const
+{
+    return csys_.localPosition(points);
 }
 
 
@@ -90,10 +157,11 @@ Foam::geomDecomp::geomDecomp
 )
 :
     decompositionMethod(decompDict),
-    coeffsDict_(findCoeffsDict(derivedType + "Coeffs", select)),
-    n_(1,1,1),
     delta_(0.001),
-    rotDelta_(I)
+    csys_(),
+    n_(1,1,1),
+    order_(0,1,2),
+    coeffsDict_(findCoeffsDict(derivedType + "Coeffs", select))
 {
     readCoeffs();
 }
@@ -108,10 +176,11 @@ Foam::geomDecomp::geomDecomp
 )
 :
     decompositionMethod(decompDict, regionName),
-    coeffsDict_(findCoeffsDict(derivedType + "Coeffs", select)),
-    n_(1,1,1),
     delta_(0.001),
-    rotDelta_(I)
+    csys_(),
+    n_(1,1,1),
+    order_(0,1,2),
+    coeffsDict_(findCoeffsDict(derivedType + "Coeffs", select))
 {
     readCoeffs();
 }
diff --git a/src/parallel/decompose/decompositionMethods/geomDecomp/geomDecomp.H b/src/parallel/decompose/decompositionMethods/geomDecomp/geomDecomp.H
index 8233d1b883..49661c9614 100644
--- a/src/parallel/decompose/decompositionMethods/geomDecomp/geomDecomp.H
+++ b/src/parallel/decompose/decompositionMethods/geomDecomp/geomDecomp.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011 OpenFOAM Foundation
-    Copyright (C) 2018 OpenCFD Ltd.
+    Copyright (C) 2018-2021 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -32,9 +32,11 @@ Description
 
     Base coefficients:
     \table
-        Property  | Description                 | Required | Default
-        n         | (nx ny nz)                  | yes
-        delta     | delta for rotation matrix   | no | 0.001
+        Property  | Description                             | Required | Default
+        n         | (nx ny nz)                              | yes |
+        order     | order of operation                      | no  | xyz
+        delta     | delta (jitter) for rotation matrix      | no  | 0.001
+        rotation  | coordinate rotation                     | no  |
     \endtable
 
 SourceFiles
@@ -46,7 +48,9 @@ SourceFiles
 #define geomDecomp_H
 
 #include "decompositionMethod.H"
+#include "cartesianCS.H"
 #include "Vector.H"
+#include "tmp.H"
 
 namespace Foam
 {
@@ -59,29 +63,45 @@ class geomDecomp
 :
     public decompositionMethod
 {
+    // Private Data
+
+        //- Small delta (default: 0.001) to avoid staggering when
+        //- mesh itself is aligned with x/y/z
+        scalar delta_;
+
+        //- Local coordinates, or delta rotation tensor
+        coordSystem::cartesian csys_;
+
+
     // Private Member Functions
 
-        //- Read input values and initialize the rotDelta_
+        //- Convert ordering string ("xyz") into list of components.
+        //  Checks for bad entries, but no check for duplicate entries.
+        void setOrder();
+
+        //- Read input values and initialize rotation matrix
         void readCoeffs();
 
 
 protected:
 
-    // Protected data
+    // Protected Data
+
+        //- The divisions
+        Vector<label> n_;
+
+        //- Decomposition order in terms of components (optional)
+        Vector<direction> order_;
 
         //- Coefficients for all derived methods
         const dictionary& coeffsDict_;
 
-        Vector<label> n_;
-
-        //- Default = 0.001
-        scalar delta_;
-
-        tensor rotDelta_;
-
 
     // Protected Member Functions
 
+        //- Apply delta (jitter) or rotation to coordinates
+        tmp<pointField> adjustPoints(const pointField&) const;
+
         //- Check that mesh directions are compatible with decomposition
         void checkDecompositionDirections(const Vector<label>&) const;
 
@@ -120,7 +140,6 @@ public:
 
         //- Decompose with uniform weights on the points
         virtual labelList decompose(const pointField& points) const = 0;
-
 };
 
 
diff --git a/src/parallel/decompose/decompositionMethods/hierarchGeomDecomp/hierarchGeomDecomp.C b/src/parallel/decompose/decompositionMethods/hierarchGeomDecomp/hierarchGeomDecomp.C
index c877fc305b..7bfc8dd6c0 100644
--- a/src/parallel/decompose/decompositionMethods/hierarchGeomDecomp/hierarchGeomDecomp.C
+++ b/src/parallel/decompose/decompositionMethods/hierarchGeomDecomp/hierarchGeomDecomp.C
@@ -47,42 +47,6 @@ namespace Foam
 
 // * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
 
-void Foam::hierarchGeomDecomp::setOrder()
-{
-    const word order(coeffsDict_.getOrDefault<word>("order", ""));
-
-    if (order.empty())
-    {
-        return;
-    }
-    else if (order.size() != 3)
-    {
-        FatalIOErrorInFunction(decompDict_)
-            << "Number of characters in order (" << order << ") != 3"
-            << exit(FatalIOError);
-    }
-
-    for (int i = 0; i < 3; ++i)
-    {
-        // Change [x-z] -> [0-2]
-
-        switch (order[i])
-        {
-            case 'x': order_[i] = 0; break;
-            case 'y': order_[i] = 1; break;
-            case 'z': order_[i] = 2; break;
-
-            default:
-                FatalIOErrorInFunction(decompDict_)
-                    << "Illegal decomposition order " << order << nl
-                    << "It should only contain x, y or z"
-                    << exit(FatalError);
-                break;
-        }
-    }
-}
-
-
 Foam::label Foam::hierarchGeomDecomp::findLower
 (
     const UList<scalar>& list,
@@ -363,7 +327,7 @@ Foam::label Foam::hierarchGeomDecomp::sortComponent
     (
         (
             sortedCoord.size()
-          ? sortedCoord[0]
+          ? sortedCoord.first()
           : GREAT
         ),
         minOp<scalar>()
@@ -567,7 +531,7 @@ Foam::label Foam::hierarchGeomDecomp::sortComponent
     (
         (
             sortedCoord.size()
-          ? sortedCoord[0]
+          ? sortedCoord.first()
           : GREAT
         ),
         minOp<scalar>()
@@ -716,11 +680,8 @@ Foam::hierarchGeomDecomp::hierarchGeomDecomp
     const word& regionName
 )
 :
-    geomDecomp(typeName, decompDict, regionName),
-    order_({0,1,2})
-{
-    setOrder();
-}
+    geomDecomp(typeName, decompDict, regionName)
+{}
 
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
@@ -736,7 +697,7 @@ Foam::labelList Foam::hierarchGeomDecomp::decompose
     // Start off with every point sorted onto itself.
     labelList slice(identity(points.size()));
 
-    pointField rotatedPoints(rotDelta_ & points);
+    const pointField rotatedPoints(adjustPoints(points));
 
     // Calculate tolerance of cell distribution. For large cases finding
     // distribution to the cell exact would cause too many iterations so allow
@@ -778,7 +739,7 @@ Foam::labelList Foam::hierarchGeomDecomp::decompose
     // Start off with every point sorted onto itself.
     labelList slice(identity(points.size()));
 
-    pointField rotatedPoints(rotDelta_ & points);
+    const pointField rotatedPoints(adjustPoints(points));
 
     // Calculate tolerance of cell distribution. For large cases finding
     // distribution to the cell exact would cause too many iterations so allow
diff --git a/src/parallel/decompose/decompositionMethods/hierarchGeomDecomp/hierarchGeomDecomp.H b/src/parallel/decompose/decompositionMethods/hierarchGeomDecomp/hierarchGeomDecomp.H
index a9bf541495..479585d022 100644
--- a/src/parallel/decompose/decompositionMethods/hierarchGeomDecomp/hierarchGeomDecomp.H
+++ b/src/parallel/decompose/decompositionMethods/hierarchGeomDecomp/hierarchGeomDecomp.H
@@ -52,8 +52,9 @@ Description
     \table
         Property  | Description                             | Required | Default
         n         | (nx ny nz)                              | yes |
-        delta     | delta for rotation matrix               | no  | 0.001
         order     | order of operation                      | no  | xyz
+        delta     | delta (jitter) for rotation matrix      | no  | 0.001
+        transform | cartesian coordinate transformation     | no  |
     \endtable
 
 SourceFiles
@@ -65,8 +66,6 @@ SourceFiles
 #define hierarchGeomDecomp_H
 
 #include "geomDecomp.H"
-#include "FixedList.H"
-#include "direction.H"
 
 namespace Foam
 {
@@ -79,18 +78,8 @@ class hierarchGeomDecomp
 :
     public geomDecomp
 {
-    // Private Data
-
-        //- Decomposition order in terms of components.
-        FixedList<direction, 3> order_;
-
-
     // Private Member Functions
 
-        //- Convert ordering string ("xyz") into list of components.
-        //  Checks for bad entries, but no check for duplicate entries.
-        void setOrder();
-
         //- Find index of value in list between
         //- first (inclusive) and last (exclusive)
         static label findLower
@@ -172,15 +161,14 @@ class hierarchGeomDecomp
         ) const;
 
 
-        //- No copy construct
-        hierarchGeomDecomp(const hierarchGeomDecomp&) = delete;
-
-        //- No copy assignment
-        void operator=(const hierarchGeomDecomp&) = delete;
-
-
 public:
 
+    //- No copy construct
+    hierarchGeomDecomp(const hierarchGeomDecomp&) = delete;
+
+    //- No copy assignment
+    void operator=(const hierarchGeomDecomp&) = delete;
+
     //- Runtime type information
     TypeName("hierarchical");
 
@@ -255,7 +243,7 @@ public:
         //  - the connections are across coupled patches
         virtual labelList decompose
         (
-            const labelListList& globalCellCells,
+            const labelListList& globalCellCells,  // unused
             const pointField& cc,
             const scalarField& cWeights
         ) const
@@ -265,7 +253,7 @@ public:
 
         virtual labelList decompose
         (
-            const labelListList& globalCellCells,
+            const labelListList& globalCellCells,  // unused
             const pointField& cc
         ) const
         {
diff --git a/src/parallel/decompose/decompositionMethods/simpleGeomDecomp/simpleGeomDecomp.C b/src/parallel/decompose/decompositionMethods/simpleGeomDecomp/simpleGeomDecomp.C
index cf11ee0896..7389d7f1df 100644
--- a/src/parallel/decompose/decompositionMethods/simpleGeomDecomp/simpleGeomDecomp.C
+++ b/src/parallel/decompose/decompositionMethods/simpleGeomDecomp/simpleGeomDecomp.C
@@ -28,7 +28,6 @@ License
 
 #include "simpleGeomDecomp.H"
 #include "addToRunTimeSelectionTable.H"
-#include "SortableList.H"
 #include "globalIndex.H"
 #include "SubField.H"
 
@@ -174,7 +173,7 @@ Foam::labelList Foam::simpleGeomDecomp::decomposeOneProc
 
     labelList pointIndices(identity(points.size()));
 
-    const pointField rotatedPoints(rotDelta_ & points);
+    const pointField rotatedPoints(adjustPoints(points));
 
     vectorLessOp sorter(rotatedPoints);
 
@@ -239,7 +238,7 @@ Foam::labelList Foam::simpleGeomDecomp::decomposeOneProc
 
     labelList pointIndices(identity(points.size()));
 
-    const pointField rotatedPoints(rotDelta_ & points);
+    const pointField rotatedPoints(adjustPoints(points));
 
     vectorLessOp sorter(rotatedPoints);
 
@@ -350,11 +349,11 @@ Foam::labelList Foam::simpleGeomDecomp::decompose
             SubField<point>(allPoints, points.size()) = points;
             nTotalPoints += points.size();
 
-            // Add slaves
-            for (const int slave : Pstream::subProcs())
+            // Add received
+            for (const int subproci : Pstream::subProcs())
             {
-                IPstream fromSlave(Pstream::commsTypes::scheduled, slave);
-                pointField nbrPoints(fromSlave);
+                IPstream fromProc(Pstream::commsTypes::scheduled, subproci);
+                pointField nbrPoints(fromProc);
                 SubField<point>
                 (
                     allPoints,
@@ -368,14 +367,14 @@ Foam::labelList Foam::simpleGeomDecomp::decompose
             labelList finalDecomp(decomposeOneProc(allPoints));
 
             // Send back
-            for (const int slave : Pstream::subProcs())
+            for (const int subproci : Pstream::subProcs())
             {
-                OPstream toSlave(Pstream::commsTypes::scheduled, slave);
-                toSlave << SubField<label>
+                OPstream toProc(Pstream::commsTypes::scheduled, subproci);
+                toProc << SubField<label>
                 (
                     finalDecomp,
-                    globalNumbers.localSize(slave),
-                    globalNumbers.offset(slave)
+                    globalNumbers.localSize(subproci),
+                    globalNumbers.offset(subproci)
                 );
             }
             // Get my own part
@@ -435,12 +434,12 @@ Foam::labelList Foam::simpleGeomDecomp::decompose
             SubField<scalar>(allWeights, points.size()) = weights;
             nTotalPoints += points.size();
 
-            // Add slaves
-            for (const int slave : Pstream::subProcs())
+            // Add received
+            for (const int subproci : Pstream::subProcs())
             {
-                IPstream fromSlave(Pstream::commsTypes::scheduled, slave);
-                pointField nbrPoints(fromSlave);
-                scalarField nbrWeights(fromSlave);
+                IPstream fromProc(Pstream::commsTypes::scheduled, subproci);
+                pointField nbrPoints(fromProc);
+                scalarField nbrWeights(fromProc);
                 SubField<point>
                 (
                     allPoints,
@@ -460,14 +459,14 @@ Foam::labelList Foam::simpleGeomDecomp::decompose
             labelList finalDecomp(decomposeOneProc(allPoints, allWeights));
 
             // Send back
-            for (const int slave : Pstream::subProcs())
+            for (const int subproci : Pstream::subProcs())
             {
-                OPstream toSlave(Pstream::commsTypes::scheduled, slave);
-                toSlave << SubField<label>
+                OPstream toProc(Pstream::commsTypes::scheduled, subproci);
+                toProc << SubField<label>
                 (
                     finalDecomp,
-                    globalNumbers.localSize(slave),
-                    globalNumbers.offset(slave)
+                    globalNumbers.localSize(subproci),
+                    globalNumbers.offset(subproci)
                 );
             }
             // Get my own part
diff --git a/src/parallel/decompose/decompositionMethods/simpleGeomDecomp/simpleGeomDecomp.H b/src/parallel/decompose/decompositionMethods/simpleGeomDecomp/simpleGeomDecomp.H
index 9781f43d26..3e9bd76ab5 100644
--- a/src/parallel/decompose/decompositionMethods/simpleGeomDecomp/simpleGeomDecomp.H
+++ b/src/parallel/decompose/decompositionMethods/simpleGeomDecomp/simpleGeomDecomp.H
@@ -32,9 +32,11 @@ Description
 
     Method coefficients:
     \table
-        Property  | Description                 | Required | Default
-        n         | (nx ny nz)                  | yes
-        delta     | delta for rotation matrix   | no | 0.001
+        Property  | Description                             | Required | Default
+        n         | (nx ny nz)                              | yes |
+        order     | order of operation (unused)             | no  | xyz
+        delta     | delta (jitter) for rotation matrix      | no  | 0.001
+        transform | cartesian coordinate transformation     | no  |
     \endtable
 
 SourceFiles
@@ -60,7 +62,11 @@ class simpleGeomDecomp
 {
     // Private Member Functions
 
-        static void assignToProcessorGroup(labelList&, const label);
+        static void assignToProcessorGroup
+        (
+            labelList& processorGroup,
+            const label nProcGroup
+        );
 
         static void assignToProcessorGroup
         (
@@ -80,15 +86,14 @@ class simpleGeomDecomp
         ) const;
 
 
-        //- No copy construct
-        void operator=(const simpleGeomDecomp&) = delete;
-
-        //- No copy assignment
-        simpleGeomDecomp(const simpleGeomDecomp&) = delete;
-
-
 public:
 
+    //- No copy construct
+    void operator=(const simpleGeomDecomp&) = delete;
+
+    //- No copy assignment
+    simpleGeomDecomp(const simpleGeomDecomp&) = delete;
+
     //- Runtime type information
     TypeName("simple");
 
@@ -151,7 +156,7 @@ public:
         //- Explicitly provided connectivity
         virtual labelList decompose
         (
-            const labelListList& globalCellCells,
+            const labelListList& globalCellCells,  // unused
             const pointField& cc,
             const scalarField& cWeights
         ) const
diff --git a/tutorials/compressible/rhoPimpleFoam/RAS/angledDuct/system/decomposeParDict.example b/tutorials/compressible/rhoPimpleFoam/RAS/angledDuct/system/decomposeParDict.example
new file mode 100644
index 0000000000..7a96eec042
--- /dev/null
+++ b/tutorials/compressible/rhoPimpleFoam/RAS/angledDuct/system/decomposeParDict.example
@@ -0,0 +1,43 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v2106                                 |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    location    "system";
+    object      decomposeParDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+numberOfSubdomains 8;
+
+method      simple;
+
+coeffs
+{
+    n       ( 2 2 2 );
+
+    // Optional coordinate transformation for sorting
+    transform
+    {
+        origin      (-0.15 0.15 0);
+        rotation
+        {
+            type    axisAngle;
+            axis    (0 0 1);
+            angle   44.5;
+
+            // Or disabled
+            //type    none;
+        }
+    }
+}
+
+
+// ************************************************************************* //