CONT: Addition of compressibleIsoInterFOam and PLIC

1) Implementation of the compressibleIsoInterFOam solver
   2) Implementation of a new PLIC interpolation scheme.
   3) New tutorials associated with the solvers

This implementation was carried out by Henning Scheufler (DLR) and Johan
Roenby (DHI), following :

\verbatim

Henning Scheufler, Johan Roenby,
Accurate and efficient surface reconstruction from volume fraction data
on general meshes, Journal of Computational Physics, 2019, doi
10.1016/j.jcp.2019.01.009

\endverbatim

The integration of the code was carried out by Andy Heather and Sergio
Ferraris from OpenCFD Ltd.

applications/utilities/preProcessing/setAlphaField/alphaFieldFunctions/implicitFunctions/composedFunction/composedFunctionImplicitFunction.C

@@ -0,0 +1,207 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 DLR
+-------------------------------------------------------------------------------
+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 "composedFunctionImplicitFunction.H"
+#include "scalarField.H"
+#include "addToRunTimeSelectionTable.H"
+
+// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
+
+namespace Foam
+{
+    namespace implicitFunctions
+    {
+        defineTypeNameAndDebug(composedFunctionImplicitFunction, 0);
+        addToRunTimeSelectionTable
+        (
+            implicitFunction,
+            composedFunctionImplicitFunction,
+            dict
+        );
+    }
+}
+
+// * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
+
+const Foam::Enum
+<
+    Foam::implicitFunctions::composedFunctionImplicitFunction::modeType
+>
+Foam::implicitFunctions::composedFunctionImplicitFunction::modeTypeNames
+({
+    { modeType::ADD, "add" },
+    { modeType::SUBTRACT, "subtract" },
+    { modeType::MINDIST, "minDist" },
+    { modeType::INTERSECT, "intersect" },
+});
+
+
+Foam::label
+Foam::implicitFunctions::composedFunctionImplicitFunction::selectFunction
+(
+    const scalarField& values
+) const
+{
+    switch (mode_)
+    {
+        case modeType::MINDIST:
+        {
+            scalarField absVal(mag(values));
+            return findMin(absVal);
+        }
+        case modeType::ADD:
+        {
+            return findMax(values);
+        }
+        case modeType::SUBTRACT:
+        {
+            // Note: start at the second entry
+            const label idx = findMin(values, 1);
+
+            if (values[idx] < values[0] && pos(values[0]))
+            {
+                return idx;
+            }
+            else
+            {
+                return 0;
+            }
+        }
+        case modeType::INTERSECT:
+        {
+            return findMin(values);
+        }
+        default:
+        {
+            FatalErrorInFunction
+                << "This mode is not supported  only " << nl
+                << "Supported modes are: " << nl
+                << modeTypeNames
+                << abort(FatalError);
+        }
+    }
+
+    return -1;
+}
+
+
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+Foam::implicitFunctions::composedFunctionImplicitFunction::
+composedFunctionImplicitFunction
+(
+    const dictionary& dict
+)
+:
+    functions_(),
+    mode_(modeTypeNames.get("mode", dict)),
+    values_()
+{
+    const dictionary& funcDict = dict.subDict("composedFunction");
+
+    functions_.resize(funcDict.size());
+    values_.resize(funcDict.size(), Zero);
+
+    label funci = 0;
+
+    for (const entry& dEntry : funcDict)
+    {
+        const word& key = dEntry.keyword();
+
+        if (!dEntry.isDict())
+        {
+            FatalIOErrorInFunction(funcDict)
+                << "Entry " << key << " is not a dictionary" << endl
+                << exit(FatalError);
+        }
+
+        const dictionary& subdict = dEntry.dict();
+
+        functions_.set
+        (
+            funci,
+            implicitFunction::New(subdict.get<word>("type"), subdict)
+        );
+
+        ++funci;
+    }
+}
+
+
+// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
+
+Foam::scalar Foam::implicitFunctions::composedFunctionImplicitFunction::value
+(
+    const vector& p
+) const
+{
+    forAll(values_,i)
+    {
+        values_[i] = functions_[i].value(p);
+    }
+
+    const label idx = selectFunction(values_);
+
+    return values_[idx];
+}
+
+
+Foam::vector Foam::implicitFunctions::composedFunctionImplicitFunction::grad
+(
+    const vector& p
+) const
+{
+    forAll(values_,i)
+    {
+        values_[i] = mag(functions_[i].value(p));
+    }
+
+    const label minIdx = findMin(values_);
+
+    return functions_[minIdx].grad(p);
+}
+
+
+Foam::scalar
+Foam::implicitFunctions::composedFunctionImplicitFunction::distanceToSurfaces
+(
+    const vector& p
+) const
+{
+    forAll(values_,i)
+    {
+        values_[i] = mag(functions_[i].value(p));
+    }
+
+    const label minIdx = findMin(values_);
+
+    return functions_[minIdx].distanceToSurfaces(p);
+}
+
+
+// ************************************************************************* //

applications/utilities/preProcessing/setAlphaField/alphaFieldFunctions/implicitFunctions/composedFunction/composedFunctionImplicitFunction.H

@@ -0,0 +1,169 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 DLR
+-------------------------------------------------------------------------------
+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::implicitFunctions::composedFunctionImplicitFunction
+
+Description
+    Handles multiple implicit functions and offers multiple ways to combine
+    them
+
+Usage
+    Example of function object partial specification:
+    \verbatim
+    function composedFunctionImplicitFunction;
+    mode minDist;
+    // following mode are available:
+    // "add" "subtract" "minDist" "intersect"
+    composedFunctionImplicitFunctions
+    {
+        plane
+        {
+            function plane;
+            origin (0 1. 0);
+            normal (0 1 0);
+        }
+
+        sphere
+        {
+            function sphere;
+            radius 0.4;
+            origin (0.5 1.5 0.5);
+            scale 1;
+        }
+
+        sphere2
+        {
+            function sphere;
+            radius 0.4;
+            origin (0.5 0.5 0.5);
+            scale -1;
+        }
+    }
+    \endverbatim
+
+    Original code supplied by Henning Scheufler, DLR (2019)
+
+SourceFiles
+    composedFunctionImplicitFunction.C
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef implicitFunctions_composedFunctionImplicitFunction_H
+#define implicitFunctions_composedFunctionImplicitFunction_H
+
+#include "implicitFunction.H"
+#include "scalarField.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+namespace implicitFunctions
+{
+
+/*---------------------------------------------------------------------------*\
+              Class composedFunctionImplicitFunction Declaration
+\*---------------------------------------------------------------------------*/
+
+class composedFunctionImplicitFunction
+:
+    public implicitFunction
+{
+    // Private Member Data
+
+        //- Enumeration defining the valid actions
+        enum class modeType
+        {
+            ADD,
+            SUBTRACT,
+            MINDIST,
+            INTERSECT
+        };
+
+        //- The setActions text representations
+        static const Enum<modeType> modeTypeNames;
+
+        //- Stores the functions
+        PtrList<implicitFunction> functions_;
+
+        //- Mode
+        modeType mode_;
+
+        //- Needed for finding the closest function.
+        //  Note: avoid creation every call
+        mutable scalarField values_;
+
+
+    // Private Member Functions
+
+        label selectFunction(const scalarField& values) const;
+
+        //- No copy construct
+        composedFunctionImplicitFunction
+        (
+            const composedFunctionImplicitFunction&
+        ) = delete;
+
+        //- No copy assignment
+        void operator=(const composedFunctionImplicitFunction&) = delete;
+
+
+public:
+
+    //- Runtime type information
+    TypeName("composedFunction");
+
+
+    // Constructors
+
+        //- Construct from dictionary
+        explicit composedFunctionImplicitFunction(const dictionary& dict);
+
+
+    //- Destructor
+    virtual ~composedFunctionImplicitFunction() = default;
+
+
+    // Member Functions
+
+        virtual scalar value(const vector& p) const;
+
+        virtual vector grad(const vector& p) const;
+
+        virtual scalar distanceToSurfaces(const vector& p) const;
+};
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+} // End namespace implicitFunctions
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //

applications/utilities/preProcessing/setAlphaField/alphaFieldFunctions/implicitFunctions/cylinder/cylinderImplicitFunction.C

@@ -0,0 +1,82 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 DLR
+-------------------------------------------------------------------------------
+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 "cylinderImplicitFunction.H"
+#include "addToRunTimeSelectionTable.H"
+
+// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
+
+namespace Foam
+{
+    namespace implicitFunctions
+    {
+        defineTypeNameAndDebug(cylinderImplicitFunction, 0);
+        addToRunTimeSelectionTable
+        (
+            implicitFunction,
+            cylinderImplicitFunction,
+            dict
+        );
+    }
+}
+
+
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+Foam::implicitFunctions::cylinderImplicitFunction::cylinderImplicitFunction
+(
+    const point& origin,
+    const scalar radius,
+    const scalar scale,
+    const vector& direction
+)
+:
+    origin_(origin),
+    radius_(radius),
+    scale_(scale),
+    direction_(normalised(direction)),
+    project_(tensor::I - direction_*direction_) // outer product
+{}
+
+
+Foam::implicitFunctions::cylinderImplicitFunction::cylinderImplicitFunction
+(
+    const dictionary& dict
+)
+:
+    cylinderImplicitFunction
+    (
+        dict.get<point>("origin"),
+        dict.get<scalar>("radius"),
+        dict.getOrDefault<scalar>("scale", 1),
+        dict.get<vector>("direction")
+    )
+{}
+
+
+// ************************************************************************* //

applications/utilities/preProcessing/setAlphaField/alphaFieldFunctions/implicitFunctions/cylinder/cylinderImplicitFunction.H

@@ -0,0 +1,132 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 DLR
+-------------------------------------------------------------------------------
+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::implicitFunctions::cylinderImplicitFunction
+
+Description
+    creates a infintite long cylinderImplicitFunction
+
+    Original code supplied by Henning Scheufler, DLR (2019)
+
+SourceFiles
+    cylinderImplicitFunction.C
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef implicitFunction_cylinderImplicitFunction_H
+#define implicitFunction_cylinderImplicitFunction_H
+
+#include "implicitFunction.H"
+#include "point.H"
+#include "tensor.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+namespace implicitFunctions
+{
+
+/*---------------------------------------------------------------------------*\
+                   Class cylinderImplicitFunction Declaration
+\*---------------------------------------------------------------------------*/
+
+class cylinderImplicitFunction
+:
+    public implicitFunction
+{
+private:
+
+    // Private Data
+
+        //- Origin point
+        const point origin_;
+
+        //- Radius
+        const scalar radius_;
+
+        const scalar scale_;
+
+        const vector direction_;
+
+        const tensor project_;
+
+
+public:
+
+    //- Runtime type information
+    TypeName("cylinder");
+
+
+    // Constructors
+
+        //- Construct from components
+        cylinderImplicitFunction
+        (
+            const point& origin,
+            const scalar radius,
+            const scalar scale,
+            const vector& direction
+        );
+
+        //- Construct from dictionary
+        explicit cylinderImplicitFunction(const dictionary& dict);
+
+
+    //- Destructor
+    virtual ~cylinderImplicitFunction() = default;
+
+
+    // Member Functions
+
+    virtual scalar value(const vector& p) const
+    {
+        return (-mag(project_ & (p - origin_)) + radius_)*scale_;
+    }
+
+    virtual vector grad(const vector& p) const
+    {
+        return -(project_ & (p - origin_))*scale_;
+    }
+
+    virtual scalar distanceToSurfaces(const vector& p) const
+    {
+        return mag(mag(project_ & (p - origin_)) - radius_)*scale_;
+    }
+};
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace implicitFunctions
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //

applications/utilities/preProcessing/setAlphaField/alphaFieldFunctions/implicitFunctions/ellipsoid/ellipsoidImplicitFunction.C

@@ -0,0 +1,73 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 DLR
+-------------------------------------------------------------------------------
+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 "ellipsoidImplicitFunction.H"
+#include "addToRunTimeSelectionTable.H"
+
+// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
+
+namespace Foam
+{
+    namespace implicitFunctions
+    {
+        defineTypeNameAndDebug(ellipsoidImplicitFunction, 0);
+        addToRunTimeSelectionTable
+        (
+            implicitFunction,
+            ellipsoidImplicitFunction,
+            dict
+        );
+    }
+}
+
+
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+Foam::implicitFunctions::ellipsoidImplicitFunction::ellipsoidImplicitFunction
+(
+    const vector& semiAxis
+)
+:
+    semiAxis_(semiAxis),
+    origin_(Zero)
+{}
+
+
+Foam::implicitFunctions::ellipsoidImplicitFunction::ellipsoidImplicitFunction
+(
+    const dictionary& dict
+)
+:
+    ellipsoidImplicitFunction
+    (
+        dict.get<vector>("semiAxis")
+    )
+{}
+
+
+// ************************************************************************* //

applications/utilities/preProcessing/setAlphaField/alphaFieldFunctions/implicitFunctions/ellipsoid/ellipsoidImplicitFunction.H

@@ -0,0 +1,131 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 DLR
+-------------------------------------------------------------------------------
+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::implicitFunctions::ellipsoidImplicitFunction
+
+Description
+    creates an ellipsoidImplicitFunction
+
+    Original code supplied by Henning Scheufler, DLR (2019)
+
+SourceFiles
+    ellipsoidImplicitFunction.C
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef implicitFunction_ellipsoidImplicitFunction_H
+#define implicitFunction_ellipsoidImplicitFunction_H
+
+#include "implicitFunction.H"
+#include "mathematicalConstants.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+namespace implicitFunctions
+{
+
+/*---------------------------------------------------------------------------*\
+                  Class ellipsoidImplicitFunction Declaration
+\*---------------------------------------------------------------------------*/
+
+class ellipsoidImplicitFunction
+:
+    public implicitFunction
+{
+    // Private Member Data
+
+        //- Axis
+        const vector semiAxis_;
+
+        //- Origin point
+        const vector origin_;
+
+
+public:
+
+    //- Runtime type information
+    TypeName("ellipsoidImplicitFunction");
+
+
+    // Constructors
+
+        //- Construct from components
+        explicit ellipsoidImplicitFunction(const vector& semiAxis);
+
+        //- Construct from dictionary
+        explicit ellipsoidImplicitFunction(const dictionary& dict);
+
+
+    //- Destructor
+    virtual ~ellipsoidImplicitFunction() = default;
+
+
+    // Member Functions
+
+    virtual scalar value(const vector& p) const
+    {
+        return
+           -sqrt
+            (
+                sqr((p.x() - origin_.x())/semiAxis_.x())
+              + sqr((p.y() - origin_.y())/semiAxis_.y())
+              + sqr((p.z() - origin_.z())/semiAxis_.z())
+            ) + 1;
+    }
+
+
+    virtual vector grad(const vector& p) const
+    {
+        // normal_ has the length of one
+        return vector
+        (
+            2*(p.x() - origin_.x())/sqr(semiAxis_.x()),
+            2*(p.y() - origin_.y())/sqr(semiAxis_.y()),
+            2*(p.z() - origin_.z())/sqr(semiAxis_.z())
+        );
+    }
+
+    virtual scalar distanceToSurfaces(const vector& p) const
+    {
+        NotImplemented;
+        return GREAT;
+    }
+};
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace implicitFunctions
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //

applications/utilities/preProcessing/setAlphaField/alphaFieldFunctions/implicitFunctions/implicitFunction.C

@@ -0,0 +1,66 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 DLR
+-------------------------------------------------------------------------------
+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 "implicitFunction.H"
+#include "error.H"
+
+// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
+
+namespace Foam
+{
+    defineTypeNameAndDebug(implicitFunction, 0);
+    defineRunTimeSelectionTable(implicitFunction, dict);
+}
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+Foam::autoPtr<Foam::implicitFunction> Foam::implicitFunction::New
+(
+    const word& implicitFunctionType,
+    const dictionary& dict
+)
+{
+    auto cstrIter = dictConstructorTablePtr_->cfind(implicitFunctionType);
+
+    if (!cstrIter.found())
+    {
+        FatalIOErrorInLookup
+        (
+            dict,
+            "implicitFunction",
+            implicitFunctionType,
+            *dictConstructorTablePtr_
+        ) << exit(FatalIOError);
+    }
+
+    return autoPtr<implicitFunction>(cstrIter()(dict));
+}
+
+
+// ************************************************************************* //

applications/utilities/preProcessing/setAlphaField/alphaFieldFunctions/implicitFunctions/implicitFunction.H

@@ -0,0 +1,122 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 DLR
+-------------------------------------------------------------------------------
+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::implicitFunction
+
+Description
+    Base class for implicit functions
+
+    Original code supplied by Henning Scheufler, DLR (2019)
+
+SourceFiles
+    implicitFunction.C
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef implicitFunction_H
+#define implicitFunction_H
+
+#include "autoPtr.H"
+#include "dictionary.H"
+#include "vector.H"
+#include "runTimeSelectionTables.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+/*---------------------------------------------------------------------------*\
+                      Class implicitFunction Declaration
+\*---------------------------------------------------------------------------*/
+
+class implicitFunction
+{
+public:
+
+    //- Runtime type information
+    TypeName("implicitFunction");
+
+    //- Declare run-time constructor selection table
+    declareRunTimeSelectionTable
+    (
+        autoPtr,
+        implicitFunction,
+        dict,
+        (
+            const dictionary& dict
+        ),
+        (dict)
+    );
+
+
+    // Constructors
+
+        //- Default construct
+        implicitFunction() = default;
+
+
+        //- Return a reference to the selected implicitFunction
+        static autoPtr<implicitFunction> New
+        (
+            const word& implicitFunctionType,
+            const dictionary& dict
+        );
+
+
+    //- Destructor
+    virtual ~implicitFunction() = default;
+
+
+    // Member Functions
+
+        virtual scalar value(const vector& p) const
+        {
+            return GREAT;
+        }
+
+        virtual vector grad(const vector& p) const
+        {
+            return vector::max;
+        }
+
+        virtual scalar distanceToSurfaces(const vector& p) const
+        {
+            return GREAT;
+        }
+};
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //

applications/utilities/preProcessing/setAlphaField/alphaFieldFunctions/implicitFunctions/paraboloid/paraboloidImplicitFunction.C

@@ -0,0 +1,73 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019 DLR
+-------------------------------------------------------------------------------
+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 "paraboloidImplicitFunction.H"
+#include "addToRunTimeSelectionTable.H"
+
+// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
+
+namespace Foam
+{
+    namespace implicitFunctions
+    {
+        defineTypeNameAndDebug(paraboloidImplicitFunction, 0);
+        addToRunTimeSelectionTable
+        (
+            implicitFunction,
+            paraboloidImplicitFunction,
+            dict
+        );
+    }
+
+}
+
+
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+Foam::implicitFunctions::paraboloidImplicitFunction::paraboloidImplicitFunction
+(
+    const vector& coeffs
+)
+:
+    coeffs_(coeffs)
+{}
+
+
+Foam::implicitFunctions::paraboloidImplicitFunction::paraboloidImplicitFunction
+(
+    const dictionary& dict
+)
+:
+    paraboloidImplicitFunction
+    (
+        dict.get<vector>("coeffs")
+    )
+{}
+
+
+// ************************************************************************* //

applications/utilities/preProcessing/setAlphaField/alphaFieldFunctions/implicitFunctions/paraboloid/paraboloidImplicitFunction.H

@@ -0,0 +1,120 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 DLR
+-------------------------------------------------------------------------------
+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::implicitFunctions::paraboloidImplicitFunction
+
+Description
+    creates a paraboloid
+
+    Original code supplied by Henning Scheufler, DLR (2019)
+
+SourceFiles
+    paraboloidImplicitFunction.C
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef implicitFunction_paraboloidImplicitFunction_H
+#define implicitFunction_paraboloidImplicitFunction_H
+
+#include "implicitFunction.H"
+#include "mathematicalConstants.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+namespace implicitFunctions
+{
+
+/*---------------------------------------------------------------------------*\
+                 Class paraboloidImplicitFunction Declaration
+\*---------------------------------------------------------------------------*/
+
+class paraboloidImplicitFunction
+:
+    public implicitFunction
+{
+    // Private Data
+
+        //- Coefficients of ax^2 + bx*y + cy^2
+        const vector coeffs_;
+
+
+public:
+
+    //- Runtime type information
+    TypeName("paraboloid");
+
+
+    // Constructors
+
+        //- Construct from components
+        explicit paraboloidImplicitFunction(const vector& coeffs);
+
+        //- Construct from dictionary
+        explicit paraboloidImplicitFunction(const dictionary& dict);
+
+
+    //- Destructor
+    virtual ~paraboloidImplicitFunction() = default;
+
+
+    // Member Functions
+
+        virtual scalar value(const vector& p) const
+        {
+            return
+                coeffs_.x()*sqr(p.x())
+              + coeffs_.y()*p.x()*p.y()
+              + coeffs_.z()*sqr(p.y())
+              - p.z();
+        }
+
+        virtual vector grad(const vector& p) const
+        {
+            NotImplemented;
+            return Zero;
+        }
+
+        virtual scalar distanceToSurfaces(const vector& p) const
+        {
+            NotImplemented;
+            return 0;
+        }
+};
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace implicitFunctions
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //

applications/utilities/preProcessing/setAlphaField/alphaFieldFunctions/implicitFunctions/plane/planeImplicitFunction.C

@@ -0,0 +1,75 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 DLR
+-------------------------------------------------------------------------------
+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 "planeImplicitFunction.H"
+#include "addToRunTimeSelectionTable.H"
+
+// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
+
+namespace Foam
+{
+    namespace implicitFunctions
+    {
+        defineTypeNameAndDebug(planeImplicitFunction, 0);
+        addToRunTimeSelectionTable
+        (
+            implicitFunction,
+            planeImplicitFunction,
+            dict
+        );
+    }
+}
+
+
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+Foam::implicitFunctions::planeImplicitFunction::planeImplicitFunction
+(
+    const vector& origin,
+    const vector& normal
+)
+:
+    origin_(origin),
+    normal_(normalised(normal))
+{}
+
+
+Foam::implicitFunctions::planeImplicitFunction::planeImplicitFunction
+(
+    const dictionary& dict
+)
+:
+    planeImplicitFunction
+    (
+        dict.get<vector>("origin"),
+        dict.get<vector>("normal")
+    )
+{}
+
+
+// ************************************************************************* //

applications/utilities/preProcessing/setAlphaField/alphaFieldFunctions/implicitFunctions/plane/planeImplicitFunction.H

@@ -0,0 +1,120 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 DLR
+-------------------------------------------------------------------------------
+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::implicitFunctions::planeImplicitFunction
+
+Description
+    creates a plane
+
+    Original code supplied by Henning Scheufler, DLR (2019)
+
+SourceFiles
+    planeImplicitFunction.C
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef implicitFunction_planeImplicitFunction_H
+#define implicitFunction_planeImplicitFunction_H
+
+#include "implicitFunction.H"
+#include "mathematicalConstants.H"
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+namespace implicitFunctions
+{
+
+/*---------------------------------------------------------------------------*\
+                    Class planeImplicitFunction Declaration
+\*---------------------------------------------------------------------------*/
+
+class planeImplicitFunction
+:
+    public implicitFunction
+{
+    // Private Data
+
+        //- Reference point
+        const vector origin_;
+
+        //- Unit-normal vector
+        const vector normal_;
+
+
+public:
+
+    //- Runtime type information
+    TypeName("plane");
+
+
+    // Constructors
+
+        //- Construct from components
+        planeImplicitFunction(const vector& origin, const vector& normal);
+
+        //- Construct from dictionary (used by implicitFunctions)
+        explicit planeImplicitFunction(const dictionary& dict);
+
+
+    //- Destructor
+    virtual ~planeImplicitFunction() = default;
+
+
+    // Member Functions
+
+        virtual scalar value(const vector& p) const
+        {
+            return -normal_ & (origin_ - p);
+        }
+
+        virtual vector grad(const vector& p) const
+        {
+            // normal_ has the length of one
+            return normal_;
+        }
+
+        virtual scalar distanceToSurfaces(const vector& p) const
+        {
+            // normal_ has the length of one
+            return mag((p - origin_) & -normal_);
+        }
+};
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace implicitFunctions
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //

applications/utilities/preProcessing/setAlphaField/alphaFieldFunctions/implicitFunctions/sin/sinImplicitFunction.C

@@ -0,0 +1,87 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 DLR
+-------------------------------------------------------------------------------
+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 "sinImplicitFunction.H"
+#include "addToRunTimeSelectionTable.H"
+
+// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
+
+namespace Foam
+{
+    namespace implicitFunctions
+    {
+        defineTypeNameAndDebug(sinImplicitFunction, 0);
+        addToRunTimeSelectionTable
+        (
+            implicitFunction,
+            sinImplicitFunction,
+            dict
+        );
+    }
+}
+
+
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+Foam::implicitFunctions::sinImplicitFunction::sinImplicitFunction
+(
+    const scalar period,
+    const scalar phase,
+    const scalar amplitude,
+    const vector& direction,
+    const vector& up,
+    const vector& origin
+)
+:
+    period_(period),
+    phase_(phase),
+    amplitude_(amplitude),
+    up_(normalised(up)),
+    direction_(normalised(direction)),
+    origin_(origin)
+{}
+
+
+Foam::implicitFunctions::sinImplicitFunction::sinImplicitFunction
+(
+    const dictionary& dict
+)
+:
+    sinImplicitFunction
+    (
+        dict.get<scalar>("period"),
+        dict.getOrDefault<scalar>("phase", 0),
+        dict.get<scalar>("amplitude"),
+        dict.get<vector>("direction"),
+        dict.get<vector>("up"),
+        dict.get<vector>("origin")
+    )
+{}
+
+
+// ************************************************************************* //

applications/utilities/preProcessing/setAlphaField/alphaFieldFunctions/implicitFunctions/sin/sinImplicitFunction.H

@@ -0,0 +1,142 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 DLR
+-------------------------------------------------------------------------------
+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::implicitFunctions::sinImplicitFunction
+
+Description
+
+    Original code supplied by Henning Scheufler, DLR (2019)
+
+SourceFiles
+    sinImplicitFunction.C
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef implicitFunction_sinImplicitFunction_H
+#define implicitFunction_sinImplicitFunction_H
+
+#include "implicitFunction.H"
+#include "mathematicalConstants.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+namespace implicitFunctions
+{
+
+/*---------------------------------------------------------------------------*\
+                     Class sinImplicitFunction Declaration
+\*---------------------------------------------------------------------------*/
+
+class sinImplicitFunction
+:
+    public implicitFunction
+{
+private:
+
+    // Private Data
+
+        //- Origin point
+        const scalar period_;
+
+        //- Radius
+        const scalar phase_;
+
+        const scalar amplitude_;
+
+        const vector up_;
+
+        const vector direction_;
+
+        const vector origin_;
+
+
+public:
+
+    //- Runtime type information
+    TypeName("sin");
+
+
+    // Constructors
+
+        //- Construct from components
+        sinImplicitFunction
+        (
+            const scalar period,
+            const scalar phase,
+            const scalar amplitude,
+            const vector& direction,
+            const vector& up,
+            const vector& origin
+        );
+
+        //- Construct from dictionary (used by implicitFunctions)
+        explicit sinImplicitFunction(const dictionary& dict);
+
+
+    //- Destructor
+    virtual ~sinImplicitFunction() = default;
+
+
+    // Member Functions
+
+        virtual scalar value(const vector& p) const
+        {
+            const scalar x = (p - origin_) & direction_;
+            const scalar z = (p - origin_) & -up_;
+
+            return
+                z
+              - amplitude_
+               *Foam::sin(2*constant::mathematical::pi*x/period_ + phase_);
+        }
+
+        virtual vector grad(const vector& p) const
+        {
+            NotImplemented;
+            return Zero;
+        }
+
+        virtual scalar distanceToSurfaces(const vector& p) const
+        {
+            NotImplemented;
+            return 0;
+        }
+};
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace implicitFunctions
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //

applications/utilities/preProcessing/setAlphaField/alphaFieldFunctions/implicitFunctions/sphere/sphereImplicitFunction.C

@@ -0,0 +1,78 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 DLR
+-------------------------------------------------------------------------------
+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 "sphereImplicitFunction.H"
+#include "addToRunTimeSelectionTable.H"
+
+// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
+
+namespace Foam
+{
+    namespace implicitFunctions
+    {
+        defineTypeNameAndDebug(sphereImplicitFunction, 0);
+        addToRunTimeSelectionTable
+        (
+            implicitFunction,
+            sphereImplicitFunction,
+            dict
+        );
+    }
+}
+
+
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+Foam::implicitFunctions::sphereImplicitFunction::sphereImplicitFunction
+(
+    const point& origin,
+    const scalar radius,
+    const scalar scale
+)
+:
+    origin_(origin),
+    radius_(radius),
+    scale_(scale)
+{}
+
+
+Foam::implicitFunctions::sphereImplicitFunction::sphereImplicitFunction
+(
+    const dictionary& dict
+)
+:
+    sphereImplicitFunction
+    (
+        dict.get<point>("origin"),
+        dict.get<scalar>("radius"),
+        dict.getOrDefault<scalar>("scale", 1)
+    )
+{}
+
+
+// ************************************************************************* //

applications/utilities/preProcessing/setAlphaField/alphaFieldFunctions/implicitFunctions/sphere/sphereImplicitFunction.H

@@ -0,0 +1,124 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 DLR
+-------------------------------------------------------------------------------
+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::implicitFunctions::sphereImplicitFunction
+
+Description
+    Creates a sphere
+
+    Original code supplied by Henning Scheufler, DLR (2019)
+
+SourceFiles
+    sphereImplicitFunction.C
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef implicitFunction_sphereImplicitFunction_H
+#define implicitFunction_sphereImplicitFunction_H
+
+#include "implicitFunction.H"
+#include "point.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+namespace implicitFunctions
+{
+
+/*---------------------------------------------------------------------------*\
+                   Class sphereImplicitFunction Declaration
+\*---------------------------------------------------------------------------*/
+
+class sphereImplicitFunction
+:
+    public implicitFunction
+{
+    // Private Data
+
+        //- Origin point
+        const point origin_;
+
+        //- Radius
+        const scalar radius_;
+
+        const scalar scale_;
+
+
+public:
+
+    //- Runtime type information
+    TypeName("sphere");
+
+
+    // Constructors
+
+        //- Construct from components
+        sphereImplicitFunction
+        (
+            const point&,
+            const scalar radius,
+            const scalar scale
+        );
+
+        //- Construct from dictionary
+        explicit sphereImplicitFunction(const dictionary& dict);
+
+
+    //- Destructor
+    virtual ~sphereImplicitFunction() = default;
+
+
+    // Member Functions
+
+        virtual scalar value(const vector& p) const
+        {
+            return (-mag(p - origin_) + radius_)*scale_;
+        }
+
+        virtual vector grad(const vector& p) const
+        {
+            return (origin_ - p)*scale_;
+        }
+
+        virtual scalar distanceToSurfaces(const vector& p) const
+        {
+            return mag(mag(p - origin_) - radius_)*scale_;
+        }
+};
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace implicitFunctions
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //