Modify averaged equations by adding pressure correction

This modification implements the following equation

\nabla \cdot \boldsymbol{\bar{u}} = 0 \quad \text{and} \quad  - \mu \Delta \boldsymbol{\bar{u}}  + \phi \nabla \bar{p} = \mathbf{f}_\text{drag}

which can be reformulated as

\nabla \cdot \boldsymbol{\bar{u}} = 0 \quad \text{and} \quad  - \mu \Delta \boldsymbol{\bar{u}}  + \nabla \bar{p} = \mathbf{f}_\text{drag} + (1-\phi) \nabla \bar{p}

Therefore, the additional term `(1-\phi) \nabla \bar{p} is added to the momentum source term.

appl/doftoelementmapper.hh

+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ *   See the file COPYING for full copying permissions.                      *
+ *                                                                           *
+ *   This program 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.                                     *
+ *                                                                           *
+ *   This program 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 this program.  If not, see <http://www.gnu.org/licenses/>.   *
+ *****************************************************************************/
+/*!
+ * \file
+ * \ingroup Mapper
+ * \brief defines a mapper to get for a velocity dof the connected elements.
+ */
+#ifndef DUMUX_FACE_DOF_TO_ELEMENT_INDEX_MAPPER_HH
+#define DUMUX_FACE_DOF_TO_ELEMENT_INDEX_MAPPER_HH
+
+#include <vector>
+#include <array>
+#include <dumux/discretization/localview.hh>
+
+namespace Dumux {
+
+/*!
+ * \ingroup Mapper
+ * \brief defines a mapper to get for a face dof the connected scvs.
+ */
+template<class GridGeometry>
+class DofToEIdxMapper
+{
+    using FVElementGeometry = typename GridGeometry::LocalView;
+    using SubControlVolume = typename FVElementGeometry::SubControlVolume;
+    using IndexType = typename SubControlVolume::Traits::GridIndexType;
+
+public:
+    DofToEIdxMapper()
+    { }
+
+    IndexType neighboringElementIdx(const SubControlVolume& scv) const
+    {
+        const auto& indices = dofToScvIdxMap_[scv.dofIndex()];
+        return (indices[0] == scv.elementIndex()) ? indices[1] : indices[0];
+    }
+
+    void update(const GridGeometry& gg)
+    { update_(gg); }
+
+protected:
+    void update_(const GridGeometry& gg)
+    {
+        std::cout << "gg.numDofs(): " << gg.numDofs() << std::endl;
+        dofToScvIdxMap_.resize(gg.numDofs(), std::array<int,2>({-1,-1}));
+
+        // assign scvs indices to each dof
+        auto fvGeometry = localView(gg);
+        for (const auto& element : elements(gg.gridView()))
+        {
+            fvGeometry.bindElement(element);
+            for (auto&& scv : scvs(fvGeometry))
+            {
+                auto& indices = dofToScvIdxMap_[scv.dofIndex()];
+                auto idx = (indices[0] == -1) ? 0 : 1;
+                indices[idx] = scv.elementIndex();
+            }
+        }
+
+    }
+    std::vector<std::array<int,2>> dofToScvIdxMap_;
+};
+
+} // end namespace Dumux
+
+#endif