From 7323fc43cab42f4648c7ab93e78548b827f086f8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Dennis=20Gl=C3=A4ser?= <dennis.glaeser@iws.uni-stuttgart.de>
Date: Fri, 13 Jul 2018 15:24:00 +0200
Subject: [PATCH] [exercise-fractures] add solution
---
exercises/solution/CMakeLists.txt | 1 +
.../exercise-fractures/CMakeLists.txt | 33 +
.../solution/exercise-fractures/README.md | 42 +
.../exercise-fractures/exercise_fractures.cc | 293 ++
.../exercise_fractures.input | 41 +
.../exercise_fractures_a.input | 41 +
.../exercise_fractures_b.input | 41 +
.../exercise_fractures_c.input | 41 +
.../exercise-fractures/fractureproblem.hh | 206 +
.../fracturespatialparams.hh | 201 +
.../exercise-fractures/grids/complex.geo | 83 +
.../exercise-fractures/grids/complex.msh | 4286 +++++++++++++++++
.../exercise-fractures/matrixproblem.hh | 277 ++
.../exercise-fractures/matrixspatialparams.hh | 120 +
14 files changed, 5706 insertions(+)
create mode 100644 exercises/solution/exercise-fractures/CMakeLists.txt
create mode 100644 exercises/solution/exercise-fractures/README.md
create mode 100644 exercises/solution/exercise-fractures/exercise_fractures.cc
create mode 100644 exercises/solution/exercise-fractures/exercise_fractures.input
create mode 100644 exercises/solution/exercise-fractures/exercise_fractures_a.input
create mode 100644 exercises/solution/exercise-fractures/exercise_fractures_b.input
create mode 100644 exercises/solution/exercise-fractures/exercise_fractures_c.input
create mode 100644 exercises/solution/exercise-fractures/fractureproblem.hh
create mode 100644 exercises/solution/exercise-fractures/fracturespatialparams.hh
create mode 100644 exercises/solution/exercise-fractures/grids/complex.geo
create mode 100644 exercises/solution/exercise-fractures/grids/complex.msh
create mode 100644 exercises/solution/exercise-fractures/matrixproblem.hh
create mode 100644 exercises/solution/exercise-fractures/matrixspatialparams.hh
diff --git a/exercises/solution/CMakeLists.txt b/exercises/solution/CMakeLists.txt
index b55b7ace..724d9269 100644
--- a/exercises/solution/CMakeLists.txt
+++ b/exercises/solution/CMakeLists.txt
@@ -1,6 +1,7 @@
add_subdirectory(exercise-basic)
add_subdirectory(exercise-coupling-ff-pm)
add_subdirectory(exercise-fluidsystem)
+add_subdirectory(exercise-fractures)
add_subdirectory(exercise-grids)
add_subdirectory(exercise-mainfile)
add_subdirectory(exercise-properties)
diff --git a/exercises/solution/exercise-fractures/CMakeLists.txt b/exercises/solution/exercise-fractures/CMakeLists.txt
new file mode 100644
index 00000000..c5d1943d
--- /dev/null
+++ b/exercises/solution/exercise-fractures/CMakeLists.txt
@@ -0,0 +1,33 @@
+dune_symlink_to_source_files(FILES "grids" "exercise_fractures.input" "exercise_fractures_a.input" "exercise_fractures_b.input" "exercise_fractures_c.input")
+
+# executable for the exercise
+add_executable(exercise_fractures_solution EXCLUDE_FROM_ALL exercise_fractures.cc)
+
+dune_add_test(NAME exercise_fractures_solution_a
+ CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+ TARGET exercise_fractures_solution
+ COMMAND ./exercise_fractures_solution
+ CMD_ARGS exercise_fractures_a.input)
+
+dune_add_test(NAME exercise_fractures_solution_b
+ CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+ TARGET exercise_fractures_solution
+ COMMAND ./exercise_fractures_solution
+ CMD_ARGS exercise_fractures_b.input)
+
+dune_add_test(NAME exercise_fractures_solution_c
+ CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+ TARGET exercise_fractures_solution
+ COMMAND ./exercise_fractures_solution
+ CMD_ARGS exercise_fractures_c.input)
+
+set(CMAKE_BUILD_TYPE Release)
+
+#install sources
+install(FILES
+exercise_fractures.cc
+matrixproblem.hh
+fractureproblem.hh
+matrixspatialparams.hh
+fracturespatialparams.hh
+DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}/exercises/exercise-fractures)
diff --git a/exercises/solution/exercise-fractures/README.md b/exercises/solution/exercise-fractures/README.md
new file mode 100644
index 00000000..59ca8d77
--- /dev/null
+++ b/exercises/solution/exercise-fractures/README.md
@@ -0,0 +1,42 @@
+# Exercise #5 (DuMuX course)
+
+In this exercise we are going to use the multidomain framework and in particular the facet coupling module, which allows defining coupled problems in which a (d-1)-dimensional domain lives on the element facets of a d-dimensional domain. Here we are going to make use of this in the context of fractured porous media, where the fractures are represented as lower-dimensional entities embedded in a porous matrix. In this framework it is required that the grid resolves the fractures by aligning the matrix element facets with the fracture geometries, for which we are using the open-source mesh generator _Gmsh_ ([see _Gmsh_ documentation](http://gmsh.info/doc/texinfo/gmsh.html)). Note that the Gmsh file format (_.msh_) is currently the only supported file format within the facet coupling module.
+
+## Problem set-up
+
+We consider a domain of 100 x 100 m with a set of ten fractures. Apart from one fracture extending up to the top boundary, all other fractures are immersed, meaning that the fracture tips lie within the domain. Both the grid and the domain are shown in the image below.
+
+
+
+In the initial setup of this exercise, we want to consider buoancy-driven upwards migration of nitrogen (gas) in an initially fully water-saturated medium. We use hydrostatic pressure conditions and a zero nitrogen saturation as initial conditions, and prescribe no-flow boundary conditions on the left and right sides. We furthermore set the initial conditions as Dirichlet values for the upper and lower boundary except for the middle part of the lower boundary ($`y = 0 \wedge x > 25 \wedge x < 75`$), where we set a non-zero nitrogen saturation. Through this segment of the lower boundary, nitrogen can intrude the domain and flow upwards driven by buoancy.
+
+## Preparing the exercise
+
+Navigate to the directory `dumux/tutorial/exercise-fractures` and familiarize yourself with the files necessary for this exercise:
+
+* The __main file__: `exercise_fractures.cc`
+* The __input file__: `exercise_fractures.input`
+* The __problem file__ for the matrix domain: `matrixproblem.hh`
+* The __problem file__ for the fracture domain: `fractureproblem.hh`
+* The __spatial parameters file__ for the matrix domain: `matrixspatialparams.hh`
+* The __spatial parameters file__ for the matrix domain: `fracturespatialparams.hh`
+
+You might want to take a closer look at the __main file__. The extensive comments above the key instructions will help you to understand the program flow of coupled problems and to identify the main differences with respect to an uncoupled _DuMuX_ model.
+
+## Running the program
+
+Head to the build directory, compile the exercise and execute the program by typing
+
+```bash
+cd build-cmake/exercises/exercise-fractures
+make exercise_fractures
+./exercise_fractures exercise_fractures.input
+```
+
+Take a look at the results by opening the files `matrix.pvd` and `fractures.pvd` with _Paraview_. In order to increase the visibility of the fracture solution, you might want to apply the tube filter to it (e.g. with a tube radius of 0.2). You will see how the fractures act as preferential flowpaths in the upwards movement of nitrogen due to their higher permeabilities. Additionally, you will observe high nitrogen saturations in the fracture tips as a result of the fractures acting as capillary traps due to the lower capillary pressures inside them. Consider turning them into capillary barriers, e.g. by setting __SpatialParams.VGAlpha = 1e-5__ in the fracture group in the input file (`exercise_fractures.input`). The nitrogen saturations in the fractures should now be lower than in the surrounding matrix. Do not forget to reset __SpatialParams.VGAlpha = 1e-1__ in the fracture group in the input file.
+
+## Task A: Change the boundary conditions and disable gravity
+
+In order for the influence of the fractures to be more visible in the resulting pressure fields, turn of gravity in the input file and change the boundary conditions in the two sub-problems (i.e. modify the function `boundaryTypesAtPos(...)` in `matrixproblem.hh` and `fractureproblem.hh`). We want to define the boundary conditions such that Neumann no-flow boundaries are used everywhere in the fracture domain and everywhere in the matrix domain except for the lower left and the upper right part of the lateral sides (i.e. $`x = 0 \wedge y < 25`$ and $`x = 100 \wedge y > 75`$).
+
+Additionally, modify the function `dirichletAtPos(...)` in `matrixproblem.hh` such that an overpressure is added and a non-zero saturation is applied on the right Dirichlet segment ($`x = 100 \wedge y > 75`$). For this you can use the private variables `boundaryOverPressure_` and `boundarySaturation_` which are stored in the matrix problem and are read from the input file.
diff --git a/exercises/solution/exercise-fractures/exercise_fractures.cc b/exercises/solution/exercise-fractures/exercise_fractures.cc
new file mode 100644
index 00000000..3021d77e
--- /dev/null
+++ b/exercises/solution/exercise-fractures/exercise_fractures.cc
@@ -0,0 +1,293 @@
+// -*- 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 2 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
+ * \brief Test for the exercise on two-phase flow in fractured porous media.
+ */
+#include <config.h>
+#include <iostream>
+
+#include <dune/common/parallel/mpihelper.hh>
+
+// include the headers of the two sub-problems
+// i.e. the problems for fractures and matrix
+#include "matrixproblem.hh"
+#include "fractureproblem.hh"
+
+#include <dumux/common/properties.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/dumuxmessage.hh>
+#include <dumux/common/timeloop.hh>
+
+#include <dumux/assembly/diffmethod.hh>
+
+#include <dumux/linear/seqsolverbackend.hh>
+#include <dumux/multidomain/newtonsolver.hh>
+#include <dumux/multidomain/fvassembler.hh>
+#include <dumux/multidomain/traits.hh>
+
+#include <dumux/multidomain/facet/gridmanager.hh>
+#include <dumux/multidomain/facet/couplingmapper.hh>
+#include <dumux/multidomain/facet/couplingmanager.hh>
+
+#include <dumux/io/vtkoutputmodule.hh>
+
+// Define some types for this test so that we can set them as properties below and
+// reuse them again in the main function with only one single definition of them here
+using MatrixTypeTag = TTAG(MatrixProblemTypeTag);
+using FractureTypeTag = TTAG(FractureProblemTypeTag);
+using MatrixFVGridGeometry = typename GET_PROP_TYPE(MatrixTypeTag, FVGridGeometry);
+using FractureFVGridGeometry = typename GET_PROP_TYPE(FractureTypeTag, FVGridGeometry);
+using TheMultiDomainTraits = Dumux::MultiDomainTraits<MatrixTypeTag, FractureTypeTag>;
+using TheCouplingMapper = Dumux::FacetCouplingMapper<MatrixFVGridGeometry, FractureFVGridGeometry>;
+using TheCouplingManager = Dumux::FacetCouplingManager<TheMultiDomainTraits, TheCouplingMapper>;
+
+// set the coupling manager property in the sub-problems
+namespace Dumux {
+namespace Properties {
+SET_TYPE_PROP(MatrixProblemTypeTag, CouplingManager, TheCouplingManager);
+SET_TYPE_PROP(FractureProblemTypeTag, CouplingManager, TheCouplingManager);
+} // end namespace Properties
+} // end namespace Dumux
+
+// main program
+int main(int argc, char** argv) try
+{
+ using namespace Dumux;
+
+ // initialize MPI, finalize is done automatically on exit
+ const auto& mpiHelper = Dune::MPIHelper::instance(argc, argv);
+
+ // print dumux start message
+ if (mpiHelper.rank() == 0)
+ DumuxMessage::print(/*firstCall=*/true);
+
+ // initialize parameter tree
+ Parameters::init(argc, argv);
+
+ // We use the grid manager from the facet coupling framework (see alias above main)
+ // This requires the grids used to be passed as template arguments, where
+ // they are assumed to be ordered in descending grid dimension. Thus,
+ // we pass the matrix grid as first and the fracture grid as second argument.
+ using MatrixGrid = typename GET_PROP_TYPE(MatrixTypeTag, Grid);
+ using FractureGrid = typename GET_PROP_TYPE(FractureTypeTag, Grid);
+ using GridManager = Dumux::FacetCouplingGridManager<MatrixGrid, FractureGrid>;
+ GridManager gridManager;
+
+ // try to create a grid (from the grid file in the input file)
+ // Init() creates the grid from the grid file specified in the input file.
+ // This works with a single grid file in which in addition to the matrix
+ // (d-dimensional) elements also the (d-1)-dimensional elements are specified
+ // which are interpreted as the fracture elements. See the .geo file in the
+ // grids folder on how to create such grids using gmsh. Note that currently
+ // only the Gmsh mesh format (.msh) is supported!
+ gridManager.init();
+ gridManager.loadBalance();
+
+ // we compute on the leaf grid views (get them from grid manager)
+ // the grid ids correspond to the order of the grids passed to the manager (see above)
+ static constexpr std::size_t matrixGridId = 0;
+ static constexpr std::size_t fractureGridId = 1;
+ const auto& matrixGridView = gridManager.template grid<matrixGridId>().leafGridView();
+ const auto& fractureGridView = gridManager.template grid<fractureGridId>().leafGridView();
+
+ // create the finite volume grid geometries
+ auto matrixFvGridGeometry = std::make_shared<MatrixFVGridGeometry>(matrixGridView);
+ auto fractureFvGridGeometry = std::make_shared<FractureFVGridGeometry>(fractureGridView);
+ matrixFvGridGeometry->update();
+ fractureFvGridGeometry->update();
+
+ // the problems (boundary/initial conditions etc)
+ using MatrixProblem = typename GET_PROP_TYPE(MatrixTypeTag, Problem);
+ using FractureProblem = typename GET_PROP_TYPE(FractureTypeTag, Problem);
+
+ // pass the model parameter group to the spatial params so that they obtain the right
+ // values from the input file since we use groups for matrix and fracture
+ // We also want to use domain markers in this exercise. For this reason, we also pass
+ // the grid data object from the grid manager to them, so that they have access to the
+ // domain markers that were specified in the grid file.
+ auto matrixGridData = gridManager.getGridData()->template getSubDomainGridData<matrixGridId>();
+ auto matrixSpatialParams = std::make_shared<typename MatrixProblem::SpatialParams>(matrixFvGridGeometry, matrixGridData, "Matrix");
+ auto matrixProblem = std::make_shared<MatrixProblem>(matrixFvGridGeometry, matrixSpatialParams, "Matrix");
+
+ // extract domain height from the matrix problem and pass to fracture problem (needed for right initial pressure distribution)
+ auto fractureGridData = gridManager.getGridData()->template getSubDomainGridData<fractureGridId>();
+ auto fractureSpatialParams = std::make_shared<typename FractureProblem::SpatialParams>(fractureFvGridGeometry, fractureGridData, "Fracture");
+ auto fractureProblem = std::make_shared<FractureProblem>(fractureFvGridGeometry, fractureSpatialParams, "Fracture");
+
+ // the solution vector
+ using SolutionVector = typename TheMultiDomainTraits::SolutionVector;
+ SolutionVector x, xOld;
+
+ // The domain ids within the multi-domain framework.
+ // They do not necessarily have to be the same as the grid ids
+ // in case you have more subdomains involved. We domain ids
+ // correspond to the order of the type tags passed to the multidomain
+ // traits (see definition of the traits class at the beginning of this file)
+ static const auto matrixDomainId = typename TheMultiDomainTraits::template DomainIdx<0>();
+ static const auto fractureDomainId = typename TheMultiDomainTraits::template DomainIdx<1>();
+
+ // resize the solution vector and write initial solution to it
+ x[matrixDomainId].resize(matrixFvGridGeometry->numDofs());
+ x[fractureDomainId].resize(fractureFvGridGeometry->numDofs());
+ matrixProblem->applyInitialSolution(x[matrixDomainId]);
+ fractureProblem->applyInitialSolution(x[fractureDomainId]);
+
+ // instantiate the class holding the coupling maps between the domains
+ // this needs the information on embeddings (connectivity between matrix
+ // and fracture domain). This information is extracted directly from the
+ // grid during file read and can therefore be obtained from the grid manager.
+ const auto embeddings = gridManager.getEmbeddings();
+ auto couplingMapper = std::make_shared<TheCouplingMapper>();
+ couplingMapper->update(*matrixFvGridGeometry, *fractureFvGridGeometry, embeddings);
+
+ // the coupling manager (needs the coupling mapper)
+ auto couplingManager = std::make_shared<TheCouplingManager>();
+ couplingManager->init(matrixProblem, fractureProblem, couplingMapper, x);
+
+ // we have to set coupling manager pointer in sub-problems
+ // they also have to be made accessible in them (see e.g. matrixproblem.hh)
+ matrixProblem->setCouplingManager(couplingManager);
+ fractureProblem->setCouplingManager(couplingManager);
+
+ // the grid variables
+ using MatrixGridVariables = typename GET_PROP_TYPE(MatrixTypeTag, GridVariables);
+ using FractureGridVariables = typename GET_PROP_TYPE(FractureTypeTag, GridVariables);
+ auto matrixGridVariables = std::make_shared<MatrixGridVariables>(matrixProblem, matrixFvGridGeometry);
+ auto fractureGridVariables = std::make_shared<FractureGridVariables>(fractureProblem, fractureFvGridGeometry);
+ matrixGridVariables->init(x[matrixDomainId]);
+ fractureGridVariables->init(x[fractureDomainId]);
+ xOld = x;
+
+ // intialize the vtk output modules
+ VtkOutputModule<MatrixTypeTag> matrixVtkWriter(*matrixProblem, *matrixFvGridGeometry, *matrixGridVariables, x[matrixDomainId], matrixProblem->name());
+ VtkOutputModule<FractureTypeTag> fractureVtkWriter(*fractureProblem, *fractureFvGridGeometry, *fractureGridVariables, x[fractureDomainId], fractureProblem->name());
+
+ // Add model specific output fields
+ using MatrixVtkOutputFields = typename GET_PROP_TYPE(MatrixTypeTag, VtkOutputFields);
+ using FractureVtkOutputFields = typename GET_PROP_TYPE(FractureTypeTag, VtkOutputFields);
+ MatrixVtkOutputFields::init(matrixVtkWriter);
+ FractureVtkOutputFields::init(fractureVtkWriter);
+
+ // add domain markers to output
+ std::vector<int> matrixDomainMarkers(matrixFvGridGeometry->gridView().size(0));
+ for (const auto& element : elements(matrixFvGridGeometry->gridView()))
+ matrixDomainMarkers[matrixFvGridGeometry->elementMapper().index(element)] = matrixProblem->spatialParams().getElementDomainMarker(element);
+ matrixVtkWriter.addField(matrixDomainMarkers, "domainMarker");
+
+ std::vector<int> fractureDomainMarkers(fractureFvGridGeometry->gridView().size(0));
+ for (const auto& element : elements(fractureFvGridGeometry->gridView()))
+ fractureDomainMarkers[fractureFvGridGeometry->elementMapper().index(element)] = fractureProblem->spatialParams().getElementDomainMarker(element);
+ fractureVtkWriter.addField(fractureDomainMarkers, "domainMarker");
+
+ // write out initial solution
+ matrixVtkWriter.write(0.0);
+ fractureVtkWriter.write(0.0);
+
+ // get some time loop parameters
+ const auto tEnd = getParam<double>("TimeLoop.TEnd");
+ const auto maxDt = getParam<double>("TimeLoop.MaxTimeStepSize");
+ auto dt = getParam<double>("TimeLoop.DtInitial");
+
+ // instantiate time loop
+ auto timeLoop = std::make_shared< TimeLoop<double> >(/*startTime*/0.0, dt, tEnd);
+ timeLoop->setMaxTimeStepSize(maxDt);
+
+ // the assembler for the coupled problem
+ using Assembler = MultiDomainFVAssembler<TheMultiDomainTraits, TheCouplingManager, DiffMethod::numeric, /*implicit?*/true>;
+ auto assembler = std::make_shared<Assembler>( std::make_tuple(matrixProblem, fractureProblem),
+ std::make_tuple(matrixFvGridGeometry, fractureFvGridGeometry),
+ std::make_tuple(matrixGridVariables, fractureGridVariables),
+ couplingManager,
+ timeLoop);
+
+ // the linear solver
+ using LinearSolver = ILU0BiCGSTABBackend;
+ auto linearSolver = std::make_shared<LinearSolver>();
+
+ // the non-linear solver
+ using NewtonSolver = Dumux::MultiDomainNewtonSolver<Assembler, LinearSolver, TheCouplingManager>;
+ auto newtonSolver = std::make_shared<NewtonSolver>(assembler, linearSolver, couplingManager);
+
+ // time loop
+ timeLoop->start(); do
+ {
+ // set previous solution for storage evaluations
+ assembler->setPreviousSolution(xOld);
+
+ // solve the non-linear system with time step control
+ newtonSolver->solve(x, *timeLoop);
+
+ // make the new solution the old solution
+ xOld = x;
+ matrixGridVariables->advanceTimeStep();
+ fractureGridVariables->advanceTimeStep();
+
+ // advance to the time loop to the next step
+ timeLoop->advanceTimeStep();
+
+ // write vtk output
+ matrixVtkWriter.write(timeLoop->time());
+ fractureVtkWriter.write(timeLoop->time());
+
+ // report statistics of this time step
+ timeLoop->reportTimeStep();
+
+ // set new dt as suggested by the Newton solver
+ timeLoop->setTimeStepSize(newtonSolver->suggestTimeStepSize(timeLoop->timeStepSize()));
+
+ } while (!timeLoop->finished());
+
+ // output some Newton statistics
+ newtonSolver->report();
+
+ // report time loop statistics
+ timeLoop->finalize();
+
+ // print dumux message to say goodbye
+ if (mpiHelper.rank() == 0)
+ DumuxMessage::print(/*firstCall=*/false);
+
+ return 0;
+
+}
+catch (Dumux::ParameterException &e)
+{
+ std::cerr << std::endl << e << " ---> Abort!" << std::endl;
+ return 1;
+}
+catch (Dune::DGFException & e)
+{
+ std::cerr << "DGF exception thrown (" << e <<
+ "). Most likely, the DGF file name is wrong "
+ "or the DGF file is corrupted, "
+ "e.g. missing hash at end of file or wrong number (dimensions) of entries."
+ << " ---> Abort!" << std::endl;
+ return 2;
+}
+catch (Dune::Exception &e)
+{
+ std::cerr << "Dune reported error: " << e << " ---> Abort!" << std::endl;
+ return 3;
+}
+catch (...)
+{
+ std::cerr << "Unknown exception thrown! ---> Abort!" << std::endl;
+ return 4;
+}
diff --git a/exercises/solution/exercise-fractures/exercise_fractures.input b/exercises/solution/exercise-fractures/exercise_fractures.input
new file mode 100644
index 00000000..9f8ce485
--- /dev/null
+++ b/exercises/solution/exercise-fractures/exercise_fractures.input
@@ -0,0 +1,41 @@
+[TimeLoop]
+TEnd = 30000 # [s]
+DtInitial = 10 # [s]
+MaxTimeStepSize = 2500 # [s]
+
+[Problem]
+EnableGravity = true
+IsExercisePartA = false
+IsExercisePartB = false
+IsExercisePartC = false
+
+[Grid]
+File = ./grids/complex.msh
+DomainMarkers = true # enable domain markers
+
+[Matrix]
+Problem.Name = matrix
+Problem.BoundaryOverPressure = 5e5
+Problem.BoundarySaturation = 0.5
+SpatialParams.Permeability = 1e-12
+SpatialParams.Porosity = 0.1
+SpatialParams.VGAlpha = 1e-3
+SpatialParams.VGN = 3
+SpatialParams.Snr = 0.0
+SpatialParams.Swr = 0.0
+
+[Fracture]
+Problem.Name = fractures
+SpatialParams.Aperture = 1e-1
+SpatialParams.Permeability = 1e-7
+SpatialParams.PermeabilityBarrier = 1e-16
+SpatialParams.Porosity = 0.85
+SpatialParams.PorosityBarrier = 0.05
+SpatialParams.VGAlpha = 1e-1
+SpatialParams.VGAlphaBarrier = 1e-4
+SpatialParams.VGN = 2
+SpatialParams.VGNBarrier = 2.5
+SpatialParams.Snr = 0.0
+SpatialParams.SnrBarrier = 0.0
+SpatialParams.Swr = 0.0
+SpatialParams.SwrBarrier = 0.0
diff --git a/exercises/solution/exercise-fractures/exercise_fractures_a.input b/exercises/solution/exercise-fractures/exercise_fractures_a.input
new file mode 100644
index 00000000..e9294a23
--- /dev/null
+++ b/exercises/solution/exercise-fractures/exercise_fractures_a.input
@@ -0,0 +1,41 @@
+[TimeLoop]
+TEnd = 30000 # [s]
+DtInitial = 10 # [s]
+MaxTimeStepSize = 2500 # [s]
+
+[Problem]
+EnableGravity = false
+IsExercisePartA = true
+IsExercisePartB = false
+IsExercisePartC = false
+
+[Grid]
+File = ./grids/complex.msh
+DomainMarkers = true # enable domain markers
+
+[Matrix]
+Problem.Name = matrix
+Problem.BoundaryOverPressure = 5e5
+Problem.BoundarySaturation = 0.5
+SpatialParams.Permeability = 1e-12
+SpatialParams.Porosity = 0.1
+SpatialParams.VGAlpha = 1e-3
+SpatialParams.VGN = 3
+SpatialParams.Snr = 0.0
+SpatialParams.Swr = 0.0
+
+[Fracture]
+Problem.Name = fractures
+SpatialParams.Aperture = 1e-1
+SpatialParams.Permeability = 1e-7
+SpatialParams.PermeabilityBarrier = 1e-16
+SpatialParams.Porosity = 0.85
+SpatialParams.PorosityBarrier = 0.05
+SpatialParams.VGAlpha = 1e-1
+SpatialParams.VGAlphaBarrier = 1e-4
+SpatialParams.VGN = 2
+SpatialParams.VGNBarrier = 2.5
+SpatialParams.Snr = 0.0
+SpatialParams.SnrBarrier = 0.0
+SpatialParams.Swr = 0.0
+SpatialParams.SwrBarrier = 0.0
diff --git a/exercises/solution/exercise-fractures/exercise_fractures_b.input b/exercises/solution/exercise-fractures/exercise_fractures_b.input
new file mode 100644
index 00000000..3797db3c
--- /dev/null
+++ b/exercises/solution/exercise-fractures/exercise_fractures_b.input
@@ -0,0 +1,41 @@
+[TimeLoop]
+TEnd = 30000 # [s]
+DtInitial = 10 # [s]
+MaxTimeStepSize = 2500 # [s]
+
+[Problem]
+EnableGravity = false
+IsExercisePartA = false
+IsExercisePartB = true
+IsExercisePartC = false
+
+[Grid]
+File = ./grids/complex.msh
+DomainMarkers = true # enable domain markers
+
+[Matrix]
+Problem.Name = matrix
+Problem.BoundaryOverPressure = 5e5
+Problem.BoundarySaturation = 0.5
+SpatialParams.Permeability = 1e-12
+SpatialParams.Porosity = 0.1
+SpatialParams.VGAlpha = 1e-3
+SpatialParams.VGN = 3
+SpatialParams.Snr = 0.0
+SpatialParams.Swr = 0.0
+
+[Fracture]
+Problem.Name = fractures
+SpatialParams.Aperture = 1e-1
+SpatialParams.Permeability = 1e-7
+SpatialParams.PermeabilityBarrier = 1e-16
+SpatialParams.Porosity = 0.85
+SpatialParams.PorosityBarrier = 0.05
+SpatialParams.VGAlpha = 1e-1
+SpatialParams.VGAlphaBarrier = 1e-4
+SpatialParams.VGN = 2
+SpatialParams.VGNBarrier = 2.5
+SpatialParams.Snr = 0.0
+SpatialParams.SnrBarrier = 0.0
+SpatialParams.Swr = 0.0
+SpatialParams.SwrBarrier = 0.0
diff --git a/exercises/solution/exercise-fractures/exercise_fractures_c.input b/exercises/solution/exercise-fractures/exercise_fractures_c.input
new file mode 100644
index 00000000..82dd9dac
--- /dev/null
+++ b/exercises/solution/exercise-fractures/exercise_fractures_c.input
@@ -0,0 +1,41 @@
+[TimeLoop]
+TEnd = 30000 # [s]
+DtInitial = 10 # [s]
+MaxTimeStepSize = 2500 # [s]
+
+[Problem]
+EnableGravity = false
+IsExercisePartA = false
+IsExercisePartB = false
+IsExercisePartC = true
+
+[Grid]
+File = ./grids/complex.msh
+DomainMarkers = true # enable domain markers
+
+[Matrix]
+Problem.Name = matrix
+Problem.BoundaryOverPressure = 5e5
+Problem.BoundarySaturation = 0.5
+SpatialParams.Permeability = 1e-12
+SpatialParams.Porosity = 0.1
+SpatialParams.VGAlpha = 1e-3
+SpatialParams.VGN = 3
+SpatialParams.Snr = 0.0
+SpatialParams.Swr = 0.0
+
+[Fracture]
+Problem.Name = fractures
+SpatialParams.Aperture = 1e-1
+SpatialParams.Permeability = 1e-7
+SpatialParams.PermeabilityBarrier = 1e-16
+SpatialParams.Porosity = 0.85
+SpatialParams.PorosityBarrier = 0.05
+SpatialParams.VGAlpha = 1e-1
+SpatialParams.VGAlphaBarrier = 1e-4
+SpatialParams.VGN = 2
+SpatialParams.VGNBarrier = 2.5
+SpatialParams.Snr = 0.0
+SpatialParams.SnrBarrier = 0.0
+SpatialParams.Swr = 0.0
+SpatialParams.SwrBarrier = 0.0
diff --git a/exercises/solution/exercise-fractures/fractureproblem.hh b/exercises/solution/exercise-fractures/fractureproblem.hh
new file mode 100644
index 00000000..1de40bb0
--- /dev/null
+++ b/exercises/solution/exercise-fractures/fractureproblem.hh
@@ -0,0 +1,206 @@
+// -*- 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 2 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 MultiDomain
+ * \ingroup MultiDomainFacet
+ * \ingroup TwoPTests
+ * \brief The sub-problem for the fracture domain in the exercise on two-phase flow in fractured porous media.
+ */
+#ifndef DUMUX_COURSE_FRACTURESEXERCISE_FRACTURE_PROBLEM_HH
+#define DUMUX_COURSE_FRACTURESEXERCISE_FRACTURE_PROBLEM_HH
+
+// we use alu grid for the discretization of the fracture domain
+// as this grid manager is able to represent network/surface grids
+#include <dune/foamgrid/foamgrid.hh>
+
+// we want to simulate nitrogen gas transport in a water-saturated medium
+#include <dumux/material/fluidsystems/h2on2.hh>
+
+// we use a cell-centered finite volume scheme with tpfa here
+#include <dumux/discretization/cellcentered/tpfa/properties.hh>
+
+// include the base problem and the model we inherit from
+#include <dumux/porousmediumflow/problem.hh>
+#include <dumux/porousmediumflow/2p/model.hh>
+
+// the spatial parameters (permeabilities, material parameters etc.)
+#include "fracturespatialparams.hh"
+
+namespace Dumux {
+// forward declarations
+template<class TypeTag> class FractureSubProblem;
+
+namespace Properties {
+NEW_PROP_TAG(GridData); // forward declaration of property
+
+// create the type tag nodes
+NEW_TYPE_TAG(FractureProblemTypeTag, INHERITS_FROM(CCTpfaModel, TwoP));
+// Set the grid type
+SET_TYPE_PROP(FractureProblemTypeTag, Grid, Dune::FoamGrid<1, 2>);
+// Set the problem type
+SET_TYPE_PROP(FractureProblemTypeTag, Problem, FractureSubProblem<TypeTag>);
+// set the spatial params
+SET_TYPE_PROP(FractureProblemTypeTag,
+ SpatialParams,
+ FractureSpatialParams< typename GET_PROP_TYPE(TypeTag, FVGridGeometry),
+ typename GET_PROP_TYPE(TypeTag, Scalar) >);
+// the fluid system
+SET_TYPE_PROP(FractureProblemTypeTag,
+ FluidSystem,
+ Dumux::FluidSystems::H2ON2<typename GET_PROP_TYPE(TypeTag, Scalar), /*useComplexRelations*/true>);
+} // end namespace Properties
+
+/*!
+ * \ingroup MultiDomain
+ * \ingroup MultiDomainFacet
+ * \ingroup TwoPTests
+ * \brief The sub-problem for the fracture domain in the exercise on two-phase flow in fractured porous media.
+ */
+template<class TypeTag>
+class FractureSubProblem : public PorousMediumFlowProblem<TypeTag>
+{
+ using ParentType = PorousMediumFlowProblem<TypeTag>;
+
+ using BoundaryTypes = typename GET_PROP_TYPE(TypeTag, BoundaryTypes);
+ using CouplingManager = typename GET_PROP_TYPE(TypeTag, CouplingManager);
+ using NumEqVector = typename GET_PROP_TYPE(TypeTag, NumEqVector);
+ using GridVariables = typename GET_PROP_TYPE(TypeTag, GridVariables);
+ using ElementVolumeVariables = typename GridVariables::GridVolumeVariables::LocalView;
+ using PrimaryVariables = typename GridVariables::PrimaryVariables;
+ using Scalar = typename GridVariables::Scalar;
+
+ using FVGridGeometry = typename GridVariables::GridGeometry;
+ using FVElementGeometry = typename FVGridGeometry::LocalView;
+ using SubControlVolume = typename FVGridGeometry::SubControlVolume;
+ using GridView = typename FVGridGeometry::GridView;
+ using Element = typename GridView::template Codim<0>::Entity;
+ using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+ // some indices for convenience
+ using Indices = typename GET_PROP_TYPE(TypeTag, ModelTraits)::Indices;
+ enum
+ {
+ pressureIdx = Indices::pressureIdx,
+ saturationIdx = Indices::saturationIdx
+ };
+
+public:
+ //! The constructor
+ FractureSubProblem(std::shared_ptr<const FVGridGeometry> fvGridGeometry,
+ std::shared_ptr<typename ParentType::SpatialParams> spatialParams,
+ const std::string& paramGroup)
+ : ParentType(fvGridGeometry, spatialParams, paramGroup)
+ , aperture_(getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Aperture"))
+ , isExercisePartA_(getParamFromGroup<bool>(paramGroup, "Problem.IsExercisePartA"))
+ , isExercisePartB_(getParamFromGroup<bool>(paramGroup, "Problem.IsExercisePartB"))
+ , isExercisePartC_(getParamFromGroup<bool>(paramGroup, "Problem.IsExercisePartC"))
+ {
+ // initialize the fluid system, i.e. the tabulation
+ // of water properties. Use the default p/T ranges.
+ using FluidSystem = typename GET_PROP_TYPE(TypeTag, FluidSystem);
+ FluidSystem::init();
+ }
+
+ //! Specifies the type of boundary condition at a given position
+ BoundaryTypes boundaryTypesAtPos(const GlobalPosition& globalPos) const
+ {
+ BoundaryTypes values;
+
+ // We only use no-flow boundary conditions for all immersed fractures
+ // in the domain (fracture tips that do not touch the domain boundary)
+ // Otherwise, we would lose mass leaving across the fracture tips.
+ values.setAllNeumann();
+
+ // However, there is one fracture reaching the top boundary. For that
+ // fracture tip we set Dirichlet Bcs - only in the unmodified state of
+ // the exercise though. In parts a, b & c we consider Neumann here.
+ if (!isExercisePartA_ && !isExercisePartB_ && !isExercisePartC_)
+ if (globalPos[1] > this->fvGridGeometry().bBoxMax()[1] - 1e-6)
+ values.setAllDirichlet();
+
+ return values;
+ }
+
+ //! Evaluate the source term at a given position
+ NumEqVector source(const Element& element,
+ const FVElementGeometry& fvGeometry,
+ const ElementVolumeVariables& elemVolVars,
+ const SubControlVolume& scv) const
+ {
+ // evaluate sources from bulk domain using the function in the coupling manager
+ auto source = couplingManagerPtr_->evalSourcesFromBulk(element, fvGeometry, elemVolVars, scv);
+
+ // these sources are in kg/s, divide by volume and extrusion to have it in kg/s/m³
+ source /= scv.volume()*elemVolVars[scv].extrusionFactor();
+ return source;
+ }
+
+ //! Set the aperture as extrusion factor.
+ Scalar extrusionFactorAtPos(const GlobalPosition& globalPos) const
+ {
+ // We treat the fractures as lower-dimensional in the grid,
+ // but we have to give it the aperture as extrusion factor
+ // such that the dimensions are correct in the end.
+ return aperture_;
+ }
+
+ //! evaluates the Dirichlet boundary condition for a given position
+ PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const
+ { return initialAtPos(globalPos); }
+
+ //! evaluate the initial conditions
+ PrimaryVariables initialAtPos(const GlobalPosition& globalPos) const
+ {
+ // For the grid used here, the height of the domain is equal
+ // to the maximum y-coordinate
+ const auto domainHeight = this->fvGridGeometry().bBoxMax()[1];
+
+ // we assume a constant water density of 1000 for initial conditions!
+ const auto& g = this->gravityAtPos(globalPos);
+ PrimaryVariables values;
+ Scalar densityW = 1000.0;
+ values[pressureIdx] = 1e5 - (domainHeight - globalPos[1])*densityW*g[1];
+ values[saturationIdx] = 0.0;
+ return values;
+ }
+
+ //! returns the temperature in \f$\mathrm{[K]}\f$ in the domain
+ Scalar temperature() const
+ { return 283.15; /*10°*/ }
+
+ //! sets the pointer to the coupling manager.
+ void setCouplingManager(std::shared_ptr<CouplingManager> cm)
+ { couplingManagerPtr_ = cm; }
+
+ //! returns reference to the coupling manager.
+ const CouplingManager& couplingManager() const
+ { return *couplingManagerPtr_; }
+
+private:
+ std::shared_ptr<CouplingManager> couplingManagerPtr_;
+ Scalar aperture_;
+ bool isExercisePartA_;
+ bool isExercisePartB_;
+ bool isExercisePartC_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/exercises/solution/exercise-fractures/fracturespatialparams.hh b/exercises/solution/exercise-fractures/fracturespatialparams.hh
new file mode 100644
index 00000000..e98e8aea
--- /dev/null
+++ b/exercises/solution/exercise-fractures/fracturespatialparams.hh
@@ -0,0 +1,201 @@
+// -*- 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 2 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 MultiDomain
+ * \ingroup MultiDomainFacet
+ * \ingroup TwoPTests
+ * \brief The spatial parameters for the fracture sub-domain in the exercise
+ * on two-phase flow in fractured porous media.
+ */
+#ifndef DUMUX_COURSE_FRACTURESEXERCISE_FRACTURE_SPATIALPARAMS_HH
+#define DUMUX_COURSE_FRACTURESEXERCISE_FRACTURE_SPATIALPARAMS_HH
+
+#include <dumux/io/grid/griddata.hh>
+
+#include <dumux/material/spatialparams/fv.hh>
+#include <dumux/material/fluidmatrixinteractions/2p/regularizedvangenuchten.hh>
+#include <dumux/material/fluidmatrixinteractions/2p/efftoabslaw.hh>
+
+namespace Dumux {
+
+/*!
+ * \ingroup MultiDomain
+ * \ingroup MultiDomainFacet
+ * \ingroup TwoPTests
+ * \brief The spatial params the two-phase facet coupling test
+ */
+template< class FVGridGeometry, class Scalar >
+class FractureSpatialParams
+: public FVSpatialParams< FVGridGeometry, Scalar, FractureSpatialParams<FVGridGeometry, Scalar> >
+{
+ using ThisType = FractureSpatialParams< FVGridGeometry, Scalar >;
+ using ParentType = FVSpatialParams< FVGridGeometry, Scalar, ThisType >;
+
+ using SubControlVolume = typename FVGridGeometry::SubControlVolume;
+ using GridView = typename FVGridGeometry::GridView;
+ using Grid = typename GridView::Grid;
+ using Element = typename GridView::template Codim<0>::Entity;
+ using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+ // use a regularized van-genuchten material law
+ using EffectiveLaw = RegularizedVanGenuchten<Scalar>;
+
+ // we identify those fractures as barriers, that have a domain marker
+ // of 2. This is what is set in the grid file (see grids/complex.geo)
+ static constexpr int barriersDomainMarker = 2;
+
+public:
+ //! export the type used for permeabilities
+ using PermeabilityType = Scalar;
+
+ //! export the material law and parameters used
+ using MaterialLaw = EffToAbsLaw< EffectiveLaw >;
+ using MaterialLawParams = typename MaterialLaw::Params;
+
+ //! the constructor
+ FractureSpatialParams(std::shared_ptr<const FVGridGeometry> fvGridGeometry,
+ std::shared_ptr<const Dumux::GridData<Grid>> gridData,
+ const std::string& paramGroup)
+ : ParentType(fvGridGeometry)
+ , gridDataPtr_(gridData)
+ , isExercisePartA_(getParamFromGroup<bool>(paramGroup, "Problem.IsExercisePartA"))
+ , isExercisePartB_(getParamFromGroup<bool>(paramGroup, "Problem.IsExercisePartB"))
+ , isExercisePartC_(getParamFromGroup<bool>(paramGroup, "Problem.IsExercisePartC"))
+ {
+ porosity_ = getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Porosity");
+ porosityBarrier_ = getParamFromGroup<Scalar>(paramGroup, "SpatialParams.PorosityBarrier");
+ permeability_ = getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Permeability");
+ permeabilityBarrier_ = getParamFromGroup<Scalar>(paramGroup, "SpatialParams.PermeabilityBarrier");
+
+ // set the material law parameters
+ materialLawParams_.setSnr(getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Snr"));
+ materialLawParams_.setSnr(getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Swr"));
+ materialLawParams_.setVgAlpha(getParamFromGroup<Scalar>(paramGroup, "SpatialParams.VGAlpha"));
+ materialLawParams_.setVgn(getParamFromGroup<Scalar>(paramGroup, "SpatialParams.VGN"));
+ materialLawParamsBarrier_.setSnr(getParamFromGroup<Scalar>(paramGroup, "SpatialParams.SnrBarrier"));
+ materialLawParamsBarrier_.setSnr(getParamFromGroup<Scalar>(paramGroup, "SpatialParams.SwrBarrier"));
+ materialLawParamsBarrier_.setVgAlpha(getParamFromGroup<Scalar>(paramGroup, "SpatialParams.VGAlphaBarrier"));
+ materialLawParamsBarrier_.setVgn(getParamFromGroup<Scalar>(paramGroup, "SpatialParams.VGNBarrier"));
+ }
+
+ //! Function for defining the (intrinsic) permeability \f$[m^2]\f$.
+ template< class ElementSolution >
+ PermeabilityType permeability(const Element& element,
+ const SubControlVolume& scv,
+ const ElementSolution& elemSol) const
+ {
+ // in the unmodified state and exercise part a return the non-barrier parameters
+ if (!isExercisePartB_ && !isExercisePartC_)
+ return permeability_;
+
+ // in exercise part b always return the barrier parameters
+ else if (isExercisePartB_)
+ return permeabilityBarrier_;
+
+ // in exercise part 3 return parameters depending on domain marker
+ else
+ {
+ if (getElementDomainMarker(element) == barriersDomainMarker)
+ return permeabilityBarrier_;
+ else
+ return permeability_;
+ }
+ }
+
+ //! Return the porosity
+ template< class ElementSolution >
+ Scalar porosity(const Element& element,
+ const SubControlVolume& scv,
+ const ElementSolution& elemSol) const
+ {
+ // in the unmodified state and exercise part a return the non-barrier parameters
+ if (!isExercisePartB_ && !isExercisePartC_)
+ return porosity_;
+
+ // in exercise part b always return the barrier parameters
+ else if (isExercisePartB_)
+ return porosityBarrier_;
+
+ // in exercise part 3 return parameters depending on domain marker
+ else
+ {
+ if (getElementDomainMarker(element) == barriersDomainMarker)
+ return porosityBarrier_;
+ else
+ return porosity_;
+ }
+ }
+
+ //! Return the material law parameters
+ template< class ElementSolution >
+ const MaterialLawParams& materialLawParams(const Element& element,
+ const SubControlVolume& scv,
+ const ElementSolution& elemSol) const
+ {
+ // in the unmodified state and exercise part a return the non-barrier parameters
+ if (!isExercisePartB_ && !isExercisePartC_)
+ return materialLawParams_;
+
+ // in exercise part b always return the barrier parameters
+ else if (isExercisePartB_)
+ return materialLawParamsBarrier_;
+
+ // in exercise part 3 return parameters depending on domain marker
+ else
+ {
+ if (getElementDomainMarker(element) == barriersDomainMarker)
+ return materialLawParamsBarrier_;
+ else
+ return materialLawParams_;
+ }
+ }
+
+ //! Water is the wetting phase
+ template< class FluidSystem >
+ int wettingPhaseAtPos(const GlobalPosition& globalPos) const
+ {
+ // we set water as the wetting phase here
+ // which is phase0Idx in the H2oN2 fluid system
+ return FluidSystem::phase0Idx;
+ }
+
+ //! returns the domain marker for an element
+ int getElementDomainMarker(const Element& element) const
+ { return gridDataPtr_->getElementDomainMarker(element); }
+
+private:
+ //! pointer to the grid data (contains domain markers)
+ std::shared_ptr<const Dumux::GridData<Grid>> gridDataPtr_;
+
+ bool isExercisePartA_;
+ bool isExercisePartB_;
+ bool isExercisePartC_;
+
+ Scalar porosity_;
+ Scalar porosityBarrier_;
+ PermeabilityType permeability_;
+ PermeabilityType permeabilityBarrier_;
+ MaterialLawParams materialLawParams_;
+ MaterialLawParams materialLawParamsBarrier_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/exercises/solution/exercise-fractures/grids/complex.geo b/exercises/solution/exercise-fractures/grids/complex.geo
new file mode 100644
index 00000000..ec651e1f
--- /dev/null
+++ b/exercises/solution/exercise-fractures/grids/complex.geo
@@ -0,0 +1,83 @@
+// grid size specifications
+lc = 5; // grid size at domain corners
+lcf = 3; // grid size at fracture points
+
+// domain corners
+Point(1) = {0, 0, 0, lc};
+Point(2) = {100, 0, 0, lc};
+Point(3) = {100, 100, 0, lc};
+Point(4) = {0, 100, 0, lc};
+
+// fracture corners
+Point(5) = {5.0000, 41.6000, 0, lcf};
+Point(6) = {22.0000, 06.2400, 0, lcf};
+Point(7) = {5.0000, 27.5000, 0, lcf};
+Point(8) = {25.0000, 13.5000, 0, lcf};
+Point(9) = {15.0000, 63.0000, 0, lcf};
+Point(10) = {45.0000, 09.0000, 0, lcf};
+Point(11) = {15.0000, 91.6700, 0, lcf};
+Point(12) = {40.0000, 50.0000, 0, lcf};
+Point(13) = {65.0000, 83.3300, 0, lcf};
+Point(15) = {70.0000, 23.5000, 0, lcf};
+Point(17) = {60.0000, 38.0000, 0, lcf};
+Point(18) = {85.0000, 26.7500, 0, lcf};
+Point(19) = {35.0000, 97.1400, 0, lcf};
+Point(20) = {80.0000, 71.4300, 0, lcf};
+Point(21) = {75.0000, 95.7400, 0, lcf};
+Point(22) = {95.0000, 81.5500, 0, lcf};
+Point(23) = {15.0000, 83.6300, 0, lcf};
+Point(24) = {40.0000, 97.2700, 0, lcf};
+Point(25) = {15.2174, 20.3478, 0, lcf};
+Point(26) = {18.6341, 85.6127, 0, lcf};
+Point(27) = {37.3260, 95.8111, 0, lcf};
+Point(28) = {66.2058, 79.3111, 0, lcf};
+Point(29) = {81.5036, 28.3234, 0, lcf};
+Point(30) = {84.9723, 16.7625, 0, lcf};
+Point(31) = {60.625, 100.0, 0, lcf};
+
+// domain outline
+Line(1) = {1, 2};
+Line(2) = {2, 3};
+Line(3) = {3, 31};
+Line(4) = {31, 4};
+Line(5) = {4, 1};
+
+// fracture lines
+Line(6) = {5, 25};
+Line(7) = {7, 25};
+Line(8) = {9, 10};
+Line(9) = {11, 26};
+Line(10) = {13, 28};
+Line(11) = {15, 30};
+Line(12) = {17, 29};
+Line(13) = {19, 27};
+Line(14) = {21, 22};
+Line(15) = {23, 26};
+Line(16) = {6, 25};
+Line(17) = {8, 25};
+Line(18) = {12, 26};
+Line(19) = {26, 27};
+Line(20) = {28, 27};
+Line(21) = {24, 27};
+Line(22) = {29, 28};
+Line(23) = {20, 28};
+Line(24) = {29, 30};
+Line(25) = {18, 29};
+Line(26) = {31, 13};
+
+// domain surface
+// Note that all entities that have physical indices
+// appear in the grid file. Thus, we give the surface
+// and all fracture lines physical indices!
+Line Loop(1) = {1, 2, 3, 4, 5};
+Plane Surface(1) = {1};
+Physical Surface(1) = {1};
+
+// make elements conforming to fractures
+Line {6:26} In Surface{1};
+
+// conductive fractures get physical index 1
+Physical Line(1) = {6,7,9,11,12,13,14,15,16,17,18,19,20,21,23,25};
+
+// blocking fractures get physical index 2
+Physical Line(2) = {8,10,22,24,26};
diff --git a/exercises/solution/exercise-fractures/grids/complex.msh b/exercises/solution/exercise-fractures/grids/complex.msh
new file mode 100644
index 00000000..4eb9e0de
--- /dev/null
+++ b/exercises/solution/exercise-fractures/grids/complex.msh
@@ -0,0 +1,4286 @@
+$MeshFormat
+2.2 0 8
+$EndMeshFormat
+$Nodes
+1406
+1 0 0 0
+2 100 0 0
+3 100 100 0
+4 0 100 0
+5 5 41.6 0
+6 22 6.24 0
+7 5 27.5 0
+8 25 13.5 0
+9 15 63 0
+10 45 9 0
+11 15 91.67 0
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+2787 2 2 1 1 500 994 1370
+2788 2 2 1 1 404 1375 1011
+2789 2 2 1 1 787 1216 1055
+2790 2 2 1 1 300 1163 1287
+2791 2 2 1 1 449 1287 1163
+2792 2 2 1 1 495 1225 1254
+2793 2 2 1 1 479 1011 1375
+2794 2 2 1 1 404 1009 1375
+2795 2 2 1 1 432 1002 1282
+2796 2 2 1 1 484 1038 1300
+2797 2 2 1 1 563 1144 1302
+2798 2 2 1 1 577 1356 1212
+2799 2 2 1 1 547 1302 1144
+2800 2 2 1 1 569 849 1135
+2801 2 2 1 1 103 1222 736
+2802 2 2 1 1 475 1125 1258
+2803 2 2 1 1 577 1212 1239
+2804 2 2 1 1 369 1312 1132
+2805 2 2 1 1 220 1089 1273
+2806 2 2 1 1 432 1373 1002
+2807 2 2 1 1 518 977 1379
+2808 2 2 1 1 529 1254 1225
+2809 2 2 1 1 690 1295 1128
+2810 2 2 1 1 246 1070 1344
+2811 2 2 1 1 511 1113 1228
+2812 2 2 1 1 435 1221 1182
+2813 2 2 1 1 473 1042 1133
+2814 2 2 1 1 571 1132 1312
+2815 2 2 1 1 313 1138 1310
+2816 2 2 1 1 452 1012 834
+2817 2 2 1 1 493 1310 1138
+2818 2 2 1 1 470 968 1316
+2819 2 2 1 1 95 1348 1014
+2820 2 2 1 1 286 1299 1178
+2821 2 2 1 1 426 1128 1295
+2822 2 2 1 1 458 1152 1334
+2823 2 2 1 1 473 1043 1042
+2824 2 2 1 1 436 934 1395
+2825 2 2 1 1 522 1347 1312
+2826 2 2 1 1 609 1344 1227
+2827 2 2 1 1 453 1371 1195
+2828 2 2 1 1 222 1119 1256
+2829 2 2 1 1 518 1343 977
+2830 2 2 1 1 522 1271 1347
+2831 2 2 1 1 294 1041 1376
+2832 2 2 1 1 282 1346 1338
+2833 2 2 1 1 571 1312 1347
+2834 2 2 1 1 568 1338 1346
+2835 2 2 1 1 525 1394 1247
+2836 2 2 1 1 194 1347 1271
+2837 2 2 1 1 304 1358 1231
+2838 2 2 1 1 266 1234 1149
+2839 2 2 1 1 519 1231 1358
+2840 2 2 1 1 466 1199 1387
+2841 2 2 1 1 104 866 1222
+2842 2 2 1 1 64 1076 1200
+2843 2 2 1 1 27 1391 1321
+2844 2 2 1 1 427 1399 1245
+2845 2 2 1 1 567 1247 1394
+2846 2 2 1 1 810 1229 1392
+2847 2 2 1 1 187 1400 1214
+2848 2 2 1 1 511 1228 1406
+2849 2 2 1 1 84 619 988
+2850 2 2 1 1 205 1164 1209
+2851 2 2 1 1 173 1055 1216
+2852 2 2 1 1 528 1321 1391
+2853 2 2 1 1 658 1245 1399
+2854 2 2 1 1 522 1270 1271
+2855 2 2 1 1 23 118 122
+2856 2 2 1 1 23 1066 118
+2857 2 2 1 1 23 1259 171
+2858 2 2 1 1 23 174 1036
+2859 2 2 1 1 25 205 1209
+2860 2 2 1 1 25 1270 205
+2861 2 2 1 1 26 195 1237
+2862 2 2 1 1 26 1007 223
+2863 2 2 1 1 27 157 1212
+2864 2 2 1 1 27 1321 207
+2865 2 2 1 1 121 122 1172
+2866 2 2 1 1 170 1111 171
+2867 2 2 1 1 173 1216 174
+2868 2 2 1 1 22 83 988
+2869 2 2 1 1 171 174 23
+2870 2 2 1 1 223 228 26
+2871 2 2 1 1 27 207 157
+$EndElements
diff --git a/exercises/solution/exercise-fractures/matrixproblem.hh b/exercises/solution/exercise-fractures/matrixproblem.hh
new file mode 100644
index 00000000..ec25d70a
--- /dev/null
+++ b/exercises/solution/exercise-fractures/matrixproblem.hh
@@ -0,0 +1,277 @@
+// -*- 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 2 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 MultiDomain
+ * \ingroup MultiDomainFacet
+ * \ingroup TwoPTests
+ * \brief The sub-problem for the matrix domain in the exercise on two-phase flow in fractured porous media.
+ */
+#ifndef DUMUX_COURSE_FRACTURESEXERCISE_MATRIX_PROBLEM_HH
+#define DUMUX_COURSE_FRACTURESEXERCISE_MATRIX_PROBLEM_HH
+
+// we use alu grid for the discretization of the matrix domain
+#include <dune/alugrid/grid.hh>
+
+// we need this in this test in order to define the domain
+// id of the fracture problem (see function interiorBoundaryTypes())
+#include <dune/common/indices.hh>
+
+// we want to simulate nitrogen gas transport in a water-saturated medium
+#include <dumux/material/fluidsystems/h2on2.hh>
+
+// We are using the framework for models that consider coupling
+// across the element facets of the bulk domain. This has some
+// properties defined, which we have to inherit here. In this
+// exercise we want to use a cell-centered finite volume scheme
+// with tpfa.
+#include <dumux/multidomain/facet/cellcentered/tpfa/properties.hh>
+
+// include the base problem and the model we inherit from
+#include <dumux/porousmediumflow/problem.hh>
+#include <dumux/porousmediumflow/2p/model.hh>
+
+// the spatial parameters (permeabilities, material parameters etc.)
+#include "matrixspatialparams.hh"
+
+namespace Dumux {
+
+// forward declaration of the problem class
+template<class TypeTag> class MatrixSubProblem;
+
+namespace Properties {
+NEW_PROP_TAG(GridData); // forward declaration of property
+
+// create the type tag node for the matrix sub-problem
+// We need to put the facet-coupling type tag after the physics-related type tag
+// because it overwrites some of the properties inherited from "TwoP". This is
+// necessary because we need e.g. a modified implementation of darcys law that
+// evaluates the coupling conditions on faces that coincide with the fractures.
+NEW_TYPE_TAG(MatrixProblemTypeTag, INHERITS_FROM(TwoP, CCTpfaFacetCouplingModel));
+// Set the grid type
+SET_TYPE_PROP(MatrixProblemTypeTag, Grid, Dune::ALUGrid<2, 2, Dune::simplex, Dune::conforming>);
+// Set the problem type
+SET_TYPE_PROP(MatrixProblemTypeTag, Problem, MatrixSubProblem<TypeTag>);
+// set the spatial params
+SET_TYPE_PROP(MatrixProblemTypeTag,
+ SpatialParams,
+ MatrixSpatialParams< typename GET_PROP_TYPE(TypeTag, FVGridGeometry),
+ typename GET_PROP_TYPE(TypeTag, Scalar) >);
+// the fluid system
+SET_TYPE_PROP(MatrixProblemTypeTag,
+ FluidSystem,
+ Dumux::FluidSystems::H2ON2<typename GET_PROP_TYPE(TypeTag, Scalar), /*useComplexRelations*/true>);
+} // end namespace Properties
+
+/*!
+ * \ingroup MultiDomain
+ * \ingroup MultiDomainFacet
+ * \ingroup TwoPTests
+ * \brief The sub-problem for the matrix domain in the exercise on two-phase flow in fractured porous media.
+ */
+template<class TypeTag>
+class MatrixSubProblem : public PorousMediumFlowProblem<TypeTag>
+{
+ using ParentType = PorousMediumFlowProblem<TypeTag>;
+
+ using BoundaryTypes = typename GET_PROP_TYPE(TypeTag, BoundaryTypes);
+ using CouplingManager = typename GET_PROP_TYPE(TypeTag, CouplingManager);
+ using NumEqVector = typename GET_PROP_TYPE(TypeTag, NumEqVector);
+ using GridVariables = typename GET_PROP_TYPE(TypeTag, GridVariables);
+ using PrimaryVariables = typename GridVariables::PrimaryVariables;
+ using Scalar = typename GridVariables::Scalar;
+
+ using FVGridGeometry = typename GridVariables::GridGeometry;
+ using FVElementGeometry = typename FVGridGeometry::LocalView;
+ using SubControlVolume = typename FVGridGeometry::SubControlVolume;
+ using SubControlVolumeFace = typename FVGridGeometry::SubControlVolumeFace;
+ using GridView = typename FVGridGeometry::GridView;
+ using Element = typename GridView::template Codim<0>::Entity;
+ using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+ // some indices for convenience
+ using Indices = typename GET_PROP_TYPE(TypeTag, ModelTraits)::Indices;
+ enum
+ {
+ pressureIdx = Indices::pressureIdx,
+ saturationIdx = Indices::saturationIdx
+ };
+
+public:
+ //! The constructor
+ MatrixSubProblem(std::shared_ptr<const FVGridGeometry> fvGridGeometry,
+ std::shared_ptr<typename ParentType::SpatialParams> spatialParams,
+ const std::string& paramGroup = "")
+ : ParentType(fvGridGeometry, spatialParams, paramGroup)
+ , boundaryOverPressure_(getParamFromGroup<Scalar>(paramGroup, "Problem.BoundaryOverPressure"))
+ , boundarySaturation_(getParamFromGroup<Scalar>(paramGroup, "Problem.BoundarySaturation"))
+ , isExercisePartA_(getParamFromGroup<bool>(paramGroup, "Problem.IsExercisePartA"))
+ , isExercisePartB_(getParamFromGroup<bool>(paramGroup, "Problem.IsExercisePartB"))
+ , isExercisePartC_(getParamFromGroup<bool>(paramGroup, "Problem.IsExercisePartC"))
+ {
+ // initialize the fluid system, i.e. the tabulation
+ // of water properties. Use the default p/T ranges.
+ using FluidSystem = typename GET_PROP_TYPE(TypeTag, FluidSystem);
+ FluidSystem::init();
+
+ // there can only be one exercise part active
+ if (isExercisePartA_ + isExercisePartB_ + isExercisePartC_ > 1)
+ DUNE_THROW(Dune::InvalidStateException, "Invalid combination of activated exercise parts");
+ }
+
+ //! Specifies the type of boundary condition at a given position
+ BoundaryTypes boundaryTypesAtPos(const GlobalPosition& globalPos) const
+ {
+ BoundaryTypes values;
+
+ // in the unmodified state, we consider buoancy-driven upwards migration
+ // of nitrogen and set Dirichlet BCs on the top and bottom boundary
+ if (!isExercisePartA_ && !isExercisePartB_ && !isExercisePartC_)
+ {
+ values.setAllNeumann();
+ if (globalPos[1] < 1e-6 || globalPos[1] > this->fvGridGeometry().bBoxMax()[1] - 1e-6)
+ values.setAllDirichlet();
+ }
+ else
+ {
+ // for exercise part a,b & c we use no-flow boundaries everywhere
+ // except for the lower quarter of the left and the upper quarter of the right boundary
+ values.setAllNeumann();
+ if ( (globalPos[0] > this->fvGridGeometry().bBoxMax()[0] - 1e-6 && globalPos[1] > 75.0) ||
+ (globalPos[0] < 1e-6 && globalPos[1] < 25.0) )
+ values.setAllDirichlet();
+ }
+
+ return values;
+ }
+
+ //! Specifies the type of interior boundary condition at a given position
+ BoundaryTypes interiorBoundaryTypes(const Element& element, const SubControlVolumeFace& scvf) const
+ {
+ BoundaryTypes values;
+
+ // Here we set the type of condition to be used on faces that coincide
+ // with a fracture. If Neumann is specified, a flux continuity condition
+ // on the basis of the normal fracture permeability is evaluated. If this
+ // permeability is lower than that of the matrix, this approach is able to
+ // represent the pressure jump across the fracture. If Dirichlet is set,
+ // the pressure jump across the fracture is neglected and the pressure inside
+ // the fracture is directly applied at the interface between fracture and matrix.
+ // This assumption is justified for highly-permeable fractures, but lead to erroneous
+ // results for low-permeable fractures.
+ // Here, we consider "open" fractures for which we cannot define a normal permeability
+ // and for which the pressure jump across the fracture is neglectable. Thus, we set
+ // the interior boundary conditions to Dirichlet.
+ // IMPORTANT: Note that you will never be asked to set any values at the interior boundaries!
+ // This simply chooses a different interface condition!
+ values.setAllDirichlet();
+
+ if (isExercisePartB_)
+ values.setAllNeumann();
+ else if (isExercisePartC_)
+ {
+ // we need to obtain the domain marker of the fracture element that is coupled to this face
+ // therefore we first get the fracture problem from the coupling manager. For this test, we
+ // know that the fracture domain id is 1 (see main file)
+ static constexpr std::size_t fractureDomainId = 1;
+ const auto& fractureProblem = couplingManager().template problem<fractureDomainId>();
+
+ // use helper function in coupling manager to obtain the element this face couples to
+ const auto fractureElement = couplingManager().getLowDimElement(element, scvf);
+
+ // obtain marker from the spatial params of the fracture problem
+ const auto fractureElementMarker = fractureProblem.spatialParams().getElementDomainMarker(fractureElement);
+
+ // now define Neumann coupling on those elements that are defined as blocking
+ // fractures, i.e. marker == 2, see .geo file in grids folder
+ if (fractureElementMarker == 2)
+ values.setAllNeumann();
+ }
+
+ return values;
+ }
+
+ //! evaluates the Dirichlet boundary condition for a given position
+ PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const
+ {
+ // initialize values with the initial conditions
+ auto values = initialAtPos(globalPos);
+
+ // In the unmodified state of the exercise nitrogen is in contact
+ // with the domain on the center half of the lower boundary
+ if (!isExercisePartA_ && !isExercisePartB_ && !isExercisePartC_)
+ {
+ if (globalPos[1] < 1e-6 && globalPos[0] > 25.0 && globalPos[0] < 75.0)
+ values[saturationIdx] = boundarySaturation_;
+ }
+ // exercise parts a, b & c
+ else
+ {
+ // apply overpressure on the right Dirichlet boundary segment
+ if (globalPos[0] > this->fvGridGeometry().bBoxMax()[0] - 1e-6)
+ {
+ values[pressureIdx] += boundaryOverPressure_;
+ values[saturationIdx] = boundarySaturation_;
+ }
+ }
+
+ return values;
+ }
+
+ //! evaluate the initial conditions
+ PrimaryVariables initialAtPos(const GlobalPosition& globalPos) const
+ {
+ // For the grid used here, the height of the domain is equal
+ // to the maximum y-coordinate
+ const auto domainHeight = this->fvGridGeometry().bBoxMax()[1];
+
+ // we assume a constant water density of 1000 for initial conditions!
+ const auto& g = this->gravityAtPos(globalPos);
+ PrimaryVariables values;
+ Scalar densityW = 1000.0;
+ values[pressureIdx] = 1e5 - (domainHeight - globalPos[1])*densityW*g[1];
+ values[saturationIdx] = 0.0;
+ return values;
+ }
+
+ //! returns the temperature in \f$\mathrm{[K]}\f$ in the domain
+ Scalar temperature() const
+ { return 283.15; /*10°*/ }
+
+ //! sets the pointer to the coupling manager.
+ void setCouplingManager(std::shared_ptr<CouplingManager> cm)
+ { couplingManagerPtr_ = cm; }
+
+ //! returns reference to the coupling manager.
+ const CouplingManager& couplingManager() const
+ { return *couplingManagerPtr_; }
+
+private:
+ std::shared_ptr<CouplingManager> couplingManagerPtr_;
+
+ Scalar boundaryOverPressure_;
+ Scalar boundarySaturation_;
+ bool isExercisePartA_;
+ bool isExercisePartB_;
+ bool isExercisePartC_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/exercises/solution/exercise-fractures/matrixspatialparams.hh b/exercises/solution/exercise-fractures/matrixspatialparams.hh
new file mode 100644
index 00000000..4ca8c72e
--- /dev/null
+++ b/exercises/solution/exercise-fractures/matrixspatialparams.hh
@@ -0,0 +1,120 @@
+// -*- 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 2 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 MultiDomain
+ * \ingroup MultiDomainFacet
+ * \ingroup TwoPTests
+ * \brief The spatial parameters for the fracture sub-domain in the exercise
+ * on two-phase flow in fractured porous media.
+ */
+#ifndef DUMUX_COURSE_FRACTURESEXERCISE_MATRIX_SPATIALPARAMS_HH
+#define DUMUX_COURSE_FRACTURESEXERCISE_MATRIX_SPATIALPARAMS_HH
+
+#include <dumux/io/grid/griddata.hh>
+
+#include <dumux/material/spatialparams/fv.hh>
+#include <dumux/material/fluidmatrixinteractions/2p/regularizedvangenuchten.hh>
+#include <dumux/material/fluidmatrixinteractions/2p/efftoabslaw.hh>
+
+namespace Dumux {
+
+/*!
+ * \ingroup MultiDomain
+ * \ingroup MultiDomainFacet
+ * \ingroup TwoPTests
+ * \brief The spatial params the two-phase facet coupling test
+ */
+template< class FVGridGeometry, class Scalar >
+class MatrixSpatialParams
+: public FVSpatialParams< FVGridGeometry, Scalar, MatrixSpatialParams<FVGridGeometry, Scalar> >
+{
+ using ThisType = MatrixSpatialParams< FVGridGeometry, Scalar >;
+ using ParentType = FVSpatialParams< FVGridGeometry, Scalar, ThisType >;
+
+ using GridView = typename FVGridGeometry::GridView;
+ using Grid = typename GridView::Grid;
+ using Element = typename GridView::template Codim<0>::Entity;
+ using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+ // use a regularized van-genuchten material law
+ using EffectiveLaw = RegularizedVanGenuchten<Scalar>;
+
+public:
+ //! export the type used for permeabilities
+ using PermeabilityType = Scalar;
+
+ //! export the material law and parameters used
+ using MaterialLaw = EffToAbsLaw< EffectiveLaw >;
+ using MaterialLawParams = typename MaterialLaw::Params;
+
+ //! the constructor
+ MatrixSpatialParams(std::shared_ptr<const FVGridGeometry> fvGridGeometry,
+ std::shared_ptr<const Dumux::GridData<Grid>> gridData,
+ const std::string& paramGroup)
+ : ParentType(fvGridGeometry)
+ , gridDataPtr_(gridData)
+ {
+ porosity_ = getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Porosity");
+ permeability_ = getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Permeability");
+
+ // set the material law parameters
+ materialLawParams_.setSnr(getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Snr"));
+ materialLawParams_.setSnr(getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Swr"));
+ materialLawParams_.setVgAlpha(getParamFromGroup<Scalar>(paramGroup, "SpatialParams.VGAlpha"));
+ materialLawParams_.setVgn(getParamFromGroup<Scalar>(paramGroup, "SpatialParams.VGN"));
+ }
+
+ //! Function for defining the (intrinsic) permeability \f$[m^2]\f$.
+ PermeabilityType permeabilityAtPos(const GlobalPosition& globalPos) const
+ { return permeability_; }
+
+ //! Return the porosity
+ Scalar porosityAtPos(const GlobalPosition& globalPos) const
+ { return porosity_; }
+
+ //! Return the material law parameters
+ const MaterialLawParams& materialLawParamsAtPos(const GlobalPosition& globalPos) const
+ { return materialLawParams_; }
+
+ //! Water is the wetting phase
+ template< class FluidSystem >
+ int wettingPhaseAtPos(const GlobalPosition& globalPos) const
+ {
+ // we set water as the wetting phase here
+ // which is phase0Idx in the H2oN2 fluid system
+ return FluidSystem::phase0Idx;
+ }
+
+ //! returns the domain marker for an element
+ int getElementDomainMarker(const Element& element) const
+ { return gridDataPtr_->getElementDomainMarker(element); }
+
+private:
+ //! pointer to the grid data (contains domain markers)
+ std::shared_ptr<const Dumux::GridData<Grid>> gridDataPtr_;
+
+ Scalar porosity_;
+ PermeabilityType permeability_;
+ MaterialLawParams materialLawParams_;
+};
+
+} // end namespace Dumux
+
+#endif
--
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