Commit e412a164 by Timo Koch

### Merge branch 'feature/improve-examples-doc' into 'master'

feature/improve-tracer-example-doc

See merge request !1897
parents 3be4f521 aec715f0
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 ... ... @@ -8,43 +8,44 @@ This example contains a contaminant transported by a base groundwater flow in a ![](./img/setup.png) ## Model description Two different models are applied to simulate the system: In a first step, the groundwater velocity is evaluated under stationary conditions. Therefore the single phase model is applied. In a second step, the contaminant gets transported based on the groundwater velocity field. It is assumed, that the dissolved contaminant does not affect density and viscosity of the groundwater and thus, it is handled as a tracer by the tracer model. The tracer model is then solved instationarily. Two different models are applied to simulate the system: In a first step, the groundwater velocity is evaluated under stationary conditions using the single phase model. In a second step, the contaminant is transported with the groundwater velocity field. It is assumed, that the dissolved contaminant does not affect density and viscosity of the groundwater, and thus, it is handled as a tracer by the tracer model. The tracer model is then solved instationarily. ### 1p Model The single phase model uses Darcy's law as the equation for the momentum conservation: math \textbf v = - \frac{\textbf K}{\mu} \left(\textbf{grad}\, p - \varrho {\textbf g} \right) \textbf v = - \frac{\textbf K}{\mu} \left(\textbf{grad}\, p - \varrho {\textbf g} \right),  With the darcy velocity $ \textbf v $, the permeability $ \textbf K$, the dynamic viscosity $ \mu$, the pressure $p$, the density $\rho$ and the gravity $\textbf g$. with the darcy velocity $ \textbf v $, the permeability $ \textbf K$, the dynamic viscosity $ \mu$, the pressure $p$, the density $\rho$ and the gravity $\textbf g$. Darcy's law is inserted into the continuity equation: Darcy's law is inserted into the mass balance equation: math \phi \frac{\partial \varrho}{\partial t} + \text{div} \textbf v = 0  with porosity $\phi$. where $\phi$ is the porosity. The equation is discretized using a cell-centered finite volume scheme as spatial discretization for the pressure as primary variable. For details on the discretization scheme, have a look at the dumux [handbook](https://dumux.org/handbook). ### Tracer Model The transport of the contaminant component $\kappa$ is based on the previously evaluated velocity field $\textbf v$ with the help the following mass balance equation: The transport of the contaminant component $\kappa$ is based on the previously evaluated velocity field $\textbf v$ with the help of the following mass balance equation: math \phi \frac{ \partial \varrho X^\kappa}{\partial t} - \text{div} \left\lbrace \varrho X^\kappa {\textbf v} + \varrho D^\kappa_\text{pm} \textbf{grad} X^\kappa \right\rbrace = 0 \phi \frac{ \partial \varrho X^\kappa}{\partial t} - \text{div} \left\lbrace \varrho X^\kappa {\textbf v} + \varrho D^\kappa_\text{pm} \textbf{grad} X^\kappa \right\rbrace = 0,  With the porosity $\phi$, the mass fraction of the contaminant component $\kappa$: $X^\kappa$, the porous medium diffusivity $ D^\kappa_\text{pm} $ and the density of the fluid phase $\varrho$. where $X^\kappa$ is the mass fraction of the contaminant component $\kappa$ and $ D^\kappa_\text{pm} $ is the effective diffusivity. The porous medium diffusivity is a function of the diffusion coefficient of the component $D^\kappa$, the porosity $\phi$ and the porous medium tortuosity $\tau$ by the following equation: The effective diffusivity is a function of the diffusion coefficient of the component $D^\kappa$ and the porosity and tortuosity $\tau$ of the porous medium (see [dumux/material/fluidmatrixinteractions/diffusivityconstanttortuosity.hh](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/-/blob/master/dumux/material/fluidmatrixinteractions/diffusivityconstanttortuosity.hh)): math D^\kappa_\text{pm}= \phi \tau D^\kappa D^\kappa_\text{pm}= \phi \tau D^\kappa.  The primary variable of this model is the mass fraction $X^\kappa$. We apply the same spatial discretization as in the single phase model and use the implicit Euler method for time discretization. For more information, have a look at the dumux handbook. The primary variable of this model is the mass fraction $X^\kappa$. We apply the same spatial discretization as in the single phase model and use the implicit Euler method for time discretization. For more information, have a look at the dumux [handbook](https://dumux.org/handbook). In the following, we take a close look at the files containing the set-up: At first, boundary conditions and spatially distributed parameters are set in problem_1p.hh and spatialparams_1p.hh, respectively, for the single phase model and subsequently in problem_tracer.hh and spatialparams_tracer.hh for the tracer model. Afterwards, we show the different steps for solving the model in the source file main.cc. At the end, we show some simulation results. In the following, we take a close look at the files containing the set-up: The boundary conditions and spatially distributed parameters for the single phase model are set in problem_1p.hh and spatialparams_1p.hh. For the tracer model, this is done in the files problem_tracer.hh and spatialparams_tracer.hh, respectively. Afterwards, we show the different steps for solving the model in the source file main.cc. Finally, some simulation results are shown.
 ... ... @@ -30,15 +30,19 @@ // and another one for in- and output. #include // Dumux is based on DUNE, the Distributed and Unified Numerics Environment, which provides several grid managers and linear solvers. So we need some includes from that. // Dumux is based on DUNE, the Distributed and Unified Numerics Environment, which provides several grid managers and linear solvers. // Here, we include classes related to parallel computations, time measurements and file I/O. #include #include #include #include // In Dumux, a property system is used to specify the model. For this, different properties are defined containing type definitions, values and methods. All properties are declared in the file properties.hh. // In Dumux, the property system is used to specify classes and compile-time options to be used by the model. // For this, different properties are defined containing type definitions, values and methods. // All properties are declared in the file properties.hh. #include // The following file contains the parameter class, which manages the definition of input parameters by a default value, the inputfile or the command line. // The following file contains the parameter class, which manages the definition and retrieval of input // parameters by a default value, the inputfile or the command line. #include // The file dumuxmessage.hh contains the class defining the start and end message of the simulation. #include ... ... @@ -60,7 +64,7 @@ int main(int argc, char** argv) try { using namespace Dumux; // We define the type tags for the two problems. They are created in the individual problem files. // Convenience aliases for the type tags of the two problems, which are defined in the individual problem files. using OnePTypeTag = Properties::TTag::IncompressibleTest; using TracerTypeTag = Properties::TTag::TracerTestCC; ... ... @@ -75,7 +79,11 @@ int main(int argc, char** argv) try Parameters::init(argc, argv); // ### Create the grid // A gridmanager tries to create the grid either from a grid file or the input file. We solve both problems on the same grid. Hence, the grid is only created once using the type tag of the 1p problem. // The GridManager class creates the grid from information given in the input file. // This can either be a grid file, or in the case of structured grids, by specifying the coordinates // of the corners of the grid and the number of cells to be used to discretize each spatial direction. // Here, we solve both the single-phase and the tracer problem on the same grid. // Hence, the grid is only created once using the grid type defined by the type tag of the 1p problem. GridManager> gridManager; gridManager.init(); ... ... @@ -83,7 +91,7 @@ int main(int argc, char** argv) try const auto& leafGridView = gridManager.grid().leafGridView(); // ### Set-up and solving of the 1p problem // In the following section, we set up and solve the 1p problem. As the result of this problem, we obtain the pressure distribution in the problem domain. // In the following section, we set up and solve the 1p problem. As the result of this problem, we obtain the pressure distribution in the domain. // #### Set-up // We create and initialize the finite volume grid geometry, the problem, the linear system, including the jacobian matrix, the residual and the solution vector and the gridvariables. // We need the finite volume geometry to build up the subcontrolvolumes (scv) and subcontrolvolume faces (scvf) for each element of the grid partition. ... ... @@ -103,13 +111,13 @@ int main(int argc, char** argv) try auto A = std::make_shared(); auto r = std::make_shared(); // The grid variables store variables on scv and scvf (volume and flux variables). // The grid variables store variables (primary and secondary variables) on sub-control volumes and faces (volume and flux variables). using OnePGridVariables = GetPropType; auto onePGridVariables = std::make_shared(problemOneP, gridGeometry); onePGridVariables->init(p); // #### Assembling the linear system // We created and inizialize the assembler. // We create and inizialize the assembler. using OnePAssembler = FVAssembler; auto assemblerOneP = std::make_shared(problemOneP, gridGeometry, onePGridVariables); assemblerOneP->setLinearSystem(A, r); ... ... @@ -157,16 +165,17 @@ int main(int argc, char** argv) try // ### Computation of the volume fluxes // We use the results of the 1p problem to calculate the volume fluxes in the model domain. using Scalar = GetPropType; std::vector volumeFlux(gridGeometry->numScvf(), 0.0); using FluxVariables = GetPropType; auto upwindTerm = [](const auto& volVars) { return volVars.mobility(0); }; // We iterate over all elements. // We iterate over all elements for (const auto& element : elements(leafGridView)) { // Compute the element-local views on geometry, primary and secondary variables // as well as variables needed for flux computations auto fvGeometry = localView(*gridGeometry); fvGeometry.bind(element); ... ... @@ -176,28 +185,17 @@ int main(int argc, char** argv) try auto elemFluxVars = localView(onePGridVariables->gridFluxVarsCache()); elemFluxVars.bind(element, fvGeometry, elemVolVars); // We calculate the volume flux for every subcontrolvolume face, which is not on a Neumann boundary (is not on the boundary or is on a Dirichlet boundary). // We calculate the volume fluxes for all sub-control volume faces except for Neumann boundary faces for (const auto& scvf : scvfs(fvGeometry)) { const auto idx = scvf.index(); if (!scvf.boundary()) { FluxVariables fluxVars; fluxVars.init(*problemOneP, element, fvGeometry, elemVolVars, scvf, elemFluxVars); volumeFlux[idx] = fluxVars.advectiveFlux(0, upwindTerm); } else { const auto bcTypes = problemOneP->boundaryTypes(element, scvf); if (bcTypes.hasOnlyDirichlet()) { FluxVariables fluxVars; fluxVars.init(*problemOneP, element, fvGeometry, elemVolVars, scvf, elemFluxVars); volumeFlux[idx] = fluxVars.advectiveFlux(0, upwindTerm); } } // skip Neumann boundary faces if (scvf.boundary() && problemOneP->boundaryTypes(element, scvf).hasNeumann()) continue; // let the FluxVariables class do the flux computation. FluxVariables fluxVars; fluxVars.init(*problemOneP, element, fvGeometry, elemVolVars, scvf, elemFluxVars); volumeFlux[scvf.index()] = fluxVars.advectiveFlux(0, upwindTerm); } } ... ... @@ -244,7 +242,7 @@ int main(int argc, char** argv) try vtkWriter.write(0.0); // For the time loop we set a check point. // We define 10 check points in the time loop at which we will write the solution to vtk files. timeLoop->setPeriodicCheckPoint(tEnd/10.0); // #### The time loop ... ... @@ -302,13 +300,15 @@ int main(int argc, char** argv) try // ### Final Output if (mpiHelper.rank() == 0) DumuxMessage::print(/*firstCall=*/false); return 0; } // ### Exception handling // In this part of the main file we catch and print possible exceptions that could // occur during the simulation. catch (Dumux::ParameterException &e) { std::cerr << std::endl << e << " ---> Abort!" << std::endl; ... ...
 ... ... @@ -19,12 +19,12 @@ // ### Header guard #ifndef DUMUX_ONEP_TRACER_TEST_PROBLEM_HH #define DUMUX_ONEP_TRACER_TEST_PROBLEM_HH #ifndef DUMUX_ONEP_TEST_PROBLEM_HH #define DUMUX_ONEP_TEST_PROBLEM_HH //Before we enter the problem class containing initial and boundary conditions, we include necessary files and introduce properties. // Before we enter the problem class containing initial and boundary conditions, we include necessary files and introduce properties. // ### Include files // The dune grid interphase is included here: // We use YaspGrid, an implementation of the dune grid interface for structured grids: #include // The cell centered, two-point-flux discretization scheme is included: ... ... @@ -34,7 +34,7 @@ // This is the porous medium problem class that this class is derived from: #include // The fluid properties are specified in the following headers: // The fluid properties are specified in the following headers (we use liquid water as the fluid phase): #include #include ... ... @@ -78,11 +78,11 @@ struct SpatialParams using type = OnePTestSpatialParams; }; // The local residual contains analytic derivative methods for incompressible flow: // We use the local residual that contains analytic derivative methods for incompressible flow: template struct LocalResidual { using type = OnePIncompressibleLocalResidual; }; // In the following we define our fluid properties. // In the following we define the fluid properties. template struct FluidSystem { ... ... @@ -102,13 +102,13 @@ struct EnableGridFluxVariablesCache { static // We enable caching for the FV grid geometry template struct EnableGridGeometryCache { static constexpr bool value = true; }; //The cache stores values that were already calculated for later usage. This makes the simulation faster. // The cache stores values that were already calculated for later usage. This increases the memory demand but makes the simulation faster. // We leave the namespace Properties. } // ### The problem class // We enter the problem class where all necessary boundary conditions and initial conditions are set for our simulation. // As this is a porous medium problem, we inherit from the basic PorousMediumFlowProblem. // As this is a porous medium problem, we inherit from the base class PorousMediumFlowProblem. template class OnePTestProblem : public PorousMediumFlowProblem { ... ... @@ -130,24 +130,25 @@ public: OnePTestProblem(std::shared_ptr gridGeometry) : ParentType(gridGeometry) {} // First, we define the type of boundary conditions depending on location. Two types of boundary conditions // First, we define the type of boundary conditions depending on the location. Two types of boundary conditions // can be specified: Dirichlet or Neumann boundary condition. On a Dirichlet boundary, the values of the // primary variables need to be fixed. On a Neumann boundary condition, values for derivatives need to be fixed. // Mixed boundary conditions (different types for different equations on the same boundary) are not accepted. // Mixed boundary conditions (different types for different equations on the same boundary) are not accepted for // cell-centered finite volume schemes. BoundaryTypes boundaryTypes(const Element &element, const SubControlVolumeFace &scvf) const { BoundaryTypes values; // we retreive the global position, i.e. the vector including the global coordinates // of the finite volume // we retrieve the global position, i.e. the vector with the global coordinates, // of the integration point on the boundary sub-control volume face scvf const auto globalPos = scvf.ipGlobal(); // we define a small epsilon value Scalar eps = 1.0e-6; // We specify Dirichlet boundaries on the top and bottom of our domain: if (globalPos[dimWorld-1] < eps || globalPos[dimWorld-1] > this->gridGeometry().bBoxMax()[dimWorld-1] - eps) values.setAllDirichlet(); // The top and bottom of our domain are Neumann boundaries: else // The top and bottom of our domain are Neumann boundaries: values.setAllNeumann(); return values; ... ... @@ -160,7 +161,7 @@ public: // we retreive again the global position const auto& pos = scvf.ipGlobal(); PrimaryVariables values(0); // we assign pressure values in [Pa] according to a pressure gradient to 1e5 Pa at the top and 1.1e5 Pa at the bottom. // and assign pressure values in [Pa] according to a pressure gradient to 1e5 Pa at the top and 1.1e5 Pa at the bottom. values[0] = 1.0e+5*(1.1 - pos[dimWorld-1]*0.1); return values; } ... ...
 ... ... @@ -23,7 +23,7 @@ //Before we enter the problem class containing initial and boundary conditions, we include necessary files and introduce properties. // ### Include files // Again, we have to include the dune grid interface: // Again, we use YaspGrid, the implementation of the dune grid interface for structured grids: #include // and the cell centered, two-point-flux discretization. #include ... ... @@ -31,7 +31,7 @@ #include // We include again the porous medium problem class that this class is derived from: #include // and the base fluidsystem // and the base fluidsystem. We will define a custom fluid system that inherits from that class. #include // We include the header that specifies all spatially variable parameters for the tracer problem: #include "spatialparams_tracer.hh" ... ... @@ -73,25 +73,29 @@ struct Problem { using type = TracerTestProblem struct SpatialParams { private: using GridGeometry = GetPropType; using Scalar = GetPropType; public: using type = TracerTestSpatialParams; }; // We define that mass fractions are used to define the concentrations // One can choose between a formulation in terms of mass or mole fractions. Here, we are using mass fractions. template struct UseMoles { static constexpr bool value = false; }; // We do not use a solution dependent molecular diffusion coefficient: // We use solution-independent molecular diffusion coefficients. Per default, solution-dependent // diffusion coefficients are assumed during the computation of the jacobian matrix entries. Specifying // solution-independent diffusion coefficients can speed up computations: template struct SolutionDependentMolecularDiffusion { static constexpr bool value = false; }; struct SolutionDependentMolecularDiffusion { static constexpr bool value = false; }; // In the following, we create a new tracer fluid system and derive it from the base fluid system. // In the following, we create a new tracer fluid system and derive from the base fluid system. template class TracerFluidSystem : public FluidSystems::Base, TracerFluidSystem> { // We define convenient shortcuts to the properties Scalar, Problem, GridView, // Element, FVElementGeometry and SubControlVolume: // We define some convenience aliases: using Scalar = GetPropType; using Problem = GetPropType; using GridView = GetPropType; ... ... @@ -100,31 +104,35 @@ class TracerFluidSystem : public FluidSystems::Base { using type = TracerFluidSystem class TracerTestProblem : public PorousMediumFlowProblem { ... ... @@ -164,9 +172,9 @@ class TracerTestProblem : public PorousMediumFlowProblem using ElementFluxVariablesCache = typename GridVariables::GridFluxVariablesCache::LocalView; using FVElementGeometry = typename GetPropType::LocalView; using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace; //We create a bool saying whether mole or mass fractions are used // We create a convenience bool stating whether mole or mass fractions are used static constexpr bool useMoles = getPropValue(); //We create additional int to make dimWorld and numComponents available in the problem // We create additional convenience integers to make dimWorld and numComponents available in the problem static constexpr int dimWorld = GridView::dimensionworld; static const int numComponents = FluidSystem::numComponents; ... ... @@ -175,7 +183,7 @@ public: TracerTestProblem(std::shared_ptr gridGeometry) : ParentType(gridGeometry) { // We print out whether mole or mass fractions are used // We print to the terminal whether mole or mass fractions are used if(useMoles) std::cout<<"problem uses mole fractions" << '\n'; else ... ... @@ -195,45 +203,48 @@ public: PrimaryVariables initialAtPos(const GlobalPosition &globalPos) const { PrimaryVariables initialValues(0.0); // The tracer concentration is located on the domain bottom: // The initial contamination is located at the bottom of the domain: if (globalPos[1] < 0.1 + eps_) { // We assign different values, depending on wether mole concentrations or mass concentrations are used: // We chose a mole fraction of $1e-9$, but in case the mass fractions // are used by the model, we have to convert this value: if (useMoles) initialValues = 1e-9; else initialValues = 1e-9*FluidSystem::molarMass(0)/this->spatialParams().fluidMolarMass(globalPos); initialValues = 1e-9*FluidSystem::molarMass(0) /this->spatialParams().fluidMolarMassAtPos(globalPos); } return initialValues; } //We implement an outflow boundary on the top of the domain and prescribe zero-flux Neumann boundary conditions on all other boundaries. NumEqVector neumann(const Element& element, const FVElementGeometry& fvGeometry, const ElementVolumeVariables& elemVolVars, const ElementFluxVariablesCache& elemFluxVarsCache, const SubControlVolumeFace& scvf) const { NumEqVector values(0.0); const auto& volVars = elemVolVars[scvf.insideScvIdx()]; const auto& globalPos = scvf.center(); // This is the outflow boundary, where tracer is transported by advection // with the given flux field and diffusive flux is enforced to be zero if (globalPos[dimWorld-1] > this->gridGeometry().bBoxMax()[dimWorld-1] - eps_) { values = this->spatialParams().volumeFlux(element, fvGeometry, elemVolVars, scvf) * volVars.massFraction(0, 0) * volVars.density(0) / scvf.area(); assert(values>=0.0 && "Volume flux at outflow boundary is expected to have a positive sign"); } //prescribe zero-flux Neumann boundary conditions elsewhere else values = 0.0; // We implement an outflow boundary on the top of the domain and prescribe zero-flux Neumann boundary conditions on all other boundaries. NumEqVector neumann(const Element& element, const FVElementGeometry& fvGeometry, const ElementVolumeVariables& elemVolVars, const ElementFluxVariablesCache& elemFluxVarsCache, const SubControlVolumeFace& scvf) const { NumEqVector values(0.0); const auto& volVars = elemVolVars[scvf.insideScvIdx()]; const auto& globalPos = scvf.center(); return values; // This is the outflow boundary, where tracer is transported by advection with the given flux field. if (globalPos[dimWorld-1] > this->gridGeometry().bBoxMax()[dimWorld-1] - eps_) { values = this->spatialParams().volumeFlux(element, fvGeometry, elemVolVars, scvf) * volVars.massFraction(0, 0) * volVars.density(0) / scvf.area(); assert(values>=0.0 && "Volume flux at outflow boundary is expected to have a positive sign"); } // Prescribe zero-flux Neumann boundary conditions elsewhere else values = 0.0; return values; } private: // We assign a private global variable for the epsilon: static constexpr Scalar eps_ = 1e-6; ... ...
 ... ... @@ -21,25 +21,26 @@ #ifndef DUMUX_INCOMPRESSIBLE_ONEP_TEST_SPATIAL_PARAMS_HH #define DUMUX_INCOMPRESSIBLE_ONEP_TEST_SPATIAL_PARAMS_HH // In this file, we generate the random permeability field in the constructor of the OnePTestSpatialParams class. Thereafter, spatial properties of the porous medium such as the permeability and the porosity are defined in various functions for the 1p problem. // We want to generate a random permeability field. For this, we use a random number generation of the C++ standard library. // In this file, we generate a random permeability field in the constructor of the OnePTestSpatialParams class. // For this, we use the random number generation facilities provided by the C++ standard library. #include // In the file properties.hh all properties are declared. // We use the properties for porous medium flow models, declared in the file properties.hh. #include // We include the spatial parameters for single-phase, finite volumes from which we will inherit. // We include the spatial parameters class for single-phase models discretized by finite volume schemes. // The spatial parameters defined for this example will inherit from those. #include namespace Dumux { // In the OnePTestSpatialParams class, we define all functions needed to describe the porous matrix, e.g. porosity and permeability for the 1p_problem. // In the OnePTestSpatialParams class, we define all functions needed to describe the porous medium, e.g. porosity and permeability for the 1p_problem. template class OnePTestSpatialParams : public FVSpatialParamsOneP> { // We introduce using declarations that are derived from the property system, which we need in this class. // We declare aliases for types that we are going to need in this class. using GridView = typename GridGeometry::GridView; using FVElementGeometry = typename GridGeometry::LocalView; using SubControlVolume = typename FVElementGeometry::SubControlVolume; ... ... @@ -51,6 +52,9 @@ class OnePTestSpatialParams using GlobalPosition = typename SubControlVolume::GlobalPosition; public: // The spatial parameters must export the type used to define permeabilities. // Here, we are using scalar permeabilities, but tensors are also supported. using PermeabilityType = Scalar; OnePTestSpatialParams(std::shared_ptr gridGeometry) : ParentType(gridGeometry), K_(gridGeometry->gridView().size(0), 0.0) ... ... @@ -60,11 +64,12 @@ public: permeability_ = getParam("SpatialParams.Permeability"); permeabilityLens_ = getParam("SpatialParams.PermeabilityLens"); // Further, we get the position of the lens, which is defined by the position of the lower left and the upper right corner. // Furthermore, we get the position of the lens, which is defined by the position of the lower left and the upper right corner. lensLowerLeft_ = getParam("SpatialParams.LensLowerLeft"); lensUpperRight_ =getParam("SpatialParams.LensUpperRight"); // We generate random fields for the permeability using a lognormal distribution, with the permeability_ as mean value and 10 % of it as standard deviation. A seperate distribution is used for the lens using permeabilityLens_. // We generate random fields for the permeability using lognormal distributions, with permeability_ as mean value and 10 % of it as standard deviation. // A separate distribution is used for the lens using permeabilityLens_. A permeability value is created for each element of the grid and is stored in the vector K_. std::mt19937 rand(0); std::lognormal_distribution K(std::log(permeability_), std::log(permeability_)*0.1); std::lognormal_distribution KLens(std::log(permeabilityLens_), std::log(permeabilityLens_)*0.1); ... ... @@ -77,7 +82,9 @@ public: } // ### Properties of the porous matrix // We define the (intrinsic) permeability $[m^2]$ using the generated random permeability field. In this test, we use element-wise distributed permeabilities. // This function returns the permeability $[m^2]$ to be used within a sub-control volume (scv) inside the element element. // One can define the permeability as function of the primary variables on the element, which are given in the provided ElementSolution. // Here, we use element-wise distributed permeabilities that were randomly generated in the constructor (see above). template const PermeabilityType& permeability(const Element& element, const SubControlVolume& scv, ... ... @@ -87,7 +94,7 @@ public: } // We set the porosity $[-]$ for the whole domain. // We set the porosity $[-]$ for the whole domain to a value of $20 \%$. Scalar porosityAtPos(const GlobalPosition &globalPos) const { return 0.2; } ... ...
 ... ... @@ -23,16 +23,16 @@ #ifndef DUMUX_TRACER_TEST_SPATIAL_PARAMS_HH #define DUMUX_TRACER_TEST_SPATIAL_PARAMS_HH // In this file, we define spatial properties of the porous medium such as the permeability and the porosity in various functions for the tracer problem. Further, spatial dependent properties of the tracer fluid system are defined and in the end two functions handel the calculated volume fluxes from the solution of the 1p problem. // In the file properties.hh, all properties are declared. // In this file, we define spatial properties of the porous medium such as the permeability and the porosity in various functions for the tracer problem. // Furthermore, spatial dependent properties of the tracer fluid system are defined and in the end two functions handle the calculated volume fluxes from the solution of the 1p problem. // We use the properties for porous medium flow models, declared in the file properties.hh. #include // As in the 1p spatialparams, we inherit from the spatial parameters for single-phase, finite volumes, which we include here. // As in the 1p spatialparams, we inherit from the spatial parameters for single-phase models using finite volumes, which we include here. #include // We enter the namespace Dumux namespace Dumux { // In the TracerTestSpatialParams class, we define all functions needed to describe spatially dependent parameters for the tracer_problem. template class TracerTestSpatialParams : public FVSpatialParamsOneP