diff --git a/README.md b/README.md
index e822a04cb35e6135864a9e67c06116c310e8cd6b..254f5276a7e611a8887e8e0b4eebdbd38faa01e5 100644
--- a/README.md
+++ b/README.md
@@ -25,7 +25,7 @@ The following resources are useful to get started with DuMux:
* [Handbook](https://dumux.org/handbook), a detailed DuMux manual,
* [DuMux course materials](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux-course/tree/master),
-* [Examples](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/tree/feature/documented-tutorials/examples), with detailed description of code and results,
+* [Examples](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/tree/master/examples), with detailed description of code and results,
* [Class documentation](https://dumux.org/classdocumentation) generated from the source code,
* [Mailing list](https://listserv.uni-stuttgart.de/mailman/listinfo/dumux),
* [Changelog](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/blob/master/CHANGELOG.md), where all changes between different release versions are listed and explained.
diff --git a/examples/CMakeLists.txt b/examples/CMakeLists.txt
index 3a825767d0c5247f8f3a631a1b29180401a1dfaa..e8da037368456c9854b21bbb6b8b7c5b5a2e8f3f 100644
--- a/examples/CMakeLists.txt
+++ b/examples/CMakeLists.txt
@@ -1,2 +1,3 @@
add_subdirectory(2pinfiltration)
add_subdirectory(1ptracer)
+add_subdirectory(shallowwaterfriction)
diff --git a/examples/README.md b/examples/README.md
index b3ee3484ff07b52adc52f9610ae34825aab93781..b5a966ce2a4e63649653f918463949255ba96035 100644
--- a/examples/README.md
+++ b/examples/README.md
@@ -2,5 +2,6 @@ Examples
===============
The following resources are useful to get started with DuMux:
-* [1ptracer](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/tree/feature/documented-tutorials/examples/1ptracer),
-* [2pinfiltration](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/tree/feature/documented-tutorials/examples/2pinfiltration).
+* [1ptracer](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/tree/master/examples/1ptracer),
+* [2pinfiltration](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/tree/master/examples/2pinfiltration).
+* [shallowwater](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/tree/master/examples/shallowwater).
diff --git a/examples/shallowwaterfriction/CMakeLists.txt b/examples/shallowwaterfriction/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..67111126e6dc62fb99897d829c2dd44e9b69da72
--- /dev/null
+++ b/examples/shallowwaterfriction/CMakeLists.txt
@@ -0,0 +1,13 @@
+add_input_file_links()
+dune_symlink_to_source_files("params.input")
+
+
+dune_add_test(NAME example_shallowwaterfriction
+ SOURCES main.cc
+ COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+ CMD_ARGS --script fuzzy
+ --files ${CMAKE_SOURCE_DIR}/test/references/example_shallowwaterfriction-reference.vtu
+ ${CMAKE_CURRENT_BINARY_DIR}/example_shallowwaterfriction-00001.vtu
+ --zeroThreshold {"velocityY":1e-14}
+ --command "${CMAKE_CURRENT_BINARY_DIR}/example_shallowwaterfriction params.input
+ -Problem.Name example_shallowwaterfriction")
diff --git a/examples/shallowwaterfriction/README.md b/examples/shallowwaterfriction/README.md
new file mode 100644
index 0000000000000000000000000000000000000000..7a4994cc8a5ee0b0fc497aebac4646fe2d4fa5e0
--- /dev/null
+++ b/examples/shallowwaterfriction/README.md
@@ -0,0 +1,815 @@
+# Shallow water flow with bottom friction
+This example shows how the shallow water flow model can be
+applied to simulate steady subcritical flow including
+bottom friction (bed shear stress).
+
+
+## Shallow water model
+The shallow water equations (SWEs) are given as:
+
+$`
+\frac{\partial \mathbf{U}}{\partial t} +
+\frac{\partial \mathbf{F}}{\partial x} +
+\frac{\partial \mathbf{G}}{\partial y} - \mathbf{S_b} - \mathbf{S_f} = 0
+`$
+
+where $U$, $F$ and $G$ defined as
+
+$`
+\mathbf{U} = \begin{bmatrix} h \\ uh \\ vh \end{bmatrix},
+\mathbf{F} = \begin{bmatrix} hu \\ hu^2 + \frac{1}{2} gh^2 \\ huv \end{bmatrix},
+\mathbf{G} = \begin{bmatrix} hv \\ huv \\ hv^2 + \frac{1}{2} gh^2 \end{bmatrix}
+`$
+
+Z is the bedSurface, h the water depth, u the velocity in
+x-direction and v the velocity in y-direction, g is the constant of gravity.
+
+The source terms for the bed friction $`S_b`$ and bed slope
+$`S_f`$ are given as
+$`
+\mathbf{S_b} = \begin{bmatrix} 0 \\ -gh \frac{\partial z}{\partial x}
+ \\ -gh \frac{\partial z}{\partial y}\end{bmatrix},
+\mathbf{S_f} = \begin{bmatrix} 0 \\ -ghS_{fx} \\ -ghS_{fy}\end{bmatrix}.
+`$
+
+For this example, a cell-centered finite volume method (cctpfa) is applied to solve the SWEs
+in combination with a fully-implicit time discretization. For cases where no sharp fronts or
+traveling waves occur it is possible to apply time steps larger than CFL number = 1 to reduce
+the computation time. Even if a steady state solution is considered, an implicit time stepping method
+is applied.
+
+## Problem set-up
+The model domain is given by a rough channel with a slope of 0.001.
+The domain is 500 meters long and 10 meters wide.
+.
+
+Bottom friction is considered by applying
+the friction law of Manning (Manning n = 0.025). At the lateral sides no friction is considered and a
+no-flow no slip boundary condition is applied. This is the default boundary condition for the shallow water model.
+
+
+At the left border a discharge boundary condition
+is applied as inflow boundary condition with q = -1.0 ($`m^2 s^{-1}`$). At the right border a water fixed depth boundary condition
+is applied for the outflow. Normal flow is assumed, therefore the water depth at the right border is calculated after
+the of Gaukler-Manning-Strickler equation:
+
+ $` v_m = 1/n * R_{hy}^{2/3} * I_s^{1/2}`$
+
+Where the mean velocity $`v_m`$ is given as
+
+$`v_m = \frac{q}{h}`$
+
+$`n`$ is the friction value after Manning. $`R_{hy}`$ the hydraulic radius, which is assumed to be equal to
+the water depth. $`I_s`$ is the bed slope and $`q`$ the unity inflow discharge
+
+The water depth h can be calculated as
+$`h = \left(\frac{n*q}{\sqrt{I_s}} \right)^{3/5}`$
+
+The formula of Gaukler Manning and Strickler is also used to calculate the analytic solution. All parameters
+for the simulation are given in the file *params.input*.
+
+
+## The file `spatialparams.hh`
+
+
+We include the basic spatial parameters for finite volumes file from which we will inherit
+```cpp
+#include <dumux/material/spatialparams/fv.hh>
+```
+The parameters header is needed to retrieve run-time parameters.
+```cpp
+#include <dumux/common/parameters.hh>
+```
+We include all friction laws, between we can choose for the calculation of the bottom friction source.
+```cpp
+#include <dumux/material/fluidmatrixinteractions/frictionlaws/frictionlaw.hh>
+#include <dumux/material/fluidmatrixinteractions/frictionlaws/manning.hh>
+#include <dumux/material/fluidmatrixinteractions/frictionlaws/nikuradse.hh>
+```
+We enter the namespace Dumux. All Dumux functions and classes are in a namespace Dumux, to make sure they don`t clash with symbols from other libraries you may want to use in conjunction with Dumux.
+```cpp
+namespace Dumux {
+```
+In the RoughChannelSpatialParams class we define all functions needed to describe the spatial distributed parameters.
+```cpp
+template<class FVGridGeometry, class Scalar, class VolumeVariables>
+class RoughChannelSpatialParams
+: public FVSpatialParams<FVGridGeometry, Scalar,
+ RoughChannelSpatialParams<FVGridGeometry, Scalar, VolumeVariables>>
+{
+```
+We introduce using declarations that are derived from the property system which we need in this class
+```cpp
+ using ThisType = RoughChannelSpatialParams<FVGridGeometry, Scalar, VolumeVariables>;
+ using ParentType = FVSpatialParams<FVGridGeometry, Scalar, ThisType>;
+ using GridView = typename FVGridGeometry::GridView;
+ using FVElementGeometry = typename FVGridGeometry::LocalView;
+ using SubControlVolume = typename FVElementGeometry::SubControlVolume;
+ using Element = typename GridView::template Codim<0>::Entity;
+ using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+public:
+```
+In the constructor be read some values from the `params.input` and initialize the friciton law.
+```cpp
+ RoughChannelSpatialParams(std::shared_ptr<const FVGridGeometry> fvGridGeometry)
+ : ParentType(fvGridGeometry)
+ {
+ gravity_ = getParam<Scalar>("Problem.Gravity");
+ bedSlope_ = getParam<Scalar>("Problem.BedSlope");
+ frictionLawType_ = getParam<std::string>("Problem.FrictionLaw");
+ initFrictionLaw();
+ }
+```
+We initialize the friction law based on the law specified in `params.input`.
+```cpp
+ void initFrictionLaw()
+ {
+ if (frictionLawType_ == "Manning")
+ {
+ Scalar manningN = getParam<Scalar>("Problem.ManningN");
+ frictionLaw_ = std::make_unique<FrictionLawManning<VolumeVariables>>(gravity_, manningN);
+ }
+ if (frictionLawType_ == "Nikuradse")
+ {
+ Scalar ks = getParam<Scalar>("Problem.Ks");
+ frictionLaw_ = std::make_unique<FrictionLawNikuradse<VolumeVariables>>(ks);
+ }
+ else
+ {
+ std::cout<<"The FrictionLaw in params.input is unknown. Valid entries are `Manning` and `Nikuradse`!"<<std::endl;
+ }
+ }
+```
+Use this function, if you want to vary the value for the gravity.
+```cpp
+ Scalar gravity(const GlobalPosition& globalPos) const
+ {
+ return gravity_;
+ }
+```
+Use this function for a constant gravity.
+```cpp
+ Scalar gravity() const
+ {
+ return gravity_;
+ }
+```
+This function returns an object of the friction law class, which is initialized with the appropriate friction values. If you want to use different friciton values or laws, you have to use a vector of unique_ptr for `frictionLaw_` and pick the right friction law instances via the `element` argument.
+```cpp
+ const FrictionLaw<VolumeVariables>& frictionLaw(const Element& element,
+ const SubControlVolume& scv) const
+ {
+ return *frictionLaw_;
+ }
+```
+Define the bed surface based on the `bedSlope_`.
+```cpp
+ Scalar bedSurface(const Element& element,
+ const SubControlVolume& scv) const
+ {
+ return 10.0 - element.geometry().center()[0] * bedSlope_;
+ }
+
+private:
+ Scalar gravity_;
+ Scalar bedSlope_;
+ std::string frictionLawType_;
+ std::unique_ptr<FrictionLaw<VolumeVariables>> frictionLaw_;
+};
+```
+end of namespace Dumux.
+```cpp
+}
+
+```
+
+
+
+## The file `problem.hh`
+
+
+## Include files
+We use the dune yasp grid.
+```cpp
+#include <dune/grid/yaspgrid.hh>
+```
+We include the cell centered, two-point-flux discretization scheme.
+```cpp
+#include <dumux/discretization/cctpfa.hh>
+```
+The parameters header is needed to retrieve run-time parameters.
+```cpp
+#include <dumux/common/parameters.hh>
+```
+We include the header which are needed for shallow water models.
+```cpp
+#include <dumux/freeflow/shallowwater/model.hh>
+#include <dumux/freeflow/shallowwater/problem.hh>
+#include <dumux/freeflow/shallowwater/boundaryfluxes.hh>
+```
+We include the header that specifies all spatially variable parameters.
+```cpp
+#include "spatialparams.hh"
+```
+## Define basic properties for our simulation
+We enter the namespace Dumux. All Dumux functions and classes are in a namespace Dumux, to make sure they don't clash with symbols from other libraries you may want to use in conjunction with Dumux. One could use these functions and classes by prefixing every use of these names by ::, but that would quickly become cumbersome and annoying. Rather, we simply import the entire Dumux namespace for general use.
+```cpp
+namespace Dumux {
+```
+The problem class is forward declared.
+```cpp
+template <class TypeTag>
+class RoughChannelProblem;
+```
+We enter the namespace Properties, which is a sub-namespace of the namespace Dumux.
+```cpp
+namespace Properties {
+```
+A TypeTag for our simulation is created which inherits from the shallow water model and the
+cell centered, two-point-flux discretization scheme.
+```cpp
+namespace TTag {
+struct RoughChannel { using InheritsFrom = std::tuple<ShallowWater, CCTpfaModel>; };
+}
+```
+We define the grid of our simulation. We use a two-dimensional Yasp Grid.
+```cpp
+template<class TypeTag>
+struct Grid<TypeTag, TTag::RoughChannel>
+{ using type = Dune::YaspGrid<2, Dune::TensorProductCoordinates<GetPropType<TypeTag, Properties::Scalar>, 2> >; };
+```
+We set the problem. The problem class specifies initial and boundary conditions and is defined below.
+```cpp
+template<class TypeTag>
+struct Problem<TypeTag, TTag::RoughChannel>
+{ using type = Dumux::RoughChannelProblem<TypeTag>; };
+```
+We define the spatial parameters for our simulation. The values are specified in the corresponding spatialparameters header file, which is included above.
+```cpp
+template<class TypeTag>
+struct SpatialParams<TypeTag, TTag::RoughChannel>
+{
+private:
+```
+We define convenient shortcuts to the properties FVGridGeometry, Scalar, ElementVolumeVariables and VolumeVariables:
+```cpp
+ using FVGridGeometry = GetPropType<TypeTag, Properties::FVGridGeometry>;
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+ using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
+ using VolumeVariables = typename ElementVolumeVariables::VolumeVariables;
+```
+Finally we set the spatial parameters:
+```cpp
+public:
+ using type = RoughChannelSpatialParams<FVGridGeometry, Scalar, VolumeVariables>;
+};
+```
+We enable caching for the FV grid geometry and the grid volume variables. The cache
+stores values that were already calculated for later usage. This makes the simulation faster.
+```cpp
+template<class TypeTag>
+struct EnableFVGridGeometryCache<TypeTag, TTag::RoughChannel>
+{ static constexpr bool value = true; };
+
+template<class TypeTag>
+struct EnableGridVolumeVariablesCache<TypeTag, TTag::RoughChannel>
+{ static constexpr bool value = false; };
+```
+We leave the namespace Properties.
+```cpp
+}
+```
+## 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 shallow water problem, we inherit from the basic ShallowWaterProblem.
+```cpp
+template <class TypeTag>
+class RoughChannelProblem : public ShallowWaterProblem<TypeTag>
+{
+```
+We use convenient declarations that we derive from the property system.
+```cpp
+ using ParentType = ShallowWaterProblem<TypeTag>;
+ using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
+ using BoundaryTypes = GetPropType<TypeTag, Properties::BoundaryTypes>;
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+ using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
+ using FVGridGeometry = GetPropType<TypeTag, Properties::FVGridGeometry>;
+ using NeumannFluxes = GetPropType<TypeTag, Properties::NumEqVector>;
+ using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
+ using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
+ using ElementFluxVariablesCache = typename GridVariables::GridFluxVariablesCache::LocalView;
+ using VolumeVariables = typename ElementVolumeVariables::VolumeVariables;
+ using FVElementGeometry = typename GetPropType<TypeTag, Properties::FVGridGeometry>::LocalView;
+ using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace;
+ using GridView = GetPropType<TypeTag, Properties::GridView>;
+ using Element = typename GridView::template Codim<0>::Entity;
+ using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+ using NumEqVector = GetPropType<TypeTag, Properties::NumEqVector>;
+ using SubControlVolume = typename FVElementGeometry::SubControlVolume;
+
+public:
+```
+This is the constructor of our problem class.
+```cpp
+ RoughChannelProblem(std::shared_ptr<const FVGridGeometry> fvGridGeometry)
+ : ParentType(fvGridGeometry)
+ {
+```
+We read the parameters from the params.input file.
+```cpp
+ name_ = getParam<std::string>("Problem.Name");
+ constManningN_ = getParam<Scalar>("Problem.ManningN");
+ bedSlope_ = getParam<Scalar>("Problem.BedSlope");
+ discharge_ = getParam<Scalar>("Problem.Discharge");
+```
+We calculate the outflow boundary condition using the Gauckler-Manning-Strickler formula.
+```cpp
+ hBoundary_ = this->gauklerManningStrickler(discharge_,constManningN_,bedSlope_);
+```
+We initialize the analytic solution to a verctor of the appropriate size filled with zeros.
+```cpp
+ exactWaterDepth_.resize(fvGridGeometry->numDofs(), 0.0);
+ exactVelocityX_.resize(fvGridGeometry->numDofs(), 0.0);
+ }
+```
+Get the analytical water depth
+```cpp
+ const std::vector<Scalar>& getExactWaterDepth()
+ {
+ return exactWaterDepth_;
+ }
+```
+Get the analytical velocity
+```cpp
+ const std::vector<Scalar>& getExactVelocityX()
+ {
+ return exactVelocityX_;
+ }
+```
+Get the water depth with Gauckler-Manning-Strickler
+```cpp
+ Scalar gauklerManningStrickler(Scalar discharge, Scalar manningN, Scalar bedSlope)
+ {
+ using std::pow;
+ using std::abs;
+ using std::sqrt;
+
+ return pow(abs(discharge)*manningN/sqrt(bedSlope), 0.6);
+ }
+```
+Get the analytical solution
+```cpp
+ void analyticalSolution()
+ {
+ using std::abs;
+
+ for (const auto& element : elements(this->fvGridGeometry().gridView()))
+ {
+ const Scalar h = this->gauklerManningStrickler(discharge_,constManningN_,bedSlope_);
+ const Scalar u = abs(discharge_)/h;
+
+ const auto eIdx = this->fvGridGeometry().elementMapper().index(element);
+ exactWaterDepth_[eIdx] = h;
+ exactVelocityX_[eIdx] = u;
+ }
+ }
+```
+Get the problem name. It is used as a prefix for files generated by the simulation.
+```cpp
+ const std::string& name() const
+ {
+ return name_;
+ }
+```
+Get the source term.
+```cpp
+ NumEqVector source(const Element& element,
+ const FVElementGeometry& fvGeometry,
+ const ElementVolumeVariables& elemVolVars,
+ const SubControlVolume &scv) const
+ {
+
+ NumEqVector source (0.0);
+```
+In this model the bottom friction is the only source.
+```cpp
+ source += bottomFrictionSource(element, fvGeometry, elemVolVars, scv);
+
+ return source;
+ }
+```
+Get the source term due to bottom friction.
+```cpp
+ NumEqVector bottomFrictionSource(const Element& element,
+ const FVElementGeometry& fvGeometry,
+ const ElementVolumeVariables& elemVolVars,
+ const SubControlVolume &scv) const
+ {
+ NumEqVector bottomFrictionSource(0.0);
+ const auto& volVars = elemVolVars[scv];
+```
+For the calculation of the source term due to bottom friction the two-dimensional bottom shear stess vector is needed. This is the force per area, which works between the flow and the bed. It is calculated within the `FrictionLaw`, which is a spatialParameter. In this model the `FrictionLawManning` is used (see `params.input`).
+```cpp
+ Dune::FieldVector<Scalar, 2> bottomShearStress = this->spatialParams().frictionLaw(element, scv).shearStress(volVars);
+```
+The bottom shear stress causes a pure loss of momentum. Thus the first entry of the `bottomFrictionSource`, which is related to the mass balance equation is zero. The second entry of the `bottomFricitonSource` corresponds to the momentum equation in x-direction and is therefore equal to the first, the x-component, of the `bottomShearStress`. Accordingly the third entry of the `bottomFrictionSource` is equal to the second component of the `bottomShearStress`.
+```cpp
+ bottomFrictionSource[0] = 0.0;
+ bottomFrictionSource[1] = bottomShearStress[0];
+ bottomFrictionSource[2] = bottomShearStress[1];
+
+ return bottomFrictionSource;
+ }
+```
+We specify the boundary condition type.
+```cpp
+ BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const
+ {
+ BoundaryTypes bcTypes;
+```
+Since we use a weak imposition all boundary conditions are of Neumann type.
+```cpp
+ bcTypes.setAllNeumann();
+ return bcTypes;
+ }
+```
+We specify the neumann boundary. Due to the weak imposition we calculate the flux at the boundary, with a Rieman solver. For this the state of a virtual cell outside of the boundary is needed (`boundaryStateVariables`), wich is calculated with the Riemann invariants (see Yoon and Kang, Finite Volume Model for Two-Dimensional Shallow Water Flows on Unstructured Grids) . The calculation of the Riemann invariants differ depending on the type of the boundary (h, q or no-flow boundary).
+```cpp
+ NeumannFluxes neumann(const Element& element,
+ const FVElementGeometry& fvGeometry,
+ const ElementVolumeVariables& elemVolVars,
+ const ElementFluxVariablesCache& elemFluxVarsCache,
+ const SubControlVolumeFace& scvf) const
+ {
+ NeumannFluxes values(0.0);
+
+ const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
+ const auto& insideVolVars = elemVolVars[insideScv];
+ const auto& nxy = scvf.unitOuterNormal();
+ const auto gravity = this->spatialParams().gravity(scvf.center());
+ std::array<Scalar, 3> boundaryStateVariables;
+```
+Calculate the rieman invariants for imposed discharge at the left side.
+```cpp
+ if (scvf.center()[0] < 0.0 + eps_)
+ {
+ boundaryStateVariables = ShallowWater::fixedDischargeBoundary(discharge_,
+ insideVolVars.waterDepth(),
+ insideVolVars.velocity(0),
+ insideVolVars.velocity(1),
+ gravity,
+ nxy);
+ }
+```
+Calculate the rieman invariants for impose water depth at the right side.
+```cpp
+ else if (scvf.center()[0] > 100.0 - eps_)
+ {
+ boundaryStateVariables = ShallowWater::fixedWaterDepthBoundary(hBoundary_,
+ insideVolVars.waterDepth(),
+ insideVolVars.velocity(0),
+ insideVolVars.velocity(1),
+ gravity,
+ nxy);
+ }
+```
+Calculate the rieman invarianty for the no-flow boundary.
+```cpp
+ else
+ {
+ boundaryStateVariables[0] = insideVolVars.waterDepth();
+ boundaryStateVariables[1] = -insideVolVars.velocity(0);
+ boundaryStateVariables[2] = -insideVolVars.velocity(1);
+ }
+```
+We calculate the boundary fluxes based on a Riemann problem.
+```cpp
+ auto riemannFlux = ShallowWater::riemannProblem(insideVolVars.waterDepth(),
+ boundaryStateVariables[0],
+ insideVolVars.velocity(0),
+ boundaryStateVariables[1],
+ insideVolVars.velocity(1),
+ boundaryStateVariables[2],
+ insideVolVars.bedSurface(),
+ insideVolVars.bedSurface(),
+ gravity,
+ nxy);
+
+ values[Indices::massBalanceIdx] = riemannFlux[0];
+ values[Indices::velocityXIdx] = riemannFlux[1];
+ values[Indices::velocityYIdx] = riemannFlux[2];
+
+ return values;
+ }
+```
+We set the initial conditions. In this example constant initial conditions are used. Therefore the argument `globalPos` is not needed. If you want to impose spatial variable initial conditions, you have to use the `globalPos`.
+```cpp
+ PrimaryVariables initialAtPos(const GlobalPosition &globalPos) const
+ {
+ PrimaryVariables values(0.0);
+```
+We set the initial water depth to one meter.
+```cpp
+ values[0] = 1.0;
+```
+We set the x-component of the initial velocity to zero.
+```cpp
+ values[1] = 0.0;
+```
+We set the y-component of the initial velocity to zero.
+```cpp
+ values[2] = 0.0;
+
+ return values;
+ };
+```
+\}
+```cpp
+
+private:
+```
+We declare the private variables of the problem. They are initialized in the problems constructor.
+We declare the variable for the analytic solution.
+```cpp
+ std::vector<Scalar> exactWaterDepth_;
+ std::vector<Scalar> exactVelocityX_;
+```
+constant friction value. An analytic solution is only available for const friction. If you want to run the simulation with a non constant friciton value (specified in the spatialParams) you have to remove the analytic solution.
+```cpp
+ Scalar constManningN_;
+```
+The constant bed slope.
+```cpp
+ Scalar bedSlope_;
+```
+The water depth at the outflow boundary.
+```cpp
+ Scalar hBoundary_;
+```
+The discharge at the inflow boundary.
+```cpp
+ Scalar discharge_;
+```
+eps is used as a small value for the definition of the boundry conditions
+```cpp
+ static constexpr Scalar eps_ = 1.0e-6;
+ std::string name_;
+};
+```
+We leave the namespace Dumux.
+```cpp
+}
+
+```
+
+
+
+## The file `main.cc`
+
+## The main file
+This is the main file for the shallow water example. Here we can see the programme sequence and how the system is solved using newton's method.
+### Includes
+```cpp
+#include <config.h>
+```
+Standard header file for C++, to get time and date information.
+```cpp
+#include <ctime>
+```
+Standard header file for C++, for in- and output.
+```cpp
+#include <iostream>
+```
+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.
+```cpp
+#include <dune/common/parallel/mpihelper.hh>
+#include <dune/common/timer.hh>
+#include <dune/grid/io/file/dgfparser/dgfexception.hh>
+#include <dune/grid/io/file/vtk.hh>
+```
+We need the following class to simplify the writing of dumux simulation data to VTK format.
+```cpp
+#include <dumux/io/vtkoutputmodule.hh>
+```
+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.
+```cpp
+#include <dumux/common/properties.hh>
+```
+The following file contains the parameter class, which manages the definition of input parameters by a default value, the inputfile or the command line.
+```cpp
+#include <dumux/common/parameters.hh>
+```
+The file dumuxmessage.hh contains the class defining the start and end message of the simulation.
+```cpp
+#include <dumux/common/dumuxmessage.hh>
+#include <dumux/common/defaultusagemessage.hh>
+```
+The gridmanager constructs a grid from the information in the input or grid file. There is a specification for the different supported grid managers.
+```cpp
+#include <dumux/io/grid/gridmanager.hh>
+```
+We include the linear solver to be used to solve the linear system
+```cpp
+#include <dumux/linear/amgbackend.hh>
+```
+We include the nonlinear newtons method
+```cpp
+#include <dumux/nonlinear/newtonsolver.hh>
+```
+Further we include assembler, which assembles the linear systems for finite volume schemes (box-scheme, tpfa-approximation, mpfa-approximation)
+```cpp
+#include <dumux/assembly/fvassembler.hh>
+```
+We include the problem file which defines initial and boundary conditions to describe our example problem
+```cpp
+#include "problem.hh"
+```
+### Beginning of the main function
+```cpp
+int main(int argc, char** argv) try
+{
+ using namespace Dumux;
+```
+We define the type tag for this problem
+```cpp
+ using TypeTag = Properties::TTag::RoughChannel;
+```
+We initialize MPI, finalize is done automatically on exit
+```cpp
+ const auto& mpiHelper = Dune::MPIHelper::instance(argc, argv);
+```
+We print dumux start message
+```cpp
+ if (mpiHelper.rank() == 0)
+ DumuxMessage::print(/*firstCall=*/true);
+```
+We parse command line arguments and input file
+```cpp
+ Parameters::init(argc, argv);
+```
+### Create the grid
+A gridmanager tries to create the grid either from a grid file or the input file.
+```cpp
+ GridManager<GetPropType<TypeTag, Properties::Grid>> gridManager;
+ gridManager.init();
+```
+We compute on the leaf grid view
+```cpp
+ const auto& leafGridView = gridManager.grid().leafGridView();
+```
+### Setup and solving of the problem
+#### Setup
+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.
+```cpp
+ using FVGridGeometry = GetPropType<TypeTag, Properties::FVGridGeometry>;
+ auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
+ fvGridGeometry->update();
+```
+In the problem, we define the boundary and initial conditions.
+```cpp
+ using Problem = GetPropType<TypeTag, Properties::Problem>;
+ auto problem = std::make_shared<Problem>(fvGridGeometry);
+```
+We initialize the solution vector
+```cpp
+ using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
+ SolutionVector x(fvGridGeometry->numDofs());
+ problem->applyInitialSolution(x);
+ auto xOld = x;
+```
+And then use the solutionvector to intialize the gridVariables.
+```cpp
+ using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
+ auto gridVariables = std::make_shared<GridVariables>(problem, fvGridGeometry);
+ gridVariables->init(x);
+```
+We get some time loop parameters from the input file.
+```cpp
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+ const auto tEnd = getParam<Scalar>("TimeLoop.TEnd");
+ const auto maxDt = getParam<Scalar>("TimeLoop.MaxTimeStepSize");
+ auto dt = getParam<Scalar>("TimeLoop.DtInitial");
+```
+We intialize the vtk output module. Each model has a predefined model specific output with relevant parameters for that model.
+```cpp
+ using IOFields = GetPropType<TypeTag, Properties::IOFields>;
+ VtkOutputModule<GridVariables, SolutionVector> vtkWriter(*gridVariables,x, problem->name());
+```
+We add the analytical solution ("exactWaterDepth" and "exactVelocityX") to the predefined specific output.
+```cpp
+ vtkWriter.addField(problem->getExactWaterDepth(), "exactWaterDepth");
+ vtkWriter.addField(problem->getExactVelocityX(), "exactVelocityX");
+```
+We calculate the analytic solution.
+```cpp
+ problem->analyticalSolution();
+ IOFields::initOutputModule(vtkWriter);
+ vtkWriter.write(0.0);
+```
+We instantiate time loop.
+```cpp
+ auto timeLoop = std::make_shared<CheckPointTimeLoop<Scalar>>(0, dt, tEnd);
+ timeLoop->setMaxTimeStepSize(maxDt);
+```
+we set the assembler with the time loop because we have an instationary problem.
+```cpp
+ using Assembler = FVAssembler<TypeTag, DiffMethod::numeric>;
+ auto assembler = std::make_shared<Assembler>(problem, fvGridGeometry, gridVariables, timeLoop);
+```
+We set the linear solver.
+```cpp
+ using LinearSolver = Dumux::AMGBackend<TypeTag>;
+ auto linearSolver = std::make_shared<LinearSolver>(leafGridView, fvGridGeometry->dofMapper());
+```
+Additionaly, we set the non-linear solver.
+```cpp
+ using NewtonSolver = Dumux::NewtonSolver<Assembler, LinearSolver>;
+ NewtonSolver nonLinearSolver(assembler, linearSolver);
+```
+We set some check point at the end of the time loop. The check point is used to trigger the vtk output.
+```cpp
+ timeLoop->setCheckPoint(tEnd);
+```
+We start the time loop.
+```cpp
+ timeLoop->start(); do
+ {
+```
+We start to calculate the new solution of that time step. First we define the old solution as the solution of the previous time step for storage evaluations.
+```cpp
+ assembler->setPreviousSolution(xOld);
+```
+We solve the non-linear system with time step control.
+```cpp
+ nonLinearSolver.solve(x,*timeLoop);
+```
+We make the new solution the old solution.
+```cpp
+ xOld = x;
+ gridVariables->advanceTimeStep();
+```
+We advance to the time loop to the next step.
+```cpp
+ timeLoop->advanceTimeStep();
+```
+We write vtk output, if we reached the check point (end of time loop)
+```cpp
+ if (timeLoop->isCheckPoint())
+ vtkWriter.write(timeLoop->time());
+```
+We report statistics of this time step.
+```cpp
+ timeLoop->reportTimeStep();
+```
+We set new dt as suggested by newton controller for the next time step.
+```cpp
+ timeLoop->setTimeStepSize(nonLinearSolver.suggestTimeStepSize(timeLoop->timeStepSize()));
+
+
+ } while (!timeLoop->finished());
+
+ timeLoop->finalize(leafGridView.comm());
+```
+### Final Output
+We print dumux end message.
+```cpp
+ if (mpiHelper.rank() == 0)
+ {
+ Parameters::print();
+ DumuxMessage::print(/*firstCall=*/false);
+ }
+
+ return 0;
+} // end main
+
+catch (const Dumux::ParameterException &e)
+{
+ std::cerr << std::endl << e << " ---> Abort!" << std::endl;
+ return 1;
+}
+catch (const 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 (const 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;
+}
+```
+
+## Results
+The solution and the analytical result for the problem is shown in .
diff --git a/examples/shallowwaterfriction/doc/intro.md b/examples/shallowwaterfriction/doc/intro.md
new file mode 100644
index 0000000000000000000000000000000000000000..b9cf6c9bf9abeffee014965d6956e403910d43a7
--- /dev/null
+++ b/examples/shallowwaterfriction/doc/intro.md
@@ -0,0 +1,69 @@
+# Shallow water flow with bottom friction
+This example shows how the shallow water flow model can be
+applied to simulate steady subcritical flow including
+bottom friction (bed shear stress).
+
+
+## Shallow water model
+The shallow water equations (SWEs) are given as:
+
+$`
+\frac{\partial \mathbf{U}}{\partial t} +
+\frac{\partial \mathbf{F}}{\partial x} +
+\frac{\partial \mathbf{G}}{\partial y} - \mathbf{S_b} - \mathbf{S_f} = 0
+`$
+
+where $U$, $F$ and $G$ defined as
+
+$`
+\mathbf{U} = \begin{bmatrix} h \\ uh \\ vh \end{bmatrix},
+\mathbf{F} = \begin{bmatrix} hu \\ hu^2 + \frac{1}{2} gh^2 \\ huv \end{bmatrix},
+\mathbf{G} = \begin{bmatrix} hv \\ huv \\ hv^2 + \frac{1}{2} gh^2 \end{bmatrix}
+`$
+
+Z is the bedSurface, h the water depth, u the velocity in
+x-direction and v the velocity in y-direction, g is the constant of gravity.
+
+The source terms for the bed friction $`S_b`$ and bed slope
+$`S_f`$ are given as
+$`
+\mathbf{S_b} = \begin{bmatrix} 0 \\ -gh \frac{\partial z}{\partial x}
+ \\ -gh \frac{\partial z}{\partial y}\end{bmatrix},
+\mathbf{S_f} = \begin{bmatrix} 0 \\ -ghS_{fx} \\ -ghS_{fy}\end{bmatrix}.
+`$
+
+For this example, a cell-centered finite volume method (cctpfa) is applied to solve the SWEs
+in combination with a fully-implicit time discretization. For cases where no sharp fronts or
+traveling waves occur it is possible to apply time steps larger than CFL number = 1 to reduce
+the computation time. Even if a steady state solution is considered, an implicit time stepping method
+is applied.
+
+## Problem set-up
+The model domain is given by a rough channel with a slope of 0.001.
+The domain is 500 meters long and 10 meters wide.
+.
+
+Bottom friction is considered by applying
+the friction law of Manning (Manning n = 0.025). At the lateral sides no friction is considered and a
+no-flow no slip boundary condition is applied. This is the default boundary condition for the shallow water model.
+
+
+At the left border a discharge boundary condition
+is applied as inflow boundary condition with q = -1.0 ($`m^2 s^{-1}`$). At the right border a water fixed depth boundary condition
+is applied for the outflow. Normal flow is assumed, therefore the water depth at the right border is calculated after
+the of Gaukler-Manning-Strickler equation:
+
+ $` v_m = 1/n * R_{hy}^{2/3} * I_s^{1/2}`$
+
+Where the mean velocity $`v_m`$ is given as
+
+$`v_m = \frac{q}{h}`$
+
+$`n`$ is the friction value after Manning. $`R_{hy}`$ the hydraulic radius, which is assumed to be equal to
+the water depth. $`I_s`$ is the bed slope and $`q`$ the unity inflow discharge
+
+The water depth h can be calculated as
+$`h = \left(\frac{n*q}{\sqrt{I_s}} \right)^{3/5}`$
+
+The formula of Gaukler Manning and Strickler is also used to calculate the analytic solution. All parameters
+for the simulation are given in the file *params.input*.
diff --git a/examples/shallowwaterfriction/doc/results.md b/examples/shallowwaterfriction/doc/results.md
new file mode 100644
index 0000000000000000000000000000000000000000..8477f8955bd357a9c7fb956c9537a7b5ed2cbe58
--- /dev/null
+++ b/examples/shallowwaterfriction/doc/results.md
@@ -0,0 +1,2 @@
+## Results
+The solution and the analytical result for the problem is shown in .
diff --git a/examples/shallowwaterfriction/img/domain.png b/examples/shallowwaterfriction/img/domain.png
new file mode 100644
index 0000000000000000000000000000000000000000..27029ab28e1de01c7736fb54be698db508f5777f
Binary files /dev/null and b/examples/shallowwaterfriction/img/domain.png differ
diff --git a/examples/shallowwaterfriction/img/result.png b/examples/shallowwaterfriction/img/result.png
new file mode 100644
index 0000000000000000000000000000000000000000..1ef7c2c9798930cfd4d6b1b8a98b78e0cb718406
Binary files /dev/null and b/examples/shallowwaterfriction/img/result.png differ
diff --git a/examples/shallowwaterfriction/main.cc b/examples/shallowwaterfriction/main.cc
new file mode 100644
index 0000000000000000000000000000000000000000..454411d73ca013209367f2d8d01a792b3968b942
--- /dev/null
+++ b/examples/shallowwaterfriction/main.cc
@@ -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 3 of the License, or *
+ * (at your option) any later version. *
+ * *
+ * This program is distributed in the hope that it will be useful, *
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of *
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
+ * GNU General Public License for more details. *
+ * *
+ * You should have received a copy of the GNU General Public License *
+ * along with this program. If not, see <http://www.gnu.org/licenses/>. *
+ *****************************************************************************/
+// ## The main file
+// This is the main file for the shallow water example. Here we can see the programme sequence and how the system is solved using newton's method.
+// ### Includes
+#include <config.h>
+
+// Standard header file for C++, to get time and date information.
+#include <ctime>
+
+// Standard header file for C++, for in- and output.
+#include <iostream>
+
+// 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.
+#include <dune/common/parallel/mpihelper.hh>
+#include <dune/common/timer.hh>
+#include <dune/grid/io/file/dgfparser/dgfexception.hh>
+#include <dune/grid/io/file/vtk.hh>
+
+// We need the following class to simplify the writing of dumux simulation data to VTK format.
+#include <dumux/io/vtkoutputmodule.hh>
+// 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.
+#include <dumux/common/properties.hh>
+// The following file contains the parameter class, which manages the definition of input parameters by a default value, the inputfile or the command line.
+#include <dumux/common/parameters.hh>
+// The file dumuxmessage.hh contains the class defining the start and end message of the simulation.
+#include <dumux/common/dumuxmessage.hh>
+#include <dumux/common/defaultusagemessage.hh>
+// The gridmanager constructs a grid from the information in the input or grid file. There is a specification for the different supported grid managers.
+#include <dumux/io/grid/gridmanager.hh>
+// We include the linear solver to be used to solve the linear system
+#include <dumux/linear/amgbackend.hh>
+// We include the nonlinear newtons method
+#include <dumux/nonlinear/newtonsolver.hh>
+// Further we include assembler, which assembles the linear systems for finite volume schemes (box-scheme, tpfa-approximation, mpfa-approximation)
+#include <dumux/assembly/fvassembler.hh>
+// We include the problem file which defines initial and boundary conditions to describe our example problem
+#include "problem.hh"
+
+// ### Beginning of the main function
+int main(int argc, char** argv) try
+{
+ using namespace Dumux;
+
+ // We define the type tag for this problem
+ using TypeTag = Properties::TTag::RoughChannel;
+
+ // We initialize MPI, finalize is done automatically on exit
+ const auto& mpiHelper = Dune::MPIHelper::instance(argc, argv);
+
+ // We print dumux start message
+ if (mpiHelper.rank() == 0)
+ DumuxMessage::print(/*firstCall=*/true);
+
+ // We parse command line arguments and input file
+ Parameters::init(argc, argv);
+
+ // ### Create the grid
+ // A gridmanager tries to create the grid either from a grid file or the input file.
+ GridManager<GetPropType<TypeTag, Properties::Grid>> gridManager;
+ gridManager.init();
+
+ // We compute on the leaf grid view
+ const auto& leafGridView = gridManager.grid().leafGridView();
+
+ // ### Setup and solving of the problem
+ // #### Setup
+ // 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.
+ using FVGridGeometry = GetPropType<TypeTag, Properties::FVGridGeometry>;
+ auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
+ fvGridGeometry->update();
+
+ // In the problem, we define the boundary and initial conditions.
+ using Problem = GetPropType<TypeTag, Properties::Problem>;
+ auto problem = std::make_shared<Problem>(fvGridGeometry);
+
+ // We initialize the solution vector
+ using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
+ SolutionVector x(fvGridGeometry->numDofs());
+ problem->applyInitialSolution(x);
+ auto xOld = x;
+
+ // And then use the solutionvector to intialize the gridVariables.
+ using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
+ auto gridVariables = std::make_shared<GridVariables>(problem, fvGridGeometry);
+ gridVariables->init(x);
+
+ // We get some time loop parameters from the input file.
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+ const auto tEnd = getParam<Scalar>("TimeLoop.TEnd");
+ const auto maxDt = getParam<Scalar>("TimeLoop.MaxTimeStepSize");
+ auto dt = getParam<Scalar>("TimeLoop.DtInitial");
+
+ // We intialize the vtk output module. Each model has a predefined model specific output with relevant parameters for that model.
+ using IOFields = GetPropType<TypeTag, Properties::IOFields>;
+ VtkOutputModule<GridVariables, SolutionVector> vtkWriter(*gridVariables,x, problem->name());
+ // We add the analytical solution ("exactWaterDepth" and "exactVelocityX") to the predefined specific output.
+ vtkWriter.addField(problem->getExactWaterDepth(), "exactWaterDepth");
+ vtkWriter.addField(problem->getExactVelocityX(), "exactVelocityX");
+ // We calculate the analytic solution.
+ problem->analyticalSolution();
+ IOFields::initOutputModule(vtkWriter);
+ vtkWriter.write(0.0);
+
+ // We instantiate time loop.
+ auto timeLoop = std::make_shared<CheckPointTimeLoop<Scalar>>(0, dt, tEnd);
+ timeLoop->setMaxTimeStepSize(maxDt);
+
+ //we set the assembler with the time loop because we have an instationary problem.
+ using Assembler = FVAssembler<TypeTag, DiffMethod::numeric>;
+ auto assembler = std::make_shared<Assembler>(problem, fvGridGeometry, gridVariables, timeLoop);
+
+ // We set the linear solver.
+ using LinearSolver = Dumux::AMGBackend<TypeTag>;
+ auto linearSolver = std::make_shared<LinearSolver>(leafGridView, fvGridGeometry->dofMapper());
+
+ // Additionaly, we set the non-linear solver.
+ using NewtonSolver = Dumux::NewtonSolver<Assembler, LinearSolver>;
+ NewtonSolver nonLinearSolver(assembler, linearSolver);
+
+ // We set some check point at the end of the time loop. The check point is used to trigger the vtk output.
+ timeLoop->setCheckPoint(tEnd);
+
+ // We start the time loop.
+ timeLoop->start(); do
+ {
+ // We start to calculate the new solution of that time step. First we define the old solution as the solution of the previous time step for storage evaluations.
+ assembler->setPreviousSolution(xOld);
+
+ // We solve the non-linear system with time step control.
+ nonLinearSolver.solve(x,*timeLoop);
+
+ // We make the new solution the old solution.
+ xOld = x;
+ gridVariables->advanceTimeStep();
+
+ // We advance to the time loop to the next step.
+ timeLoop->advanceTimeStep();
+
+ // We write vtk output, if we reached the check point (end of time loop)
+ if (timeLoop->isCheckPoint())
+ vtkWriter.write(timeLoop->time());
+
+ // We report statistics of this time step.
+ timeLoop->reportTimeStep();
+
+ // We set new dt as suggested by newton controller for the next time step.
+ timeLoop->setTimeStepSize(nonLinearSolver.suggestTimeStepSize(timeLoop->timeStepSize()));
+
+
+ } while (!timeLoop->finished());
+
+ timeLoop->finalize(leafGridView.comm());
+
+ // ### Final Output
+ // We print dumux end message.
+ if (mpiHelper.rank() == 0)
+ {
+ Parameters::print();
+ DumuxMessage::print(/*firstCall=*/false);
+ }
+
+ return 0;
+} // end main
+
+catch (const Dumux::ParameterException &e)
+{
+ std::cerr << std::endl << e << " ---> Abort!" << std::endl;
+ return 1;
+}
+catch (const 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 (const 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/examples/shallowwaterfriction/params.input b/examples/shallowwaterfriction/params.input
new file mode 100644
index 0000000000000000000000000000000000000000..d5bbaaceb4ef21ad7b4f9bc3da42dd59d9fb7e7c
--- /dev/null
+++ b/examples/shallowwaterfriction/params.input
@@ -0,0 +1,22 @@
+[Problem]
+Name = roughchannel
+BedSlope = 0.001 # [-]
+Gravity = 9.81 # [m/s^2]
+Discharge = -1.0 # [m^2/s] discharge per meter at the inflow boundary
+FrictionLaw = Manning
+ManningN = 0.025 # [-]
+# Ks = 0.15 # [m] equivalent sand roughness
+
+[TimeLoop]
+TEnd = 900.0 # [s]
+MaxTimeStepSize = 60.0 # [s]
+DtInitial = 1.0 # [s]
+
+[Grid]
+Positions0 = 0.0 500.0
+Positions1 = 0.0 5.0
+Cells0 = 500
+Cells1 = 5
+
+[Newton]
+EnablePartialReassembly = true
diff --git a/examples/shallowwaterfriction/problem.hh b/examples/shallowwaterfriction/problem.hh
new file mode 100644
index 0000000000000000000000000000000000000000..d3a9293f305927d752adef5ae7ed84228536d8a8
--- /dev/null
+++ b/examples/shallowwaterfriction/problem.hh
@@ -0,0 +1,322 @@
+// -*- 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/>. *
+ *****************************************************************************/
+
+// ## Header guard
+// The header guard (or include guard) prevents compilation errors due to duplicate definitions. Here, a unique name needs to be defined for the header file:
+#ifndef DUMUX_ROUGH_CHANNEL_TEST_PROBLEM_HH
+#define DUMUX_ROUGH_CHANNEL_TEST_PROBLEM_HH
+
+// ## Include files
+// We use the dune yasp grid.
+#include <dune/grid/yaspgrid.hh>
+// We include the cell centered, two-point-flux discretization scheme.
+#include <dumux/discretization/cctpfa.hh>
+// The parameters header is needed to retrieve run-time parameters.
+#include <dumux/common/parameters.hh>
+
+// We include the header which are needed for shallow water models.
+#include <dumux/freeflow/shallowwater/model.hh>
+#include <dumux/freeflow/shallowwater/problem.hh>
+#include <dumux/freeflow/shallowwater/boundaryfluxes.hh>
+
+// We include the header that specifies all spatially variable parameters.
+#include "spatialparams.hh"
+
+// ## Define basic properties for our simulation
+// We enter the namespace Dumux. All Dumux functions and classes are in a namespace Dumux, to make sure they don't clash with symbols from other libraries you may want to use in conjunction with Dumux. One could use these functions and classes by prefixing every use of these names by ::, but that would quickly become cumbersome and annoying. Rather, we simply import the entire Dumux namespace for general use.
+namespace Dumux {
+// The problem class is forward declared.
+template <class TypeTag>
+class RoughChannelProblem;
+
+// We enter the namespace Properties, which is a sub-namespace of the namespace Dumux.
+namespace Properties {
+
+// A TypeTag for our simulation is created which inherits from the shallow water model and the
+// cell centered, two-point-flux discretization scheme.
+namespace TTag {
+struct RoughChannel { using InheritsFrom = std::tuple<ShallowWater, CCTpfaModel>; };
+}
+// We define the grid of our simulation. We use a two-dimensional Yasp Grid.
+template<class TypeTag>
+struct Grid<TypeTag, TTag::RoughChannel>
+{ using type = Dune::YaspGrid<2, Dune::TensorProductCoordinates<GetPropType<TypeTag, Properties::Scalar>, 2> >; };
+
+// We set the problem. The problem class specifies initial and boundary conditions and is defined below.
+template<class TypeTag>
+struct Problem<TypeTag, TTag::RoughChannel>
+{ using type = Dumux::RoughChannelProblem<TypeTag>; };
+
+// We define the spatial parameters for our simulation. The values are specified in the corresponding spatialparameters header file, which is included above.
+template<class TypeTag>
+struct SpatialParams<TypeTag, TTag::RoughChannel>
+{
+private:
+ // We define convenient shortcuts to the properties FVGridGeometry, Scalar, ElementVolumeVariables and VolumeVariables:
+ using FVGridGeometry = GetPropType<TypeTag, Properties::FVGridGeometry>;
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+ using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
+ using VolumeVariables = typename ElementVolumeVariables::VolumeVariables;
+ // Finally we set the spatial parameters:
+public:
+ using type = RoughChannelSpatialParams<FVGridGeometry, Scalar, VolumeVariables>;
+};
+
+// We enable caching for the FV grid geometry and the grid volume variables. The cache
+// stores values that were already calculated for later usage. This makes the simulation faster.
+template<class TypeTag>
+struct EnableFVGridGeometryCache<TypeTag, TTag::RoughChannel>
+{ static constexpr bool value = true; };
+
+template<class TypeTag>
+struct EnableGridVolumeVariablesCache<TypeTag, TTag::RoughChannel>
+{ static constexpr bool value = false; };
+
+// 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 shallow water problem, we inherit from the basic ShallowWaterProblem.
+template <class TypeTag>
+class RoughChannelProblem : public ShallowWaterProblem<TypeTag>
+{
+ // We use convenient declarations that we derive from the property system.
+ using ParentType = ShallowWaterProblem<TypeTag>;
+ using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
+ using BoundaryTypes = GetPropType<TypeTag, Properties::BoundaryTypes>;
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+ using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
+ using FVGridGeometry = GetPropType<TypeTag, Properties::FVGridGeometry>;
+ using NeumannFluxes = GetPropType<TypeTag, Properties::NumEqVector>;
+ using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
+ using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
+ using ElementFluxVariablesCache = typename GridVariables::GridFluxVariablesCache::LocalView;
+ using VolumeVariables = typename ElementVolumeVariables::VolumeVariables;
+ using FVElementGeometry = typename GetPropType<TypeTag, Properties::FVGridGeometry>::LocalView;
+ using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace;
+ using GridView = GetPropType<TypeTag, Properties::GridView>;
+ using Element = typename GridView::template Codim<0>::Entity;
+ using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+ using NumEqVector = GetPropType<TypeTag, Properties::NumEqVector>;
+ using SubControlVolume = typename FVElementGeometry::SubControlVolume;
+
+public:
+ // This is the constructor of our problem class.
+ RoughChannelProblem(std::shared_ptr<const FVGridGeometry> fvGridGeometry)
+ : ParentType(fvGridGeometry)
+ {
+ // We read the parameters from the params.input file.
+ name_ = getParam<std::string>("Problem.Name");
+ constManningN_ = getParam<Scalar>("Problem.ManningN");
+ bedSlope_ = getParam<Scalar>("Problem.BedSlope");
+ discharge_ = getParam<Scalar>("Problem.Discharge");
+ // We calculate the outflow boundary condition using the Gauckler-Manning-Strickler formula.
+ hBoundary_ = this->gauklerManningStrickler(discharge_,constManningN_,bedSlope_);
+ // We initialize the analytic solution to a verctor of the appropriate size filled with zeros.
+ exactWaterDepth_.resize(fvGridGeometry->numDofs(), 0.0);
+ exactVelocityX_.resize(fvGridGeometry->numDofs(), 0.0);
+ }
+
+ // Get the analytical water depth
+ const std::vector<Scalar>& getExactWaterDepth()
+ {
+ return exactWaterDepth_;
+ }
+
+ // Get the analytical velocity
+ const std::vector<Scalar>& getExactVelocityX()
+ {
+ return exactVelocityX_;
+ }
+
+ // Get the water depth with Gauckler-Manning-Strickler
+ Scalar gauklerManningStrickler(Scalar discharge, Scalar manningN, Scalar bedSlope)
+ {
+ using std::pow;
+ using std::abs;
+ using std::sqrt;
+
+ return pow(abs(discharge)*manningN/sqrt(bedSlope), 0.6);
+ }
+
+ // Get the analytical solution
+ void analyticalSolution()
+ {
+ using std::abs;
+
+ for (const auto& element : elements(this->fvGridGeometry().gridView()))
+ {
+ const Scalar h = this->gauklerManningStrickler(discharge_,constManningN_,bedSlope_);
+ const Scalar u = abs(discharge_)/h;
+
+ const auto eIdx = this->fvGridGeometry().elementMapper().index(element);
+ exactWaterDepth_[eIdx] = h;
+ exactVelocityX_[eIdx] = u;
+ }
+ }
+
+ // Get the problem name. It is used as a prefix for files generated by the simulation.
+ const std::string& name() const
+ {
+ return name_;
+ }
+
+ // Get the source term.
+ NumEqVector source(const Element& element,
+ const FVElementGeometry& fvGeometry,
+ const ElementVolumeVariables& elemVolVars,
+ const SubControlVolume &scv) const
+ {
+
+ NumEqVector source (0.0);
+
+ // In this model the bottom friction is the only source.
+ source += bottomFrictionSource(element, fvGeometry, elemVolVars, scv);
+
+ return source;
+ }
+
+ // Get the source term due to bottom friction.
+ NumEqVector bottomFrictionSource(const Element& element,
+ const FVElementGeometry& fvGeometry,
+ const ElementVolumeVariables& elemVolVars,
+ const SubControlVolume &scv) const
+ {
+ NumEqVector bottomFrictionSource(0.0);
+ const auto& volVars = elemVolVars[scv];
+
+ // For the calculation of the source term due to bottom friction the two-dimensional bottom shear stess vector is needed. This is the force per area, which works between the flow and the bed. It is calculated within the `FrictionLaw`, which is a spatialParameter. In this model the `FrictionLawManning` is used (see `params.input`).
+ Dune::FieldVector<Scalar, 2> bottomShearStress = this->spatialParams().frictionLaw(element, scv).shearStress(volVars);
+
+ // The bottom shear stress causes a pure loss of momentum. Thus the first entry of the `bottomFrictionSource`, which is related to the mass balance equation is zero. The second entry of the `bottomFricitonSource` corresponds to the momentum equation in x-direction and is therefore equal to the first, the x-component, of the `bottomShearStress`. Accordingly the third entry of the `bottomFrictionSource` is equal to the second component of the `bottomShearStress`.
+ bottomFrictionSource[0] = 0.0;
+ bottomFrictionSource[1] = bottomShearStress[0];
+ bottomFrictionSource[2] = bottomShearStress[1];
+
+ return bottomFrictionSource;
+ }
+
+ // We specify the boundary condition type.
+ BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const
+ {
+ BoundaryTypes bcTypes;
+ // Since we use a weak imposition all boundary conditions are of Neumann type.
+ bcTypes.setAllNeumann();
+ return bcTypes;
+ }
+
+ // We specify the neumann boundary. Due to the weak imposition we calculate the flux at the boundary, with a Rieman solver. For this the state of a virtual cell outside of the boundary is needed (`boundaryStateVariables`), wich is calculated with the Riemann invariants (see Yoon and Kang, Finite Volume Model for Two-Dimensional Shallow Water Flows on Unstructured Grids) . The calculation of the Riemann invariants differ depending on the type of the boundary (h, q or no-flow boundary).
+ NeumannFluxes neumann(const Element& element,
+ const FVElementGeometry& fvGeometry,
+ const ElementVolumeVariables& elemVolVars,
+ const ElementFluxVariablesCache& elemFluxVarsCache,
+ const SubControlVolumeFace& scvf) const
+ {
+ NeumannFluxes values(0.0);
+
+ const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
+ const auto& insideVolVars = elemVolVars[insideScv];
+ const auto& nxy = scvf.unitOuterNormal();
+ const auto gravity = this->spatialParams().gravity(scvf.center());
+ std::array<Scalar, 3> boundaryStateVariables;
+
+ // Calculate the rieman invariants for imposed discharge at the left side.
+ if (scvf.center()[0] < 0.0 + eps_)
+ {
+ boundaryStateVariables = ShallowWater::fixedDischargeBoundary(discharge_,
+ insideVolVars.waterDepth(),
+ insideVolVars.velocity(0),
+ insideVolVars.velocity(1),
+ gravity,
+ nxy);
+ }
+ // Calculate the rieman invariants for impose water depth at the right side.
+ else if (scvf.center()[0] > 100.0 - eps_)
+ {
+ boundaryStateVariables = ShallowWater::fixedWaterDepthBoundary(hBoundary_,
+ insideVolVars.waterDepth(),
+ insideVolVars.velocity(0),
+ insideVolVars.velocity(1),
+ gravity,
+ nxy);
+ }
+ // Calculate the rieman invarianty for the no-flow boundary.
+ else
+ {
+ boundaryStateVariables[0] = insideVolVars.waterDepth();
+ boundaryStateVariables[1] = -insideVolVars.velocity(0);
+ boundaryStateVariables[2] = -insideVolVars.velocity(1);
+ }
+ // We calculate the boundary fluxes based on a Riemann problem.
+ auto riemannFlux = ShallowWater::riemannProblem(insideVolVars.waterDepth(),
+ boundaryStateVariables[0],
+ insideVolVars.velocity(0),
+ boundaryStateVariables[1],
+ insideVolVars.velocity(1),
+ boundaryStateVariables[2],
+ insideVolVars.bedSurface(),
+ insideVolVars.bedSurface(),
+ gravity,
+ nxy);
+
+ values[Indices::massBalanceIdx] = riemannFlux[0];
+ values[Indices::velocityXIdx] = riemannFlux[1];
+ values[Indices::velocityYIdx] = riemannFlux[2];
+
+ return values;
+ }
+
+ // We set the initial conditions. In this example constant initial conditions are used. Therefore the argument `globalPos` is not needed. If you want to impose spatial variable initial conditions, you have to use the `globalPos`.
+ PrimaryVariables initialAtPos(const GlobalPosition &globalPos) const
+ {
+ PrimaryVariables values(0.0);
+ // We set the initial water depth to one meter.
+ values[0] = 1.0;
+ // We set the x-component of the initial velocity to zero.
+ values[1] = 0.0;
+ // We set the y-component of the initial velocity to zero.
+ values[2] = 0.0;
+
+ return values;
+ };
+
+ // \}
+
+private:
+ // We declare the private variables of the problem. They are initialized in the problems constructor.
+ // We declare the variable for the analytic solution.
+ std::vector<Scalar> exactWaterDepth_;
+ std::vector<Scalar> exactVelocityX_;
+ // constant friction value. An analytic solution is only available for const friction. If you want to run the simulation with a non constant friciton value (specified in the spatialParams) you have to remove the analytic solution.
+ Scalar constManningN_;
+ // The constant bed slope.
+ Scalar bedSlope_;
+ // The water depth at the outflow boundary.
+ Scalar hBoundary_;
+ // The discharge at the inflow boundary.
+ Scalar discharge_;
+ // eps is used as a small value for the definition of the boundry conditions
+ static constexpr Scalar eps_ = 1.0e-6;
+ std::string name_;
+};
+// We leave the namespace Dumux.
+}
+
+#endif
diff --git a/examples/shallowwaterfriction/spatialparams.hh b/examples/shallowwaterfriction/spatialparams.hh
new file mode 100644
index 0000000000000000000000000000000000000000..a6e6f315afe0435dfc7eebc5e1568115464960a1
--- /dev/null
+++ b/examples/shallowwaterfriction/spatialparams.hh
@@ -0,0 +1,116 @@
+// -*- 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/>. *
+ *****************************************************************************/
+
+// the header guard
+#ifndef DUMUX_ROUGH_CHANNEL_SPATIAL_PARAMETERS_HH
+#define DUMUX_ROUGH_CHANNEL_SPATIAL_PARAMETERS_HH
+
+// We include the basic spatial parameters for finite volumes file from which we will inherit
+#include <dumux/material/spatialparams/fv.hh>
+// The parameters header is needed to retrieve run-time parameters.
+#include <dumux/common/parameters.hh>
+// We include all friction laws, between we can choose for the calculation of the bottom friction source.
+#include <dumux/material/fluidmatrixinteractions/frictionlaws/frictionlaw.hh>
+#include <dumux/material/fluidmatrixinteractions/frictionlaws/manning.hh>
+#include <dumux/material/fluidmatrixinteractions/frictionlaws/nikuradse.hh>
+
+// We enter the namespace Dumux. All Dumux functions and classes are in a namespace Dumux, to make sure they don`t clash with symbols from other libraries you may want to use in conjunction with Dumux.
+namespace Dumux {
+
+//In the RoughChannelSpatialParams class we define all functions needed to describe the spatial distributed parameters.
+template<class FVGridGeometry, class Scalar, class VolumeVariables>
+class RoughChannelSpatialParams
+: public FVSpatialParams<FVGridGeometry, Scalar,
+ RoughChannelSpatialParams<FVGridGeometry, Scalar, VolumeVariables>>
+{
+ // We introduce using declarations that are derived from the property system which we need in this class
+ using ThisType = RoughChannelSpatialParams<FVGridGeometry, Scalar, VolumeVariables>;
+ using ParentType = FVSpatialParams<FVGridGeometry, Scalar, ThisType>;
+ using GridView = typename FVGridGeometry::GridView;
+ using FVElementGeometry = typename FVGridGeometry::LocalView;
+ using SubControlVolume = typename FVElementGeometry::SubControlVolume;
+ using Element = typename GridView::template Codim<0>::Entity;
+ using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+public:
+ // In the constructor be read some values from the `params.input` and initialize the friciton law.
+ RoughChannelSpatialParams(std::shared_ptr<const FVGridGeometry> fvGridGeometry)
+ : ParentType(fvGridGeometry)
+ {
+ gravity_ = getParam<Scalar>("Problem.Gravity");
+ bedSlope_ = getParam<Scalar>("Problem.BedSlope");
+ frictionLawType_ = getParam<std::string>("Problem.FrictionLaw");
+ initFrictionLaw();
+ }
+
+ // We initialize the friction law based on the law specified in `params.input`.
+ void initFrictionLaw()
+ {
+ if (frictionLawType_ == "Manning")
+ {
+ Scalar manningN = getParam<Scalar>("Problem.ManningN");
+ frictionLaw_ = std::make_unique<FrictionLawManning<VolumeVariables>>(gravity_, manningN);
+ }
+ else if (frictionLawType_ == "Nikuradse")
+ {
+ Scalar ks = getParam<Scalar>("Problem.Ks");
+ frictionLaw_ = std::make_unique<FrictionLawNikuradse<VolumeVariables>>(ks);
+ }
+ else
+ {
+ std::cout<<"The FrictionLaw in params.input is unknown. Valid entries are `Manning` and `Nikuradse`!"<<std::endl;
+ }
+ }
+
+ // Use this function, if you want to vary the value for the gravity.
+ Scalar gravity(const GlobalPosition& globalPos) const
+ {
+ return gravity_;
+ }
+
+ // Use this function for a constant gravity.
+ Scalar gravity() const
+ {
+ return gravity_;
+ }
+
+ // This function returns an object of the friction law class, which is initialized with the appropriate friction values. If you want to use different friciton values or laws, you have to use a vector of unique_ptr for `frictionLaw_` and pick the right friction law instances via the `element` argument.
+ const FrictionLaw<VolumeVariables>& frictionLaw(const Element& element,
+ const SubControlVolume& scv) const
+ {
+ return *frictionLaw_;
+ }
+
+ // Define the bed surface based on the `bedSlope_`.
+ Scalar bedSurface(const Element& element,
+ const SubControlVolume& scv) const
+ {
+ return 10.0 - element.geometry().center()[0] * bedSlope_;
+ }
+
+private:
+ Scalar gravity_;
+ Scalar bedSlope_;
+ std::string frictionLawType_;
+ std::unique_ptr<FrictionLaw<VolumeVariables>> frictionLaw_;
+};
+// end of namespace Dumux.
+}
+
+#endif
diff --git a/test/references/example_shallowwaterfriction-reference.vtu b/test/references/example_shallowwaterfriction-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..160635612376f8d5f8c6f97493f952ecff6546eb
--- /dev/null
+++ b/test/references/example_shallowwaterfriction-reference.vtu
@@ -0,0 +1,3713 @@
+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="0.1" byte_order="LittleEndian">
+ <UnstructuredGrid>
+ <Piece NumberOfCells="2500" NumberOfPoints="3006">
+ <CellData Scalars="waterDepth">
+ <DataArray type="Float32" Name="waterDepth" NumberOfComponents="1" format="ascii">
+ 0.868698 0.868375 0.868376 0.868377 0.868378 0.868379 0.86838 0.868381 0.868382 0.868382 0.868383 0.868384
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