From 33fe841be9c05c3b4856461a93d4760ae20197c9 Mon Sep 17 00:00:00 2001
From: "leopold.stadler" <leopold.stadler@baw.de>
Date: Wed, 4 Mar 2020 14:30:10 +0100
Subject: [PATCH] [test][shallowwater] Add bowl test for new upwind mobility
---
test/freeflow/shallowwater/CMakeLists.txt | 1 +
.../freeflow/shallowwater/bowl/CMakeLists.txt | 11 +
test/freeflow/shallowwater/bowl/main.cc | 203 +
test/freeflow/shallowwater/bowl/params.input | 39 +
test/freeflow/shallowwater/bowl/problem.hh | 385 ++
.../shallowwater/bowl/spatialparams.hh | 136 +
.../test_ff_shallowwater_bowl-reference.vtu | 3401 +++++++++++++++++
7 files changed, 4176 insertions(+)
create mode 100644 test/freeflow/shallowwater/bowl/CMakeLists.txt
create mode 100644 test/freeflow/shallowwater/bowl/main.cc
create mode 100644 test/freeflow/shallowwater/bowl/params.input
create mode 100644 test/freeflow/shallowwater/bowl/problem.hh
create mode 100644 test/freeflow/shallowwater/bowl/spatialparams.hh
create mode 100644 test/references/test_ff_shallowwater_bowl-reference.vtu
diff --git a/test/freeflow/shallowwater/CMakeLists.txt b/test/freeflow/shallowwater/CMakeLists.txt
index dcb3adcc65..a2d8ca961e 100644
--- a/test/freeflow/shallowwater/CMakeLists.txt
+++ b/test/freeflow/shallowwater/CMakeLists.txt
@@ -1,2 +1,3 @@
+add_subdirectory(bowl)
add_subdirectory(dambreak)
add_subdirectory(roughchannel)
diff --git a/test/freeflow/shallowwater/bowl/CMakeLists.txt b/test/freeflow/shallowwater/bowl/CMakeLists.txt
new file mode 100644
index 0000000000..a456bb95c9
--- /dev/null
+++ b/test/freeflow/shallowwater/bowl/CMakeLists.txt
@@ -0,0 +1,11 @@
+dune_symlink_to_source_files(FILES "params.input")
+
+dumux_add_test(NAME test_shallowwater_bowl
+ SOURCES main.cc
+ COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+ CMD_ARGS --script fuzzy
+ --files ${CMAKE_SOURCE_DIR}/test/references/test_ff_shallowwater_bowl-reference.vtu
+ ${CMAKE_CURRENT_BINARY_DIR}/bowl-00001.vtu
+ --zeroThreshold {"velocityY":1e-14}
+ --command "${CMAKE_CURRENT_BINARY_DIR}/test_shallowwater_bowl params.input
+ -Problem.Name bowl")
diff --git a/test/freeflow/shallowwater/bowl/main.cc b/test/freeflow/shallowwater/bowl/main.cc
new file mode 100644
index 0000000000..606c600286
--- /dev/null
+++ b/test/freeflow/shallowwater/bowl/main.cc
@@ -0,0 +1,203 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ * See the file COPYING for full copying permissions. *
+ * *
+ * This program is free software: you can redistribute it and/or modify *
+ * it under the terms of the GNU General Public License as published by *
+ * the Free Software Foundation, either version 2 of the License, or *
+ * (at your option) any later version. *
+ * *
+ * This program is distributed in the hope that it will be useful, *
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of *
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
+ * GNU General Public License for more details. *
+ * *
+ * You should have received a copy of the GNU General Public License *
+ * along with this program. If not, see <http://www.gnu.org/licenses/>. *
+ *****************************************************************************/
+/*!
+ * \file
+ * \ingroup ShallowWaterTests
+ * \brief A test for the shallow water model (bowl).
+ */
+#include <config.h>
+
+#include <ctime>
+#include <iostream>
+
+#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>
+#include <dumux/io/vtkoutputmodule.hh>
+
+#include <dumux/common/properties.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/dumuxmessage.hh>
+
+#include <dumux/io/grid/gridmanager.hh>
+#include <dumux/linear/amgbackend.hh>
+#include <dumux/nonlinear/newtonsolver.hh>
+
+#include <dumux/assembly/fvassembler.hh>
+
+#include "problem.hh"
+
+////////////////////////
+// the main function
+////////////////////////
+int main(int argc, char** argv) try
+{
+ using namespace Dumux;
+
+ // define the type tag for this problem
+ using TypeTag = Properties::TTag::Bowl;
+
+ // initialize MPI, finalize is done automatically on exit
+ const auto& mpiHelper = Dune::MPIHelper::instance(argc, argv);
+
+ // print dumux start message
+ if (mpiHelper.rank() == 0)
+ DumuxMessage::print(/*firstCall=*/true);
+
+ // parse command line arguments and input file
+ Parameters::init(argc, argv);
+
+ // try to create a grid (from the given grid file or the input file)
+ GridManager<GetPropType<TypeTag, Properties::Grid>> gridManager;
+ gridManager.init();
+
+ ////////////////////////////////////////////////////////////
+ // run instationary non-linear problem on this grid
+ ////////////////////////////////////////////////////////////
+
+ // we compute on the leaf grid view
+ const auto& leafGridView = gridManager.grid().leafGridView();
+
+ // create the finite volume grid geometry
+ using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+ auto gridGeometry = std::make_shared<GridGeometry>(leafGridView);
+ gridGeometry->update();
+
+ // the problem (initial and boundary conditions)
+ using Problem = GetPropType<TypeTag, Properties::Problem>;
+ auto problem = std::make_shared<Problem>(gridGeometry);
+
+ // the solution vector
+ using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
+ SolutionVector x(gridGeometry->numDofs());
+ problem->applyInitialSolution(x);
+ auto xOld = x;
+
+ // the grid variables
+ using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
+ auto gridVariables = std::make_shared<GridVariables>(problem, gridGeometry);
+ gridVariables->init(x);
+
+ // get some time loop parameters
+ 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");
+
+ // intialize the vtk output module
+ using IOFields = GetPropType<TypeTag, Properties::IOFields>;
+
+ VtkOutputModule<GridVariables, SolutionVector> vtkWriter(*gridVariables,x, problem->name());
+ vtkWriter.addField(problem->getExactWaterDepth(), "exactWaterDepth");
+ problem->updateAnalyticalSolution(0.0);
+ IOFields::initOutputModule(vtkWriter);
+ vtkWriter.write(0.0);
+
+ // instantiate time loop
+ auto timeLoop = std::make_shared<CheckPointTimeLoop<Scalar>>(0, dt, tEnd);
+ timeLoop->setMaxTimeStepSize(maxDt);
+
+ // the assembler with time loop for instationary problem
+ using Assembler = FVAssembler<TypeTag, DiffMethod::numeric>;
+ auto assembler = std::make_shared<Assembler>(problem, gridGeometry, gridVariables, timeLoop, xOld);
+
+ // the linear solver
+ using LinearSolver = AMGBiCGSTABBackend<LinearSolverTraits<GridGeometry>>;
+ auto linearSolver = std::make_shared<LinearSolver>(leafGridView, gridGeometry->dofMapper());
+
+ // the non-linear solver
+ using NewtonSolver = Dumux::NewtonSolver<Assembler, LinearSolver>;
+ NewtonSolver nonLinearSolver(assembler, linearSolver);
+
+ //! set some check point at the end of the time loop
+ timeLoop->setCheckPoint(tEnd);
+
+ //! Compute L2 error for the initial solution (should be zero)
+ problem->computeL2error(timeLoop->time(), x, *gridVariables);
+
+ // time loop
+ timeLoop->start(); do
+ {
+ nonLinearSolver.solve(x,*timeLoop);
+
+ // make the new solution the old solution
+ xOld = x;
+ gridVariables->advanceTimeStep();
+
+ // update the analytical solution
+ problem->updateAnalyticalSolution(timeLoop->time());
+ problem->computeL2error(timeLoop->time(), x, *gridVariables);
+
+ // advance to the time loop to the next step
+ timeLoop->advanceTimeStep();
+
+ // write vtk output
+ if (timeLoop->isCheckPoint())
+ vtkWriter.write(timeLoop->time());
+
+ // report statistics of this time step
+ timeLoop->reportTimeStep();
+
+ // set new dt as suggested by newton controller
+ timeLoop->setTimeStepSize(nonLinearSolver.suggestTimeStepSize(timeLoop->timeStepSize()));
+
+
+ } while (!timeLoop->finished());
+
+ timeLoop->finalize(leafGridView.comm());
+
+ ////////////////////////////////////////////////////////////
+ // finalize, print dumux message to say goodbye
+ ////////////////////////////////////////////////////////////
+
+ // print dumux end message
+ if (mpiHelper.rank() == 0)
+ {
+ Parameters::print();
+ DumuxMessage::print(/*firstCall=*/false);
+ }
+
+ return 0;
+}
+
+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/test/freeflow/shallowwater/bowl/params.input b/test/freeflow/shallowwater/bowl/params.input
new file mode 100644
index 0000000000..6c91f7db0e
--- /dev/null
+++ b/test/freeflow/shallowwater/bowl/params.input
@@ -0,0 +1,39 @@
+[Problem]
+Name = bowl
+BowlDepthAtCenter = 0.03 # [m]
+BowlParaboloidRadius = 1.6 # [m]
+BowlInitialWaterElevationAtCenter = 0.005 # [m]
+Gravity = 9.81 # [m/s^2]
+
+[FluxLimiterLET]
+UpperWaterDepth = 1.0E-5
+LowerWaterDepth = 1.0E-7
+UpwindFluxLimiting = true
+
+[TimeLoop]
+TEnd = 13.104 # [s] 6.552 is one period
+MaxTimeStepSize = 0.1 # [s]
+DtInitial = 0.01 # [s]
+
+[Grid]
+Positions0 = -2.0 2.0
+Positions1 = -2.0 2.0
+Cells0 = 50
+Cells1 = 50
+
+[Newton]
+EnableAbsoluteResidualCriterion = true
+MaxAbsoluteResidual = 1e-6
+RetryTimeStepReductionFactor = 0.5
+SatisfyResidualAndShiftCriterion = "false"
+EnableDynamicOutput = false
+EnablePartialReassembly = false
+TargetSteps = 6
+MaxSteps = 10
+UseLineSearch = true
+
+[LinearSolver]
+MaxIterations = 200
+ResidualReduction = 1e-5
+
+
diff --git a/test/freeflow/shallowwater/bowl/problem.hh b/test/freeflow/shallowwater/bowl/problem.hh
new file mode 100644
index 0000000000..89a09b7200
--- /dev/null
+++ b/test/freeflow/shallowwater/bowl/problem.hh
@@ -0,0 +1,385 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ * See the file COPYING for full copying permissions. *
+ * *
+ * This program is free software: you can redistribute it and/or modify *
+ * it under the terms of the GNU General Public License as published by *
+ * the Free Software Foundation, either version 2 of the License, or *
+ * (at your option) any later version. *
+ * *
+ * This program is distributed in the hope that it will be useful, *
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of *
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
+ * GNU General Public License for more details. *
+ * *
+ * You should have received a copy of the GNU General Public License *
+ * along with this program. If not, see <http://www.gnu.org/licenses/>. *
+ *****************************************************************************/
+/*!
+ * \file
+ * \ingroup ShallowWaterTests
+ * \brief A test for the Shallow water model (bowl).
+ */
+#ifndef DUMUX_BOWL_TEST_PROBLEM_HH
+#define DUMUX_BOWL_TEST_PROBLEM_HH
+
+#include <dune/grid/yaspgrid.hh>
+#include <dumux/discretization/cctpfa.hh>
+#include "spatialparams.hh"
+#include <dumux/common/parameters.hh>
+
+#include <dumux/freeflow/shallowwater/model.hh>
+#include <dumux/freeflow/shallowwater/problem.hh>
+#include <dumux/freeflow/shallowwater/boundaryfluxes.hh>
+
+namespace Dumux {
+
+template <class TypeTag>
+class BowlProblem;
+
+// Specify the properties for the problem
+namespace Properties {
+
+// Create new type tags
+namespace TTag {
+struct Bowl { using InheritsFrom = std::tuple<ShallowWater, CCTpfaModel>; };
+} // end namespace TTag
+
+template<class TypeTag>
+struct Grid<TypeTag, TTag::Bowl>
+{ using type = Dune::YaspGrid<2, Dune::TensorProductCoordinates<GetPropType<TypeTag, Properties::Scalar>, 2> >; };
+
+// Set the problem property
+template<class TypeTag>
+struct Problem<TypeTag, TTag::Bowl>
+{ using type = Dumux::BowlProblem<TypeTag>; };
+
+// Set the spatial parameters
+template<class TypeTag>
+struct SpatialParams<TypeTag, TTag::Bowl>
+{
+private:
+ using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+ using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
+ using VolumeVariables = typename ElementVolumeVariables::VolumeVariables;
+public:
+ using type = BowlSpatialParams<GridGeometry, Scalar, VolumeVariables>;
+};
+
+template<class TypeTag>
+struct EnableGridGeometryCache<TypeTag, TTag::Bowl>
+{ static constexpr bool value = true; };
+
+template<class TypeTag>
+struct EnableGridVolumeVariablesCache<TypeTag, TTag::Bowl>
+{ static constexpr bool value = false; };
+} // end namespace Properties
+
+/*!
+ * \ingroup ShallowWaterTests
+ * \brief A wetting and drying test with sloshing water in a bowl.
+ *
+ * The domain is 4 meters long and 4 meters wide. The center of the domain is loacted at
+ * x = 0 and y = 0. There is no flow over the boundaries and no friction is considered.
+ *
+ * This example is demanding for the implicit model if a high mesh resolution is applied
+ * (e.g. 150x150 cells) in combination with a large time step size. Using the new limiting
+ * (UpwindFluxLimiting = true) will help to improve the convergence for such cases.
+ *
+ * This test uses a low mesh resoultion and only ensures that UpwindFluxLimiting for the mobility
+ * works.
+ *
+ * The results are checked against a analytical solution which is based on the "Thacker-Solution"
+ * (William Thacker, "Some exact solutions to the nonlinear shallow-water wave equations", Journal
+ * of Fluid Mechanics, 107:499–508, 1981). Further examples and details on the solution are given
+ * in SWASHES (Shallow Water Analytic Solutions for Hydraulic and Environmental Studies,
+ * https://www.idpoisson.fr/swashes/).
+ *
+ * This problem uses the \ref ShallowWaterModel
+ */
+template <class TypeTag>
+class BowlProblem : public ShallowWaterProblem<TypeTag>
+{
+ 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 GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+ 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::GridGeometry>::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;
+ using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
+
+public:
+ BowlProblem(std::shared_ptr<const GridGeometry> gridGeometry)
+ : ParentType(gridGeometry)
+ {
+ using std::sqrt;
+ using std::pow;
+
+ name_ = getParam<std::string>("Problem.Name");
+ gravity_ = getParam<Scalar>("Problem.Gravity");
+ bowlDepthAtCenter_ = getParam<Scalar>("Problem.BowlDepthAtCenter");
+ bowlParaboloidRadius_ = getParam<Scalar>("Problem.BowlParaboloidRadius");
+ bowlInitialWaterElevationAtCenter_ = getParam<Scalar>("Problem.BowlInitialWaterElevationAtCenter");
+ bowlAnalyticParameterOmega_ = sqrt(8.0 * gravity_ * bowlDepthAtCenter_) / bowlParaboloidRadius_;
+ bowlAnalyticParameterA_ = (pow(bowlDepthAtCenter_ + bowlInitialWaterElevationAtCenter_, 2.0) -
+ pow(bowlDepthAtCenter_, 2.0)) /
+ (pow(bowlDepthAtCenter_ + bowlInitialWaterElevationAtCenter_, 2.0)+
+ pow(bowlDepthAtCenter_, 2.0));
+ exactWaterDepth_.resize(gridGeometry->numDofs(), 0.0);
+ updateAnalyticalSolution(0.0);
+ }
+
+ //! Get the analytical water depth
+ const std::vector<Scalar>& getExactWaterDepth()
+ {
+ return exactWaterDepth_;
+ }
+
+ //! Get the analctic water depth at
+ Scalar calculateAnalyticWaterDepth(Scalar time, Scalar x, Scalar y)
+ {
+ using std::max;
+ using std::sqrt;
+ using std::pow;
+ using std::cos;
+
+ auto waterDepth = max(bowlDepthAtCenter_* ((sqrt(1.0 - pow(bowlAnalyticParameterA_, 2.0)))/
+ (1.0 - bowlAnalyticParameterA_ * cos(bowlAnalyticParameterOmega_ * time))-
+ 1.0 - (pow(x, 2.0) + pow(y, 2.0)) / pow(bowlParaboloidRadius_, 2.0) *
+ ((1.0- pow(bowlAnalyticParameterA_, 2.0)) /
+ (pow(1.0 - bowlAnalyticParameterA_ *
+ cos(bowlAnalyticParameterOmega_ * time), 2.0)) - 1.0)) -
+ bowlDepthAtCenter_ *((pow(x, 2.0) + pow(y, 2.0))/
+ pow(bowlParaboloidRadius_, 2.0) - 1.0), 1.0E-5);
+
+ return waterDepth;
+ }
+
+ //! Compute L2 error
+ void computeL2error(const Scalar time,
+ const SolutionVector& curSol,
+ const GridVariables& gridVariables)
+ {
+ Scalar l2error = 0.0;
+
+ //first ensure that the Analytical solution is up-to-date
+ updateAnalyticalSolution(time);
+
+ for (const auto& element : elements(this->gridGeometry().gridView()))
+ {
+ const auto eIdx = this->gridGeometry().elementMapper().index(element);
+ const auto& globalPos = element.geometry().center();
+ auto fvGeometry = localView(this->gridGeometry());
+ fvGeometry.bindElement(element);
+ auto elemVolVars = localView(gridVariables.curGridVolVars());
+ elemVolVars.bindElement(element, fvGeometry, curSol);
+ exactWaterDepth_[eIdx] = calculateAnalyticWaterDepth(time, globalPos[0], globalPos[1]);
+
+ for (auto&& scv : scvs(fvGeometry))
+ {
+ using std::pow;
+ l2error += pow(exactWaterDepth_[eIdx] - elemVolVars[scv].waterDepth(), 2.0);
+ }
+ }
+ using std::sqrt;
+ l2error = sqrt(l2error);
+ l2error = this->gridGeometry().gridView().comm().sum(l2error);
+
+ if (this->gridGeometry().gridView().comm().rank() == 0)
+ {
+ std::cout << "L2 error at t = "
+ << time << " seconds "
+ << " for "
+ << std::setw(6) << this->gridGeometry().gridView().size(0)
+ << " elements: "
+ << std::scientific
+ << l2error
+ << std::endl;
+ }
+ }
+
+ //! Udpate the analytical solution
+ void updateAnalyticalSolution(const Scalar time)
+ {
+ for (const auto& element : elements(this->gridGeometry().gridView()))
+ {
+ const auto eIdx = this->gridGeometry().elementMapper().index(element);
+ const auto& globalPos = element.geometry().center();
+
+ exactWaterDepth_[eIdx] = calculateAnalyticWaterDepth(time, globalPos[0], globalPos[1]);
+ }
+ }
+
+ /*!
+ * \name Problem parameters
+ */
+ // \{
+
+ /*!
+ * \brief The problem name
+ *
+ * This is used as a prefix for files generated by the simulation.
+ */
+ const std::string& name() const
+ {
+ return name_;
+ }
+
+ /*!
+ * \brief Evaluate the source term for all balance equations within a given
+ * sub-control-volume.
+ *
+ * This is the method for the case where the source term is
+ * potentially solution dependent and requires some quantities that
+ * are specific to the fully-implicit method.
+ *
+ * \param element The finite element
+ * \param fvGeometry The finite-volume geometry
+ * \param elemVolVars All volume variables for the element
+ * \param scv The sub control volume
+ *
+ * For this method, the \a values parameter stores the conserved quantity rate
+ * generated or annihilate per volume unit. Positive values mean
+ * that the conserved quantity is created, negative ones mean that it vanishes.
+ * E.g. for the mass balance that would be a mass rate in \f$ [ kg / (m^3 \cdot s)] \f$.
+ */
+ NumEqVector source(const Element& element,
+ const FVElementGeometry& fvGeometry,
+ const ElementVolumeVariables& elemVolVars,
+ const SubControlVolume &scv) const
+ {
+ NumEqVector source (0.0);
+
+ return source;
+ }
+
+ // \}
+
+ /*!
+ * \name Boundary conditions
+ */
+ // \{
+
+ /*!
+ * \brief Specifies which kind of boundary condition should be
+ * used for which equation on a given boundary segment.
+ *
+ * \param globalPos The position for which the boundary type is set
+ */
+ BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const
+ {
+ BoundaryTypes bcTypes;
+ bcTypes.setAllNeumann();
+ return bcTypes;
+ }
+
+ /*!
+ * \brief Specifies the neumann boundary
+ *
+ * We need the Riemann invariants to compute the values depending of the boundary type.
+ * Since we use a weak imposition we do not have a dirichlet value. We impose fluxes
+ * based on q, h, etc. computed with the Riemann invariants
+ *
+ * \param element
+ * \param fvGeometry
+ * \param elemVolVars
+ * \param scvf
+ */
+ 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;
+
+ //no flow with zero normal velocity and tangential velocity
+ const auto vNormalGhost = -(nxy[0] * insideVolVars.velocity(0) + nxy[1] * insideVolVars.velocity(1));
+ const auto vTangentialGhost = -nxy[1] * insideVolVars.velocity(0) + nxy[0] * insideVolVars.velocity(1);
+
+ boundaryStateVariables[0] = insideVolVars.waterDepth();
+ boundaryStateVariables[1] = nxy[0] * vNormalGhost - nxy[1] * vTangentialGhost;
+ boundaryStateVariables[2] = nxy[1] * vNormalGhost + nxy[0] * vTangentialGhost;
+
+ 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;
+ }
+
+ // \}
+
+ /*!
+ * \name Volume terms
+ */
+ // \{
+
+ /*!
+ * \brief Evaluate the initial values for a control volume.
+ *
+ * For this method, the \a values parameter stores primary
+ * variables.
+ *
+ * \param globalPos The position for which the boundary type is set
+ */
+ PrimaryVariables initial(const Element& element) const
+ {
+ PrimaryVariables values(0.0);
+
+ auto elemId = this->gridGeometry().elementMapper().index(element);
+ values[0] = exactWaterDepth_[elemId];
+ values[1] = 0.0;
+ values[2] = 0.0;
+
+ return values;
+ };
+
+ // \}
+
+private:
+ std::vector<Scalar> exactWaterDepth_;
+ Scalar gravity_;
+ Scalar bowlDepthAtCenter_;
+ Scalar bowlParaboloidRadius_;
+ Scalar bowlInitialWaterElevationAtCenter_;
+ Scalar bowlAnalyticParameterOmega_;
+ Scalar bowlAnalyticParameterA_;
+ static constexpr Scalar eps_ = 1.0e-6;
+ std::string name_;
+};
+
+} //end namespace Dumux
+
+#endif
diff --git a/test/freeflow/shallowwater/bowl/spatialparams.hh b/test/freeflow/shallowwater/bowl/spatialparams.hh
new file mode 100644
index 0000000000..b69824c5c6
--- /dev/null
+++ b/test/freeflow/shallowwater/bowl/spatialparams.hh
@@ -0,0 +1,136 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ * See the file COPYING for full copying permissions. *
+ * *
+ * This program is free software: you can redistribute it and/or modify *
+ * it under the terms of the GNU General Public License as published by *
+ * the Free Software Foundation, either version 2 of the License, or *
+ * (at your option) any later version. *
+ * *
+ * This program is distributed in the hope that it will be useful, *
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of *
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
+ * GNU General Public License for more details. *
+ * *
+ * You should have received a copy of the GNU General Public License *
+ * along with this program. If not, see <http://www.gnu.org/licenses/>. *
+ *****************************************************************************/
+/*!
+ * \file
+ * \ingroup ShallowWaterTests
+ * \brief The spatial parameters for the bowl problem.
+ */
+#ifndef DUMUX_BOWL_SPATIAL_PARAMETERS_HH
+#define DUMUX_BOWL_SPATIAL_PARAMETERS_HH
+
+#include <dumux/material/spatialparams/fv.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/material/fluidmatrixinteractions/frictionlaws/frictionlaw.hh>
+#include <dumux/material/fluidmatrixinteractions/frictionlaws/nofriction.hh>
+
+namespace Dumux {
+
+/*!
+ * \ingroup ShallowWaterTests
+ * \brief The spatial parameters class for the bowl test.
+ *
+ */
+template<class GridGeometry, class Scalar, class VolumeVariables>
+class BowlSpatialParams
+: public FVSpatialParams<GridGeometry, Scalar,
+ BowlSpatialParams<GridGeometry, Scalar, VolumeVariables>>
+{
+ using ThisType = BowlSpatialParams<GridGeometry, Scalar, VolumeVariables>;
+ using ParentType = FVSpatialParams<GridGeometry, Scalar, ThisType>;
+ using GridView = typename GridGeometry::GridView;
+ using FVElementGeometry = typename GridGeometry::LocalView;
+ using SubControlVolume = typename FVElementGeometry::SubControlVolume;
+ using Element = typename GridView::template Codim<0>::Entity;
+ using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+public:
+ BowlSpatialParams(std::shared_ptr<const GridGeometry> gridGeometry)
+ : ParentType(gridGeometry)
+ {
+ gravity_ = getParam<Scalar>("Problem.Gravity");
+ const Scalar bowlDepthAtCenter = getParam<Scalar>("Problem.BowlDepthAtCenter");
+ const Scalar bowlParaboloidRadius = getParam<Scalar>("Problem.BowlParaboloidRadius");
+ initFrictionLaw();
+ bedSurface_.assign(this->gridGeometry().gridView().size(0), 0.0);
+
+ //compute the bedSurface for all elements
+ for (const auto& element : elements(this->gridGeometry().gridView()))
+ {
+ const auto eIdx = this->gridGeometry().elementMapper().index(element);
+ const auto& globalPos = element.geometry().center();
+ bedSurface_[eIdx] = bowlDepthAtCenter *(((globalPos[0] * globalPos[0]) +
+ (globalPos[1] * globalPos[1])) /
+ (bowlParaboloidRadius * bowlParaboloidRadius) - 1.0) + 1.0;
+ }
+
+ }
+
+ /*!
+ * \brief Initialize the FrictionLaw
+ */
+ void initFrictionLaw()
+ {
+ frictionLaw_ = std::make_unique<FrictionLawNoFriction<VolumeVariables>>();
+ }
+
+ /*! \brief Define the gravitation.
+ *
+ * \return gravity constant
+ */
+ Scalar gravity(const GlobalPosition& globalPos) const
+ {
+ return gravity_;
+ }
+
+ /*! \brief Define the gravitation.
+ *
+ * \return gravity constant
+ */
+ Scalar gravity() const
+ {
+ return gravity_;
+ }
+
+ /*! \brief Get the frictionLaw.
+ *
+ * Get the frictionLaw, which already includes the friction value.
+ *
+ * \return frictionLaw
+ */
+
+ const FrictionLaw<VolumeVariables>& frictionLaw(const Element& element,
+ const SubControlVolume& scv) const
+ {
+ return *frictionLaw_;
+ }
+
+ /*! \brief Define the bed surface
+ *
+ * \param element The current element
+ * \param scv The sub-control volume inside the element.
+ *
+ * \return The bed surface
+ */
+ Scalar bedSurface(const Element& element,
+ const SubControlVolume& scv) const
+ {
+ auto eIdx = scv.elementIndex();
+ return bedSurface_[eIdx];
+ }
+
+private:
+ std::vector<Scalar> bedSurface_;
+ Scalar gravity_;
+ std::string frictionLawType_;
+ std::unique_ptr<FrictionLaw<VolumeVariables>> frictionLaw_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/test/references/test_ff_shallowwater_bowl-reference.vtu b/test/references/test_ff_shallowwater_bowl-reference.vtu
new file mode 100644
index 0000000000..51a73f2ea7
--- /dev/null
+++ b/test/references/test_ff_shallowwater_bowl-reference.vtu
@@ -0,0 +1,3401 @@
+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="0.1" byte_order="LittleEndian">
+ <UnstructuredGrid>
+ <Piece NumberOfCells="2500" NumberOfPoints="2601">
+ <CellData Scalars="waterDepth">
+ <DataArray type="Float32" Name="waterDepth" NumberOfComponents="1" format="ascii">
+ 4.97967e-06 5.45262e-06 5.85379e-06 6.12838e-06 6.28307e-06 6.35455e-06 6.38208e-06 6.39111e-06 6.39368e-06 6.39434e-06 6.39449e-06 6.39452e-06
+ 6.39452e-06 6.39452e-06 6.39452e-06 6.39452e-06 6.39452e-06 6.39452e-06 6.39452e-06 6.39452e-06 6.39452e-06 6.39452e-06 6.39452e-06 6.39452e-06
+ 9.75747e-06 9.75747e-06 6.39452e-06 6.39452e-06 6.39452e-06 6.39452e-06 6.39452e-06 6.39452e-06 6.39452e-06 6.39452e-06 6.39452e-06 6.39452e-06
+ 6.39452e-06 6.39452e-06 6.39452e-06 6.39449e-06 6.39434e-06 6.39368e-06 6.39111e-06 6.38208e-06 6.35455e-06 6.28307e-06 6.12838e-06 5.85379e-06
+ 5.45262e-06 4.97967e-06 5.45262e-06 6.05905e-06 6.63775e-06 7.06219e-06 7.31107e-06 7.42984e-06 7.47732e-06 7.4936e-06 7.49848e-06 7.49978e-06
+ 7.50009e-06 7.50016e-06 7.50017e-06 7.50017e-06 7.50017e-06 7.50017e-06 7.50017e-06 7.50017e-06 7.50017e-06 7.50017e-06 7.50017e-06 7.50017e-06
+ 7.50017e-06 7.50017e-06 1.29211e-05 1.29211e-05 7.50017e-06 7.50017e-06 7.50017e-06 7.50017e-06 7.50017e-06 7.50017e-06 7.50017e-06 7.50017e-06
+ 7.50017e-06 7.50017e-06 7.50017e-06 7.50017e-06 7.50016e-06 7.50009e-06 7.49978e-06 7.49848e-06 7.4936e-06 7.47732e-06 7.42984e-06 7.31107e-06
+ 7.06219e-06 6.63775e-06 6.05905e-06 5.45262e-06 5.85379e-06 6.63775e-06 7.42978e-06 8.0105e-06 8.34165e-06 8.49638e-06 8.5579e-06 8.57912e-06
+ 8.58556e-06 8.5873e-06 8.58772e-06 8.58781e-06 8.58783e-06 8.58784e-06 8.58784e-06 8.58784e-06 8.58784e-06 8.58784e-06 8.58784e-06 8.58784e-06
+ 8.58784e-06 8.58784e-06 8.58784e-06 8.58784e-06 1.5404e-05 1.5404e-05 8.58784e-06 8.58784e-06 8.58784e-06 8.58784e-06 8.58784e-06 8.58784e-06
+ 8.58784e-06 8.58784e-06 8.58784e-06 8.58784e-06 8.58784e-06 8.58783e-06 8.58781e-06 8.58772e-06 8.5873e-06 8.58556e-06 8.57912e-06 8.5579e-06
+ 8.49638e-06 8.34165e-06 8.0105e-06 7.42978e-06 6.63775e-06 5.85379e-06 6.12838e-06 7.06219e-06 8.0105e-06 8.68279e-06 9.05252e-06 9.22233e-06
+ 9.28962e-06 9.3129e-06 9.32001e-06 9.32194e-06 9.32242e-06 9.32253e-06 9.32255e-06 9.32255e-06 9.32255e-06 9.32255e-06 9.32255e-06 9.32255e-06
+ 9.32255e-06 9.32255e-06 9.32255e-06 9.32255e-06 9.32255e-06 9.32255e-06 1.69614e-05 1.69614e-05 9.32255e-06 9.32255e-06 9.32255e-06 9.32255e-06
+ 9.32255e-06 9.32255e-06 9.32255e-06 9.32255e-06 9.32255e-06 9.32255e-06 9.32255e-06 9.32255e-06 9.32253e-06 9.32242e-06 9.32194e-06 9.32001e-06
+ 9.3129e-06 9.28962e-06 9.22233e-06 9.05252e-06 8.68279e-06 8.0105e-06 7.06219e-06 6.12838e-06 6.28307e-06 7.31107e-06 8.34165e-06 9.05252e-06
+ 9.43617e-06 9.61139e-06 9.68087e-06 9.70497e-06 9.71235e-06 9.71437e-06 9.71486e-06 9.71498e-06 9.715e-06 9.715e-06 9.71501e-06 9.71501e-06
+ 9.71501e-06 9.71501e-06 9.71501e-06 9.71501e-06 9.71501e-06 5.61796e-05 6.16977e-05 8.81145e-05 0.000201285 0.000201285 8.81145e-05 6.16977e-05
+ 5.61796e-05 9.71501e-06 9.71501e-06 9.71501e-06 9.71501e-06 9.71501e-06 9.71501e-06 9.71501e-06 9.715e-06 9.715e-06 9.71498e-06 9.71486e-06
+ 9.71437e-06 9.71235e-06 9.70497e-06 9.68087e-06 9.61139e-06 9.43617e-06 9.05252e-06 8.34165e-06 7.31107e-06 6.28307e-06 6.35455e-06 7.42984e-06
+ 8.49638e-06 9.22233e-06 9.61139e-06 9.78886e-06 9.85928e-06 9.88374e-06 9.89125e-06 9.8933e-06 9.89381e-06 9.89392e-06 9.89395e-06 9.89395e-06
+ 9.89395e-06 9.89395e-06 9.89395e-06 5.61841e-05 3.51334e-05 3.55726e-05 0.000418909 0.00089611 0.00125089 0.00148811 0.00160839 0.00160839
+ 0.00148811 0.00125089 0.00089611 0.000418909 3.55726e-05 3.51334e-05 5.61841e-05 9.89395e-06 9.89395e-06 9.89395e-06 9.89395e-06 9.89395e-06
+ 9.89392e-06 9.89381e-06 9.8933e-06 9.89125e-06 9.88374e-06 9.85928e-06 9.78886e-06 9.61139e-06 9.22233e-06 8.49638e-06 7.42984e-06 6.35455e-06
+ 6.38208e-06 7.47732e-06 8.5579e-06 9.28962e-06 9.68087e-06 9.85928e-06 9.9301e-06 9.95471e-06 9.96226e-06 9.96433e-06 9.96485e-06 9.96496e-06
+ 9.96499e-06 9.96499e-06 9.96499e-06 5.10079e-05 3.09133e-05 0.000514883 0.00115083 0.00194582 0.00270055 0.00333359 0.00379681 0.00409798
+ 0.00424502 0.00424502 0.00409798 0.00379681 0.00333359 0.00270055 0.00194582 0.00115083 0.000514883 3.09133e-05 5.10079e-05 9.96499e-06
+ 9.96499e-06 9.96499e-06 9.96496e-06 9.96485e-06 9.96433e-06 9.96226e-06 9.95471e-06 9.9301e-06 9.85928e-06 9.68087e-06 9.28962e-06 8.5579e-06
+ 7.47732e-06 6.38208e-06 6.39111e-06 7.4936e-06 8.57912e-06 9.3129e-06 9.70497e-06 9.88374e-06 9.95471e-06 9.97938e-06 9.98695e-06 9.98902e-06
+ 9.98954e-06 9.98965e-06 9.98968e-06 6.13224e-05 2.38563e-05 0.000516693 0.00140891 0.00255584 0.00362139 0.00455437 0.00534618 0.00598455
+ 0.00645932 0.00677164 0.0069265 0.0069265 0.00677164 0.00645932 0.00598455 0.00534618 0.00455437 0.00362139 0.00255584 0.00140891
+ 0.000516693 2.38563e-05 6.13224e-05 9.98968e-06 9.98965e-06 9.98954e-06 9.98902e-06 9.98695e-06 9.97938e-06 9.95471e-06 9.88374e-06 9.70497e-06
+ 9.3129e-06 8.57912e-06 7.4936e-06 6.39111e-06 6.39368e-06 7.49848e-06 8.58556e-06 9.32001e-06 9.71235e-06 9.89125e-06 9.96226e-06 9.98695e-06
+ 9.99452e-06 9.9966e-06 9.99712e-06 9.99723e-06 3.20343e-05 0.000346156 0.00109015 0.00246955 0.00383475 0.00508197 0.00617885 0.00712069
+ 0.00790999 0.00854383 0.00901822 0.00933268 0.00948981 0.00948981 0.00933268 0.00901822 0.00854383 0.00790999 0.00712069 0.00617885
+ 0.00508197 0.00383475 0.00246955 0.00109015 0.000346156 3.20343e-05 9.99723e-06 9.99712e-06 9.9966e-06 9.99452e-06 9.98695e-06 9.96226e-06
+ 9.89125e-06 9.71235e-06 9.32001e-06 8.58556e-06 7.49848e-06 6.39368e-06 6.39434e-06 7.49978e-06 8.5873e-06 9.32194e-06 9.71437e-06 9.8933e-06
+ 9.96433e-06 9.98902e-06 9.9966e-06 9.99868e-06 9.99919e-06 1.9095e-05 0.000472582 0.00169702 0.00332648 0.00487046 0.00626909 0.00751952
+ 0.00861504 0.00955467 0.0103398 0.0109695 0.0114421 0.0117568 0.0119146 0.0119146 0.0117568 0.0114421 0.0109695 0.0103398
+ 0.00955467 0.00861504 0.00751952 0.00626909 0.00487046 0.00332648 0.00169702 0.000472582 1.9095e-05 9.99919e-06 9.99868e-06 9.9966e-06
+ 9.98902e-06 9.96433e-06 9.8933e-06 9.71437e-06 9.32194e-06 8.5873e-06 7.49978e-06 6.39434e-06 6.39449e-06 7.50009e-06 8.58772e-06 9.32242e-06
+ 9.71486e-06 9.89381e-06 9.96485e-06 9.98954e-06 9.99712e-06 9.99919e-06 1.60408e-05 0.000552876 0.00208705 0.00390344 0.00560987 0.00716621
+ 0.00856661 0.00981424 0.0109068 0.0118438 0.0126257 0.0132523 0.0137229 0.0140371 0.014195 0.014195 0.0140371 0.0137229
+ 0.0132523 0.0126257 0.0118438 0.0109068 0.00981424 0.00856661 0.00716621 0.00560987 0.00390344 0.00208705 0.000552876 1.60408e-05
+ 9.99919e-06 9.99712e-06 9.98954e-06 9.96485e-06 9.89381e-06 9.71486e-06 9.32242e-06 8.58772e-06 7.50009e-06 6.39449e-06 6.39452e-06 7.50016e-06
+ 8.58781e-06 9.32253e-06 9.71498e-06 9.89392e-06 9.96496e-06 9.98965e-06 9.99723e-06 1.9095e-05 0.000552876 0.00222464 0.00419761 0.00605485
+ 0.00776286 0.00931701 0.0107155 0.01196 0.0130497 0.0139844 0.0147638 0.0153881 0.015857 0.0161704 0.0163281 0.0163281
+ 0.0161704 0.015857 0.0153881 0.0147638 0.0139844 0.0130497 0.01196 0.0107155 0.00931701 0.00776286 0.00605485 0.00419761
+ 0.00222464 0.000552876 1.9095e-05 9.99723e-06 9.98965e-06 9.96496e-06 9.89392e-06 9.71498e-06 9.32253e-06 8.58781e-06 7.50016e-06 6.39452e-06
+ 6.39452e-06 7.50017e-06 8.58783e-06 9.32255e-06 9.715e-06 9.89395e-06 9.96499e-06 9.98968e-06 3.20343e-05 0.000472582 0.00208705 0.00419761
+ 0.00620501 0.00806181 0.00976652 0.0113173 0.0127133 0.013955 0.0150422 0.0159748 0.0167522 0.0173747 0.0178422 0.0181548
+ 0.0183121 0.0183121 0.0181548 0.0178422 0.0173747 0.0167522 0.0159748 0.0150422 0.013955 0.0127133 0.0113173 0.00976652
+ 0.00806181 0.00620501 0.00419761 0.00208705 0.000472582 3.20343e-05 9.98968e-06 9.96499e-06 9.89395e-06 9.715e-06 9.32255e-06 8.58783e-06
+ 7.50017e-06 6.39452e-06 6.39452e-06 7.50017e-06 8.58784e-06 9.32255e-06 9.715e-06 9.89395e-06 9.96499e-06 6.13224e-05 0.000346156 0.00169702
+ 0.00390344 0.00605485 0.00806181 0.00991585 0.0116175 0.0131653 0.014559 0.0157983 0.0168834 0.0178141 0.0185899 0.0192109
+ 0.0196772 0.019989 0.0201458 0.0201458 0.019989 0.0196772 0.0192109 0.0185899 0.0178141 0.0168834 0.0157983 0.014559
+ 0.0131653 0.0116175 0.00991585 0.00806181 0.00605485 0.00390344 0.00169702 0.000346156 6.13224e-05 9.96499e-06 9.89395e-06 9.715e-06
+ 9.32255e-06 8.58784e-06 7.50017e-06 6.39452e-06 6.39452e-06 7.50017e-06 8.58784e-06 9.32255e-06 9.71501e-06 9.89395e-06 9.96499e-06 2.38563e-05
+ 0.00109015 0.00332648 0.00560987 0.00776286 0.00976652 0.0116175 0.0133161 0.0148611 0.0162524 0.0174896 0.0185728 0.0195017
+ 0.0202761 0.0208959 0.0213612 0.0216723 0.0218286 0.0218286 0.0216723 0.0213612 0.0208959 0.0202761 0.0195017 0.0185728
+ 0.0174896 0.0162524 0.0148611 0.0133161 0.0116175 0.00976652 0.00776286 0.00560987 0.00332648 0.00109015 2.38563e-05 9.96499e-06
+ 9.89395e-06 9.71501e-06 9.32255e-06 8.58784e-06 7.50017e-06 6.39452e-06 6.39452e-06 7.50017e-06 8.58784e-06 9.32255e-06 9.71501e-06 9.89395e-06
+ 5.10079e-05 0.000516693 0.00246955 0.00487046 0.00716621 0.00931701 0.0113173 0.0131653 0.0148611 0.0164037 0.0177929 0.0190281
+ 0.0201097 0.0210371 0.0218103 0.022429 0.0228935 0.0232039 0.0233598 0.0233598 0.0232039 0.0228935 0.022429 0.0218103
+ 0.0210371 0.0201097 0.0190281 0.0177929 0.0164037 0.0148611 0.0131653 0.0113173 0.00931701 0.00716621 0.00487046 0.00246955
+ 0.000516693 5.10079e-05 9.89395e-06 9.71501e-06 9.32255e-06 8.58784e-06 7.50017e-06 6.39452e-06 6.39452e-06 7.50017e-06 8.58784e-06 9.32255e-06
+ 9.71501e-06 9.89395e-06 3.09133e-05 0.00140891 0.00383475 0.00626909 0.00856661 0.0107155 0.0127133 0.014559 0.0162524 0.0177929
+ 0.0191801 0.0204137 0.0214938 0.02242 0.0231921 0.02381 0.0242737 0.0245835 0.024739 0.024739 0.0245835 0.0242737
+ 0.02381 0.0231921 0.02242 0.0214938 0.0204137 0.0191801 0.0177929 0.0162524 0.014559 0.0127133 0.0107155 0.00856661
+ 0.00626909 0.00383475 0.00140891 3.09133e-05 9.89395e-06 9.71501e-06 9.32255e-06 8.58784e-06 7.50017e-06 6.39452e-06 6.39452e-06 7.50017e-06
+ 8.58784e-06 9.32255e-06 9.71501e-06 5.61841e-05 0.000514883 0.00255584 0.00508197 0.00751952 0.00981424 0.01196 0.013955 0.0157983
+ 0.0174896 0.0190281 0.0204137 0.0216459 0.0227247 0.0236498 0.0244209 0.0250381 0.0255012 0.0258105 0.0259657 0.0259657
+ 0.0258105 0.0255012 0.0250381 0.0244209 0.0236498 0.0227247 0.0216459 0.0204137 0.0190281 0.0174896 0.0157983 0.013955
+ 0.01196 0.00981424 0.00751952 0.00508197 0.00255584 0.000514883 5.61841e-05 9.71501e-06 9.32255e-06 8.58784e-06 7.50017e-06 6.39452e-06
+ 6.39452e-06 7.50017e-06 8.58784e-06 9.32255e-06 9.71501e-06 3.51334e-05 0.00115083 0.00362139 0.00617885 0.00861504 0.0109068 0.0130497
+ 0.0150422 0.0168834 0.0185728 0.0201097 0.0214938 0.0227247 0.0238025 0.0247266 0.0254969 0.0261135 0.0265761 0.0268849
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--
GitLab