From 48752199effe5e5bbdef20e00c99b0981ec7a8cf Mon Sep 17 00:00:00 2001
From: Timo Koch <timo.koch@iws.uni-stuttgart.de>
Date: Thu, 23 Apr 2020 10:19:33 +0000
Subject: [PATCH] Merge branch 'feature/rot-symmetry-example' into 'master'
Feature/rot symmetry example
See merge request dumux-repositories/dumux!2039
(cherry picked from commit 84c6fb826a9241b88ffca1e4d5e69d8048864516)
219e7879 [examples] implement rotation-symmetric example
297e729b [examples][rotationsymmetry] add images and more docu
34bbeecc [examples][rotsym] add structural elements and compile docu
---
examples/1protationsymmetry/.doc_config | 35 +
examples/1protationsymmetry/CMakeLists.txt | 10 +
examples/1protationsymmetry/README.md | 113 ++
examples/1protationsymmetry/doc/_intro.md | 94 ++
examples/1protationsymmetry/doc/main.md | 253 ++++
examples/1protationsymmetry/doc/main_intro.md | 9 +
examples/1protationsymmetry/doc/paraview.md | 24 +
.../1protationsymmetry/doc/paraview_doc.md | 14 +
examples/1protationsymmetry/doc/problem.md | 376 +++++
.../1protationsymmetry/doc/problem_intro.md | 5 +
examples/1protationsymmetry/img/result.png | Bin 0 -> 319365 bytes
examples/1protationsymmetry/img/setup.svg | 1042 ++++++++++++++
examples/1protationsymmetry/main.cc | 225 +++
examples/1protationsymmetry/params.input | 18 +
examples/1protationsymmetry/problem.hh | 123 ++
examples/1protationsymmetry/properties.hh | 146 ++
examples/1protationsymmetry/spatialparams.hh | 82 ++
examples/CMakeLists.txt | 1 +
examples/README.md | 17 +
.../example_rotationsymmetry-reference.vtp | 1231 +++++++++++++++++
20 files changed, 3818 insertions(+)
create mode 100644 examples/1protationsymmetry/.doc_config
create mode 100644 examples/1protationsymmetry/CMakeLists.txt
create mode 100644 examples/1protationsymmetry/README.md
create mode 100644 examples/1protationsymmetry/doc/_intro.md
create mode 100644 examples/1protationsymmetry/doc/main.md
create mode 100644 examples/1protationsymmetry/doc/main_intro.md
create mode 100644 examples/1protationsymmetry/doc/paraview.md
create mode 100644 examples/1protationsymmetry/doc/paraview_doc.md
create mode 100644 examples/1protationsymmetry/doc/problem.md
create mode 100644 examples/1protationsymmetry/doc/problem_intro.md
create mode 100644 examples/1protationsymmetry/img/result.png
create mode 100644 examples/1protationsymmetry/img/setup.svg
create mode 100644 examples/1protationsymmetry/main.cc
create mode 100644 examples/1protationsymmetry/params.input
create mode 100644 examples/1protationsymmetry/problem.hh
create mode 100644 examples/1protationsymmetry/properties.hh
create mode 100644 examples/1protationsymmetry/spatialparams.hh
create mode 100644 test/references/example_rotationsymmetry-reference.vtp
diff --git a/examples/1protationsymmetry/.doc_config b/examples/1protationsymmetry/.doc_config
new file mode 100644
index 0000000000..f85531dc67
--- /dev/null
+++ b/examples/1protationsymmetry/.doc_config
@@ -0,0 +1,35 @@
+{
+ "README.md" : [
+ "doc/_intro.md"
+ ],
+
+ "doc/problem.md" : [
+ "doc/problem_intro.md",
+ "properties.hh",
+ "problem.hh",
+ "spatialparams.hh"
+ ],
+
+ "doc/main.md" : [
+ "doc/main_intro.md",
+ "main.cc"
+ ],
+
+ "doc/paraview.md" : [
+ "doc/paraview_doc.md"
+ ],
+
+ "navigation" : {
+ "mainpage" : "README.md",
+ "subpages" : [
+ "doc/problem.md",
+ "doc/main.md",
+ "doc/paraview.md"
+ ],
+ "subtitles" : [
+ "Rotation-symmetric one-phase flow simulation setup",
+ "Main program flow",
+ "Post-processing with ParaView"
+ ]
+ }
+}
diff --git a/examples/1protationsymmetry/CMakeLists.txt b/examples/1protationsymmetry/CMakeLists.txt
new file mode 100644
index 0000000000..cb926b1fd8
--- /dev/null
+++ b/examples/1protationsymmetry/CMakeLists.txt
@@ -0,0 +1,10 @@
+dune_symlink_to_source_files(FILES "params.input")
+
+dune_add_test(NAME example_1p_rotationsymmetry
+ LABELS porousmediumflow 1p
+ SOURCES main.cc
+ COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+ CMD_ARGS --script fuzzy
+ --files ${CMAKE_SOURCE_DIR}/test/references/example_rotationsymmetry-reference.vtp
+ ${CMAKE_CURRENT_BINARY_DIR}/example_rotationsymmetry-00000.vtp
+ --command "${CMAKE_CURRENT_BINARY_DIR}/example_1p_rotationsymmetry params.input -Problem.Name example_rotationsymmetry")
diff --git a/examples/1protationsymmetry/README.md b/examples/1protationsymmetry/README.md
new file mode 100644
index 0000000000..11cb39cdf2
--- /dev/null
+++ b/examples/1protationsymmetry/README.md
@@ -0,0 +1,113 @@
+<!-- Important: This file has been automatically generated by generate_example_docs.py. Do not edit this file directly! -->
+
+# Rotation-symmetric pressure distribution
+
+__In this example, you will learn how to__
+
+* solve a rotation-symmetric problem one-dimensionally
+* perform a convergence test against an analytical solution
+* apply the `Rotational Extrusion` filters in [ParaView](https://www.paraview.org/) for a two-dimensional visualization of the one-dimensional results
+
+
+__Result__. With the `Rotational Extrusion` and the `Warp By Scalar` filters in [ParaView](https://www.paraview.org/),
+the pressure distribution of this example looks as shown in the following picture:
+
+<figure>
+ <center>
+ <img src="img/result.png" alt="Rotation-symmetric pressure distribution" width="60%"/>
+ <figcaption> <b> Fig.1 </b> - Rotation-symmetric pressure distribution on a disc (warped to 3D). </figcaption>
+ </center>
+</figure>
+
+
+__Table of contents__. This description is structured as follows:
+
+[[_TOC_]]
+
+
+## Problem setup
+
+We consider a single-phase problem that leads to a rotation-symmetric pressure distribution.
+The following figure illustrates the setup:
+
+<figure>
+ <center>
+ <img src="img/setup.svg" alt="Rotation-symmetric setup" width="60%"/>
+ <figcaption> <b> Fig.2 </b> - Setup for the rotation-symmetric problem. The pressure boundary conditions are shown by the colored lines and the simulation domain is depicted in grey.</figcaption>
+ </center>
+</figure>
+
+This could, for example, represent a cross section of an injection/extraction well in a homogeneous
+and isotropic porous medium, where the well with radius $`r_1`$ is cut out and the
+injection/extraction pressure $`p_1`$ is prescribed as a Dirichlet boundary condition. At the outer
+radius $`r_2`$, we set the pressure $`p_2`$. In the polar coordinates $`r`$ and $`\varphi`$, the
+solution to this problem is independent of the angular coordinate $`\varphi`$ and can be reduced to
+a one-dimensional problem in the radial coordinate $`r`$. Therefore, in this example, we want to
+solve the problem on a one-dimensional computational domain as illustrated by the orange line in
+the above figure.
+
+## Mathematical model
+
+In this example we are using the single-phase model of DuMu<sup>x</sup>, which considers Darcy's law to relate
+the Darcy velocity $`\textbf u`$ to gradients of the pressure $`p`$. In the case of rotational
+symmetry, the mass balance equation for the fluid phase can be transformed using polar coordinates:
+
+```math
+-\frac{1}{r} \frac{\partial}{\partial r} \left( r \frac{\varrho k}{\mu} \frac{\partial p}{\partial r} \right) = 0,
+```
+
+where we identify the Darcy velocity in radial direction $`u_r = -\frac{k}{\mu} \frac{\partial p}{\partial r}`$,
+and where $`k`$ is the permeability of the porous medium, $`\mu`$ is the dynamic viscosity of the
+fluid, and $`\varrho`$ is the fluid density.
+
+## Discretization
+
+We employ a finite-volume scheme to spatially discretize the mass balance equation shown above.
+Let us consider a discretization of the one-dimensional domain into control volumes
+$`K_i = \left[ r_i, r_{i+1} \right]`$. The discrete equation describing mass conservation inside a control volume
+$`K_i`$ is obtained by integration and reads:
+
+```math
+ - 2 \pi r_{i+1} \left( \varrho u_r \right)_{r_{i+1}}
+ + 2 \pi r_i \left( \varrho u_r \right)_{r_i}
+ = 0.
+```
+
+For this type of equation, the implementation of the finite-volume schemes in DuMu<sup>x</sup> is based on
+the general form:
+
+```math
+\sum_{\sigma \in \mathcal{S}_K} | \sigma | \left( \varrho \textbf u \cdot \textbf n \right)_\sigma = 0,
+```
+
+where $`\sigma`$ are the faces of the control volume and where the notation
+$`( \cdot )_\sigma`$ was used to denote quantities evaluated for a face $`\sigma`$.
+The area of a face is denoted with $`| \sigma |`$. Thus, comparing the two equations
+we identify $`| \sigma | = 2 \pi r_\sigma`$ for the case of rotational symmetry
+on a disc. Here, $`r_\sigma`$ refers to the radius at which the face is situated
+in the one-dimensional discretization.
+
+In DuMu<sup>x</sup>, this is realized in the classes `RotationSymmetricSubControlVolume` and
+`RotationSymmetricSubControlVolumeFace`, which implement one-dimensional control
+volumes and faces, that take into account the extrusion about the rotation axes
+of symmetry in the computations of volumes and areas. This will be discussed in part 1
+of the documentation.
+
+# Implementation & Post processing
+
+## Part 1: Rotation-symmetric one-phase flow simulation setup
+
+| [:arrow_right: Click to continue with part 1 of the documentation](doc/problem.md) |
+|---:|
+
+
+## Part 2: Main program flow
+
+| [:arrow_right: Click to continue with part 2 of the documentation](doc/main.md) |
+|---:|
+
+
+## Part 3: Post-processing with ParaView
+
+| [:arrow_right: Click to continue with part 3 of the documentation](doc/paraview.md) |
+|---:|
\ No newline at end of file
diff --git a/examples/1protationsymmetry/doc/_intro.md b/examples/1protationsymmetry/doc/_intro.md
new file mode 100644
index 0000000000..8c60975f59
--- /dev/null
+++ b/examples/1protationsymmetry/doc/_intro.md
@@ -0,0 +1,94 @@
+# Rotation-symmetric pressure distribution
+
+__In this example, you will learn how to__
+
+* solve a rotation-symmetric problem one-dimensionally
+* perform a convergence test against an analytical solution
+* apply the `Rotational Extrusion` filters in [ParaView](https://www.paraview.org/) for a two-dimensional visualization of the one-dimensional results
+
+
+__Result__. With the `Rotational Extrusion` and the `Warp By Scalar` filters in [ParaView](https://www.paraview.org/),
+the pressure distribution of this example looks as shown in the following picture:
+
+<figure>
+ <center>
+ <img src="img/result.png" alt="Rotation-symmetric pressure distribution" width="60%"/>
+ <figcaption> <b> Fig.1 </b> - Rotation-symmetric pressure distribution on a disc (warped to 3D). </figcaption>
+ </center>
+</figure>
+
+
+__Table of contents__. This description is structured as follows:
+
+[[_TOC_]]
+
+
+## Problem setup
+
+We consider a single-phase problem that leads to a rotation-symmetric pressure distribution.
+The following figure illustrates the setup:
+
+<figure>
+ <center>
+ <img src="img/setup.svg" alt="Rotation-symmetric setup" width="60%"/>
+ <figcaption> <b> Fig.2 </b> - Setup for the rotation-symmetric problem. The pressure boundary conditions are shown by the colored lines and the simulation domain is depicted in grey.</figcaption>
+ </center>
+</figure>
+
+This could, for example, represent a cross section of an injection/extraction well in a homogeneous
+and isotropic porous medium, where the well with radius $`r_1`$ is cut out and the
+injection/extraction pressure $`p_1`$ is prescribed as a Dirichlet boundary condition. At the outer
+radius $`r_2`$, we set the pressure $`p_2`$. In the polar coordinates $`r`$ and $`\varphi`$, the
+solution to this problem is independent of the angular coordinate $`\varphi`$ and can be reduced to
+a one-dimensional problem in the radial coordinate $`r`$. Therefore, in this example, we want to
+solve the problem on a one-dimensional computational domain as illustrated by the orange line in
+the above figure.
+
+## Mathematical model
+
+In this example we are using the single-phase model of DuMu<sup>x</sup>, which considers Darcy's law to relate
+the Darcy velocity $`\textbf u`$ to gradients of the pressure $`p`$. In the case of rotational
+symmetry, the mass balance equation for the fluid phase can be transformed using polar coordinates:
+
+```math
+-\frac{1}{r} \frac{\partial}{\partial r} \left( r \frac{\varrho k}{\mu} \frac{\partial p}{\partial r} \right) = 0,
+```
+
+where we identify the Darcy velocity in radial direction $`u_r = -\frac{k}{\mu} \frac{\partial p}{\partial r}`$,
+and where $`k`$ is the permeability of the porous medium, $`\mu`$ is the dynamic viscosity of the
+fluid, and $`\varrho`$ is the fluid density.
+
+## Discretization
+
+We employ a finite-volume scheme to spatially discretize the mass balance equation shown above.
+Let us consider a discretization of the one-dimensional domain into control volumes
+$`K_i = \left[ r_i, r_{i+1} \right]`$. The discrete equation describing mass conservation inside a control volume
+$`K_i`$ is obtained by integration and reads:
+
+```math
+ - 2 \pi r_{i+1} \left( \varrho u_r \right)_{r_{i+1}}
+ + 2 \pi r_i \left( \varrho u_r \right)_{r_i}
+ = 0.
+```
+
+For this type of equation, the implementation of the finite-volume schemes in DuMu<sup>x</sup> is based on
+the general form:
+
+```math
+\sum_{\sigma \in \mathcal{S}_K} | \sigma | \left( \varrho \textbf u \cdot \textbf n \right)_\sigma = 0,
+```
+
+where $`\sigma`$ are the faces of the control volume and where the notation
+$`( \cdot )_\sigma`$ was used to denote quantities evaluated for a face $`\sigma`$.
+The area of a face is denoted with $`| \sigma |`$. Thus, comparing the two equations
+we identify $`| \sigma | = 2 \pi r_\sigma`$ for the case of rotational symmetry
+on a disc. Here, $`r_\sigma`$ refers to the radius at which the face is situated
+in the one-dimensional discretization.
+
+In DuMu<sup>x</sup>, this is realized in the classes `RotationSymmetricSubControlVolume` and
+`RotationSymmetricSubControlVolumeFace`, which implement one-dimensional control
+volumes and faces, that take into account the extrusion about the rotation axes
+of symmetry in the computations of volumes and areas. This will be discussed in part 1
+of the documentation.
+
+# Implementation & Post processing
diff --git a/examples/1protationsymmetry/doc/main.md b/examples/1protationsymmetry/doc/main.md
new file mode 100644
index 0000000000..ebb097d694
--- /dev/null
+++ b/examples/1protationsymmetry/doc/main.md
@@ -0,0 +1,253 @@
+<!-- Important: This file has been automatically generated by generate_example_docs.py. Do not edit this file directly! -->
+
+
+| [:arrow_left: Back to the main documentation](../README.md) | [:arrow_left: Go back to part 1](problem.md) | [:arrow_right: Continue with part 3](paraview.md) |
+|---|---|---:|
+
+# Part 2: Main program flow
+
+We want to solve a rotational symmetric Laplace problem on a disc and
+conduct a grid convergence study against an analytical solution.
+The main program flow is implemented in file `main.cc` described below.
+
+The code documentation is structured as follows:
+
+[[_TOC_]]
+
+
+## The main program (`main.cc`)
+This file contains the main program flow. In this example, we solve a stationary
+and rotationally symmetric single-phase problem for a sequence of refined grids
+and compute the convergence rates.
+
+<details open>
+<summary><b>Click to hide/show the file documentation</b> (or inspect the [source code](../main.cc))</summary>
+
+### Includes
+<details><summary> Click to show includes</summary>
+
+```cpp
+#include <config.h>
+
+#include <iostream>
+#include <dune/common/parallel/mpihelper.hh>
+
+#include <dumux/common/properties.hh> // for GetPropType
+#include <dumux/common/parameters.hh> // for getParam
+#include <dumux/common/integrate.hh> // for integrateL2Error
+
+#include <dumux/linear/seqsolverbackend.hh> // for UMFPackBackend
+#include <dumux/linear/pdesolver.hh> // for LinearPDESolver
+#include <dumux/assembly/fvassembler.hh>
+#include <dumux/assembly/diffmethod.hh>
+
+#include <dumux/io/vtkoutputmodule.hh>
+#include <dumux/io/grid/gridmanager_yasp.hh>
+
+#include "properties.hh"
+```
+
+</details>
+
+### Beginning of the main function
+
+```cpp
+int main(int argc, char** argv) try
+{
+ using namespace Dumux;
+
+ // We initialize MPI. Finalization is done automatically on exit.
+ Dune::MPIHelper::instance(argc, argv);
+
+ // We parse the command line arguments.
+ Parameters::init(argc, argv);
+
+ // Convenience alias for the type tag of the problem.
+ using TypeTag = Properties::TTag::OnePRotSym;
+```
+
+### Create the grid and the grid geometry
+
+```cpp
+ // The grid manager can be used to create a grid from the input file
+ using Grid = GetPropType<TypeTag, Properties::Grid>;
+ GridManager<Grid> gridManager;
+ gridManager.init();
+
+ // We compute on the leaf grid view.
+ const auto& leafGridView = gridManager.grid().leafGridView();
+
+ // instantiate the grid geometry
+ using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+ auto gridGeometry = std::make_shared<GridGeometry>(leafGridView);
+ gridGeometry->update();
+```
+
+### Initialize the problem and grid variables
+
+```cpp
+ using Problem = GetPropType<TypeTag, Properties::Problem>;
+ auto problem = std::make_shared<Problem>(gridGeometry);
+
+ // We define a function to update the discrete analytical solution vector
+ // using the exactSolution() function in the problem
+ const auto updateAnalyticalSolution = [&](auto& pExact)
+ {
+ pExact.resize(gridGeometry->numDofs());
+ for (const auto& element : elements(gridGeometry->gridView()))
+ {
+ auto fvGeometry = localView(*gridGeometry);
+ fvGeometry.bindElement(element);
+ for (auto&& scv : scvs(fvGeometry))
+ pExact[scv.dofIndex()] = problem->exactSolution(scv.dofPosition());
+ }
+ };
+
+ // instantiate and initialize the discrete and exact solution vectors
+ using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
+ SolutionVector p(gridGeometry->numDofs());
+ SolutionVector pExact; updateAnalyticalSolution(pExact);
+
+ // instantiate and initialize the grid variables
+ using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
+ auto gridVariables = std::make_shared<GridVariables>(problem, gridGeometry);
+ gridVariables->init(p);
+```
+
+### Initialize VTK output
+
+```cpp
+ VtkOutputModule<GridVariables, SolutionVector> vtkWriter(*gridVariables, p, problem->name());
+ GetPropType<TypeTag, Properties::IOFields>::initOutputModule(vtkWriter);
+ vtkWriter.addField(pExact, "pExact"); // add the exact solution to the output fields
+```
+
+### Instantiate the solver
+We use the `LinearPDESolver` class, which is instantiated on the basis
+of an assembler and a linear solver. When the `solve` function of the
+`LinearPDESolver` is called, it uses the assembler and linear
+solver classes to assemble and solve the linear system around the provided
+solution and stores the result therein.
+
+```cpp
+ using Assembler = FVAssembler<TypeTag, DiffMethod::analytic>;
+ auto assembler = std::make_shared<Assembler>(problem, gridGeometry, gridVariables);
+
+ using LinearSolver = UMFPackBackend;
+ auto linearSolver = std::make_shared<LinearSolver>();
+ LinearPDESolver<Assembler, LinearSolver> solver(assembler, linearSolver);
+ solver.setVerbose(false); // suppress output during solve()
+```
+
+### Solution of the problem and error computation
+The problem is solved by calling `solve` on the instance of `LinearPDESolver`
+that we have created above. In the following piece of code, we solve the
+problem on the initial refinement and compute the corresponding L2 error.
+For a convenient way of computing the L2 error, the function `integrateL2Error`
+can be used.
+
+```cpp
+ solver.solve(p);
+
+ // container to store the L2 errors for the different refinements
+ const int numRefinements = getParam<int>("Grid.RefinementSteps");
+ std::vector<double> l2Errors(numRefinements);
+
+ // use third order error integration
+ constexpr int orderQuadratureRule = 3;
+
+ // compute initial L2 error
+ l2Errors[0] = integrateL2Error(*gridGeometry, p, pExact, orderQuadratureRule);
+```
+
+This procedure is now repeated for the number of refinements as specified
+in the input file.
+
+```cpp
+ for (int stepIdx = 1; stepIdx < numRefinements; stepIdx++)
+ {
+ // Globally refine the grid once
+ gridManager.grid().globalRefine(1);
+
+ // update the grid geometry, the grid variables and
+ // the solution vectors now that the grid has been refined
+ gridGeometry->update();
+ gridVariables->updateAfterGridAdaption(p);
+
+ p.resize(gridGeometry->numDofs());
+ updateAnalyticalSolution(pExact);
+
+ // this recreates the linear system, i.e. the sizes of
+ // the right hand side vector and the Jacobian matrix,
+ // and its sparsity pattern.
+ assembler->setLinearSystem();
+
+ // solve problem on refined grid
+ solver.solve(p);
+```
+
+#### Post-processing and output
+At the end of each refinement step, the convergence
+rate is printed to the terminal.
+
+```cpp
+ // Calculate the L2 error using the numerical solution
+ l2Errors[stepIdx] = integrateL2Error(*gridGeometry, p, pExact, orderQuadratureRule);
+
+ // Print the error and convergence rate
+ const auto rate = std::log(l2Errors[stepIdx]/l2Errors[stepIdx-1])/std::log(0.5);
+ const auto numDofs = gridGeometry->numDofs();
+ std::cout << std::setprecision(8) << std::scientific
+ << "-- L2 error for " << std::setw(5) << numDofs << " dofs: " << l2Errors[stepIdx]
+ << ", rate: " << rate
+ << std::endl;
+ }
+```
+
+After the last refinement, we write the solution to VTK file format on the
+finest grid and exit the main function.
+
+```cpp
+ vtkWriter.write(0.0);
+
+ // program end, return with 0 exit code (success)
+ return 0;
+}
+```
+
+### Exception handling
+In this part of the main file we catch and print possible exceptions that could
+occur during the simulation.
+<details><summary> Click to show error handler</summary>
+
+```cpp
+
+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;
+}
+```
+
+</details>
+
+</details>
+
+
+| [:arrow_left: Back to the main documentation](../README.md) | [:arrow_left: Go back to part 1](problem.md) | [:arrow_right: Continue with part 3](paraview.md) |
+|---|---|---:|
+
diff --git a/examples/1protationsymmetry/doc/main_intro.md b/examples/1protationsymmetry/doc/main_intro.md
new file mode 100644
index 0000000000..9909b61a5b
--- /dev/null
+++ b/examples/1protationsymmetry/doc/main_intro.md
@@ -0,0 +1,9 @@
+# Part 2: Main program flow
+
+We want to solve a rotational symmetric Laplace problem on a disc and
+conduct a grid convergence study against an analytical solution.
+The main program flow is implemented in file `main.cc` described below.
+
+The code documentation is structured as follows:
+
+[[_TOC_]]
diff --git a/examples/1protationsymmetry/doc/paraview.md b/examples/1protationsymmetry/doc/paraview.md
new file mode 100644
index 0000000000..3cae53afc6
--- /dev/null
+++ b/examples/1protationsymmetry/doc/paraview.md
@@ -0,0 +1,24 @@
+<!-- Important: This file has been automatically generated by generate_example_docs.py. Do not edit this file directly! -->
+
+
+| [:arrow_left: Back to the main documentation](../README.md) | [:arrow_left: Go back to part 2](main.md) |
+|---|---:|
+
+# Part 3: Post-processing with ParaView
+
+The result file `example_rotationsymmetry.pvd` can be opened with the software [ParaView](https://www.paraview.org/).
+To obtain a visualisation as shown in the introduction of this documented example, after loading
+the result file, choose `Filters`>`Alphabetical`>`Rotational Extrusion`.
+You might have to reset your view and switch to `3D`. Then apply `Filters`>`Alphabetical`>`Warp By Scalar`.
+The result should look like this:
+
+<figure>
+ <center>
+ <img src="../img/result.png" alt="Rotation-symmetric pressure distribution" width="60%"/>
+ <figcaption> <b> Fig.1 - </b>Rotation-symmetric pressure distribution on a disc (warped to 3D)</figcaption>
+ </center>
+</figure>
+
+| [:arrow_left: Back to the main documentation](../README.md) | [:arrow_left: Go back to part 2](main.md) |
+|---|---:|
+
diff --git a/examples/1protationsymmetry/doc/paraview_doc.md b/examples/1protationsymmetry/doc/paraview_doc.md
new file mode 100644
index 0000000000..a5c127ee10
--- /dev/null
+++ b/examples/1protationsymmetry/doc/paraview_doc.md
@@ -0,0 +1,14 @@
+# Part 3: Post-processing with ParaView
+
+The result file `example_rotationsymmetry.pvd` can be opened with the software [ParaView](https://www.paraview.org/).
+To obtain a visualisation as shown in the introduction of this documented example, after loading
+the result file, choose `Filters`>`Alphabetical`>`Rotational Extrusion`.
+You might have to reset your view and switch to `3D`. Then apply `Filters`>`Alphabetical`>`Warp By Scalar`.
+The result should look like this:
+
+<figure>
+ <center>
+ <img src="../img/result.png" alt="Rotation-symmetric pressure distribution" width="60%"/>
+ <figcaption> <b> Fig.1 - </b>Rotation-symmetric pressure distribution on a disc (warped to 3D)</figcaption>
+ </center>
+</figure>
diff --git a/examples/1protationsymmetry/doc/problem.md b/examples/1protationsymmetry/doc/problem.md
new file mode 100644
index 0000000000..983554ea60
--- /dev/null
+++ b/examples/1protationsymmetry/doc/problem.md
@@ -0,0 +1,376 @@
+<!-- Important: This file has been automatically generated by generate_example_docs.py. Do not edit this file directly! -->
+
+
+| [:arrow_left: Back to the main documentation](../README.md) | [:arrow_right: Continue with part 2](main.md) |
+|---|---:|
+
+# Part 1: Simulation setup
+
+The code documentation is structured as follows:
+
+[[_TOC_]]
+
+
+## Compile-time settings (`properties.hh`)
+This file defines the `TypeTag` used for the simulation in this example, for
+which we specialize a number of compile-time `properties`.
+
+<details open>
+<summary><b>Click to hide/show the file documentation</b> (or inspect the [source code](../properties.hh))</summary>
+
+### Includes
+<details><summary> Click to show includes</summary>
+
+```cpp
+
+#include <dune/grid/yaspgrid.hh> // for `Dune::YaspGrid`
+#include <dumux/discretization/box.hh> // for `TTag::BoxModel`
+```
+
+The `OneP` type tag specializes most of the `properties` required for single-
+phase flow simulations in DuMu<sup>x</sup>. We will use this in the following to inherit the
+respective properties, and subsequently specialize those properties for our
+type tag, which we want to modify or for which no meaningful default can be set.
+
+```cpp
+#include <dumux/porousmediumflow/1p/model.hh> // for `TTag::OneP`
+```
+
+The local residual for incompressible flow is included.
+The one-phase flow model (included above) uses a default implementation of the
+local residual for single-phase flow. However, in this example we are using an
+incompressible fluid phase. Therefore, we are including the specialized local
+residual which contains functionality to analytically compute the entries of
+the Jacobian matrix. We will use this in the main file.
+
+```cpp
+#include <dumux/porousmediumflow/1p/incompressiblelocalresidual.hh>
+```
+
+We will use a single liquid phase consisting of a component with constant fluid properties.
+
+```cpp
+#include <dumux/material/components/constant.hh>
+#include <dumux/material/fluidsystems/1pliquid.hh>
+```
+
+As mentioned at the beginning of the documentation of this example, DuMu<sup>x</sup>
+provides specialized implementations of control volumes and faces for
+rotation-symmetric problems. These take care of adjusting volume and area
+computations to account for the extrusion about the symmetry axes.
+These implementations are exported by the `RotationSymmetricGridGeometryTraits`.
+
+```cpp
+#include <dumux/discretization/rotationsymmetricgridgeometrytraits.hh>
+```
+
+The classes that define the problem and parameters used in this simulation
+
+```cpp
+#include "problem.hh"
+#include "spatialparams.hh"
+```
+
+</details>
+
+### `TypeTag` definition
+A `TypeTag` for our simulation is defined, which inherits properties from the
+single-phase flow model and the box scheme.
+
+```cpp
+namespace Dumux::Properties {
+namespace TTag {
+struct OnePRotSym { using InheritsFrom = std::tuple<OneP, BoxModel>; };
+}
+```
+
+### Property specializations
+
+In the following piece of code, mandatory `properties` for which no meaningful
+default can be set, are specialized for our type tag `OnePRotSym`.
+
+```cpp
+// We use a structured 1D grid with an offset. This allows us to define the
+// computational domain to be between the radii $`r_1`$ and $`r_2`$ as illustrated
+// in the beginning of the documentation of this example
+template<class TypeTag>
+struct Grid<TypeTag, TTag::OnePRotSym>
+{ using type = Dune::YaspGrid<1, Dune::EquidistantOffsetCoordinates<double, 1>>; };
+
+// The problem class specifying initial and boundary conditions:
+template<class TypeTag>
+struct Problem<TypeTag, TTag::OnePRotSym>
+{ using type = RotSymExampleProblem<TypeTag>; };
+
+// Our spatial parameters class defining the permeability and porosity of the porous medium:
+template<class TypeTag>
+struct SpatialParams<TypeTag, TTag::OnePRotSym>
+{
+private:
+ using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+public:
+ using type = RotSymExampleSpatialParams<GridGeometry, Scalar>;
+};
+
+// We use a single liquid phase consisting of a component with constant fluid properties.
+template<class TypeTag>
+struct FluidSystem<TypeTag, TTag::OnePRotSym>
+{
+private:
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+public:
+ using type = FluidSystems::OnePLiquid<Scalar, Components::Constant<1, Scalar> >;
+};
+```
+
+As mentioned before, DuMu<sup>x</sup> provides specialized implementations of sub-control
+volumes and faces for rotation-symmetric problems, which are exported by the
+`RotationSymmetricGridGeometryTraits`.
+Here, we pass these traits to the grid geometry of the box scheme (the scheme
+that we use here) and specialize the `GridGeometry` property accordingly.
+
+```cpp
+template<class TypeTag>
+struct GridGeometry<TypeTag, TTag::OnePRotSym>
+{
+private:
+ static constexpr bool enableCache = getPropValue<TypeTag, Properties::EnableGridGeometryCache>();
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+ using GridView = typename GetPropType<TypeTag, Properties::Grid>::LeafGridView;
+
+ // The default traits for box grid geometries
+ using DefaultTraits = BoxDefaultGridGeometryTraits<GridView>;
+
+ // On the basis of the default traits, define the traits for rotational symmetry.
+ // These will export the corresponding rotation-symmetric sub-control volumes and faces.
+ using GGTraits = RotationSymmetricGridGeometryTraits<DefaultTraits, RotationPolicy::disc>;
+
+public:
+ // Pass the above traits to the box grid geometry such that it uses the
+ // rotation-symmetric sub-control volumes and faces.
+ using type = BoxFVGridGeometry<Scalar, GridView, enableCache, GGTraits>;
+};
+```
+
+Moreover, here we use a local residual specialized for incompressible flow
+that contains functionality related to analytic differentiation.
+
+```cpp
+template<class TypeTag>
+struct LocalResidual<TypeTag, TTag::OnePRotSym>
+{ using type = OnePIncompressibleLocalResidual<TypeTag>; };
+
+} // end namespace Dumux::Properties
+```
+
+
+</details>
+
+
+
+## The problem class (`problem.hh`)
+This file contains the __problem class__ which defines the initial and boundary
+conditions for the single-phase flow simulation.
+
+<details open>
+<summary><b>Click to hide/show the file documentation</b> (or inspect the [source code](../problem.hh))</summary>
+
+### Includes
+
+```cpp
+#include <cmath> // for `std::log`
+#include <dumux/common/properties.hh> // for `GetPropType`
+#include <dumux/common/parameters.hh> // for `getParam`
+#include <dumux/porousmediumflow/problem.hh> // for `PorousMediumFlowProblem`
+```
+
+### The problem class
+We enter the problem class where all necessary boundary conditions and initial conditions are set for our simulation.
+As this is a porous medium flow problem, we inherit from the base class `PorousMediumFlowProblem`.
+
+```cpp
+namespace Dumux {
+
+template<class TypeTag>
+class RotSymExampleProblem : public PorousMediumFlowProblem<TypeTag>
+{
+ using ParentType = PorousMediumFlowProblem<TypeTag>;
+ using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+ using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
+ using BoundaryTypes = GetPropType<TypeTag, Properties::BoundaryTypes>;
+ using Element = typename GridGeometry::GridView::template Codim<0>::Entity;
+ using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+public:
+```
+
+In the constructor, we obtain a number of parameters, related to fluid
+properties and boundary conditions, from the input file.
+
+```cpp
+ RotSymExampleProblem(std::shared_ptr<const GridGeometry> gridGeometry)
+ : ParentType(gridGeometry)
+ {
+ // fluid properties
+ k_ = getParam<Scalar>("SpatialParams.Permeability");
+ nu_ = getParam<Scalar>("Component.LiquidKinematicViscosity");
+
+ // The inner radius r1 can be determined from the grid
+ r1_ = gridGeometry->bBoxMin()[0];
+
+ // boundary conditions
+ q1_ = getParam<Scalar>("Problem.Q1"); // mass flux into the domain at r1 in kg/s/m
+ p1_ = getParam<Scalar>("Problem.P1"); // pressure at the inner boundary at r1
+
+ }
+```
+
+We need to specify a constant temperature for our isothermal problem.
+Fluid properties that depend on temperature will be calculated with this value.
+
+```cpp
+ Scalar temperature() const
+ { return 283.15; }
+```
+
+#### Specify the types of boundary conditions
+This function is used to define the type of boundary conditions used depending on the location.
+Two types of boundary conditions can be specified: Dirichlet or Neumann boundary condition.
+On a Dirichlet boundary, the values of the primary variables need to be fixed. On a Neumann
+boundary condition, values for derivatives need to be fixed. Here, we use Dirichlet boundary
+conditions on all boundaries.
+
+```cpp
+ BoundaryTypes boundaryTypesAtPos(const GlobalPosition& globalPos) const
+ {
+ BoundaryTypes values;
+ values.setAllDirichlet();
+ return values;
+ }
+```
+
+#### Specify Dirichlet boundary condition values
+This function is used to specify the values of the primary variables at Dirichlet boundaries.
+Here, we evaluate the analytical solution (see below) to define the pressures at the boundaries.
+
+```cpp
+ PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const
+ { return exactSolution(globalPos); }
+```
+
+#### Analytical solution
+The analytical solution to the problem of this example reads:
+
+```math
+p = p (r) = p_1 - \frac{q_1 \nu}{2 \pi k} \text{ln} (\frac{r}{r_1}),
+```
+
+where $`q_1`$ is the mass flux into the domain at the inner radius $`r_1`$
+(in kg/s/m) and $`\nu = \mu/\varrho`$ is the kinematic viscosity.
+The following function evaluates this solution depending on the
+position in the domain. We use this function here both to specify Dirichlet
+boundaries and to evaluate the error of the numerical solutions obtained for
+different levels of grid refinement.
+
+```cpp
+ PrimaryVariables exactSolution(const GlobalPosition& globalPos) const
+ {
+ const auto r = globalPos[0];
+ const auto p = p1_ - 1.0/(2*M_PI)*nu_/k_*q1_*std::log(r/r1_);
+ return p;
+ }
+
+private:
+ // private data members required for the analytical solution
+ Scalar q1_, k_, nu_, r1_, p1_;
+};
+
+} // end namespace Dumux
+```
+
+
+</details>
+
+
+
+## Parameter distributions (`spatialparams.hh`)
+
+This file contains the __spatial parameters class__ which defines the
+distributions for the porous medium parameters permeability and porosity
+over the computational grid.
+
+<details open>
+<summary><b>Click to hide/show the file documentation</b> (or inspect the [source code](../spatialparams.hh))</summary>
+
+We include the spatial parameters class for single-phase models discretized
+by finite volume schemes, from which the spatial parameters defined for this
+example inherit.
+
+```cpp
+#include <dumux/material/spatialparams/fv1p.hh>
+```
+
+### The spatial parameters class
+
+In the `RotSymExampleSpatialParams` class, we define the functions needed to describe
+the porous medium, that is, porosity and permeability.
+We inherit from the `FVSpatialParamsOneP` class here, which is the base class
+for spatial parameters in the context of single-phase porous medium flow
+applications using finite volume discretization schemes.
+
+```cpp
+namespace Dumux {
+
+template<class GridGeometry, class Scalar>
+class RotSymExampleSpatialParams
+: public FVSpatialParamsOneP<GridGeometry, Scalar, RotSymExampleSpatialParams<GridGeometry, Scalar>>
+{
+ using ThisType = RotSymExampleSpatialParams<GridGeometry, Scalar>;
+ using ParentType = FVSpatialParamsOneP<GridGeometry, Scalar, ThisType>;
+ using Element = typename GridGeometry::GridView::template Codim<0>::Entity;
+ using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+public:
+ // Spatial parameter classes for porous medium flow applications need to
+ // export the type used for intrinsic permeabilities.
+ using PermeabilityType = Scalar;
+
+ // In the constructor we obtain the permeability value from the input file.
+ RotSymExampleSpatialParams(std::shared_ptr<const GridGeometry> gridGeometry)
+ : ParentType(gridGeometry)
+ { permeability_ = getParam<Scalar>("SpatialParams.Permeability"); }
+```
+
+#### Porosity distribution
+This function is used to define the porosity distribution in the
+computational domain. Here, we use a constant porosity of 1.0.
+
+```cpp
+ Scalar porosityAtPos(const GlobalPosition& globalPos) const
+ { return 1.0; }
+```
+
+#### Permeability distribution
+This function is used to define the permeability distribution in the
+computational domain. Here, we use a constant permeability that is
+defined in the input file.
+
+```cpp
+ PermeabilityType permeabilityAtPos(const GlobalPosition& globalPos) const
+ { return permeability_; }
+
+private:
+ Scalar permeability_;
+};
+
+} // end namespace Dumux
+```
+
+
+</details>
+
+
+| [:arrow_left: Back to the main documentation](../README.md) | [:arrow_right: Continue with part 2](main.md) |
+|---|---:|
+
diff --git a/examples/1protationsymmetry/doc/problem_intro.md b/examples/1protationsymmetry/doc/problem_intro.md
new file mode 100644
index 0000000000..106967a62f
--- /dev/null
+++ b/examples/1protationsymmetry/doc/problem_intro.md
@@ -0,0 +1,5 @@
+# Part 1: Simulation setup
+
+The code documentation is structured as follows:
+
+[[_TOC_]]
diff --git a/examples/1protationsymmetry/img/result.png b/examples/1protationsymmetry/img/result.png
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diff --git a/examples/1protationsymmetry/main.cc b/examples/1protationsymmetry/main.cc
new file mode 100644
index 0000000000..6db3dcd673
--- /dev/null
+++ b/examples/1protationsymmetry/main.cc
@@ -0,0 +1,225 @@
+// -*- 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 program (`main.cc`)
+// This file contains the main program flow. In this example, we solve a stationary
+// and rotationally symmetric single-phase problem for a sequence of refined grids
+// and compute the convergence rates.
+// [[content]]
+// ### Includes
+// [[details]] includes
+// [[codeblock]]
+#include <config.h>
+
+#include <iostream>
+#include <dune/common/parallel/mpihelper.hh>
+
+#include <dumux/common/properties.hh> // for GetPropType
+#include <dumux/common/parameters.hh> // for getParam
+#include <dumux/common/integrate.hh> // for integrateL2Error
+
+#include <dumux/linear/seqsolverbackend.hh> // for UMFPackBackend
+#include <dumux/linear/pdesolver.hh> // for LinearPDESolver
+#include <dumux/assembly/fvassembler.hh>
+#include <dumux/assembly/diffmethod.hh>
+
+#include <dumux/io/vtkoutputmodule.hh>
+#include <dumux/io/grid/gridmanager_yasp.hh>
+
+#include "properties.hh"
+// [[/codeblock]]
+// [[/details]]
+//
+// ### Beginning of the main function
+// [[codeblock]]
+int main(int argc, char** argv) try
+{
+ using namespace Dumux;
+
+ // We initialize MPI. Finalization is done automatically on exit.
+ Dune::MPIHelper::instance(argc, argv);
+
+ // We parse the command line arguments.
+ Parameters::init(argc, argv);
+
+ // Convenience alias for the type tag of the problem.
+ using TypeTag = Properties::TTag::OnePRotSym;
+ // [[/codeblock]]
+
+ // ### Create the grid and the grid geometry
+ // [[codeblock]]
+ // The grid manager can be used to create a grid from the input file
+ using Grid = GetPropType<TypeTag, Properties::Grid>;
+ GridManager<Grid> gridManager;
+ gridManager.init();
+
+ // We compute on the leaf grid view.
+ const auto& leafGridView = gridManager.grid().leafGridView();
+
+ // instantiate the grid geometry
+ using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+ auto gridGeometry = std::make_shared<GridGeometry>(leafGridView);
+ gridGeometry->update();
+ // [[/codeblock]]
+
+ // ### Initialize the problem and grid variables
+ // [[codeblock]]
+ using Problem = GetPropType<TypeTag, Properties::Problem>;
+ auto problem = std::make_shared<Problem>(gridGeometry);
+
+ // We define a function to update the discrete analytical solution vector
+ // using the exactSolution() function in the problem
+ const auto updateAnalyticalSolution = [&](auto& pExact)
+ {
+ pExact.resize(gridGeometry->numDofs());
+ for (const auto& element : elements(gridGeometry->gridView()))
+ {
+ auto fvGeometry = localView(*gridGeometry);
+ fvGeometry.bindElement(element);
+ for (auto&& scv : scvs(fvGeometry))
+ pExact[scv.dofIndex()] = problem->exactSolution(scv.dofPosition());
+ }
+ };
+
+ // instantiate and initialize the discrete and exact solution vectors
+ using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
+ SolutionVector p(gridGeometry->numDofs());
+ SolutionVector pExact; updateAnalyticalSolution(pExact);
+
+ // instantiate and initialize the grid variables
+ using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
+ auto gridVariables = std::make_shared<GridVariables>(problem, gridGeometry);
+ gridVariables->init(p);
+ // [[/codeblock]]
+
+ // ### Initialize VTK output
+ VtkOutputModule<GridVariables, SolutionVector> vtkWriter(*gridVariables, p, problem->name());
+ GetPropType<TypeTag, Properties::IOFields>::initOutputModule(vtkWriter);
+ vtkWriter.addField(pExact, "pExact"); // add the exact solution to the output fields
+
+ // ### Instantiate the solver
+ // We use the `LinearPDESolver` class, which is instantiated on the basis
+ // of an assembler and a linear solver. When the `solve` function of the
+ // `LinearPDESolver` is called, it uses the assembler and linear
+ // solver classes to assemble and solve the linear system around the provided
+ // solution and stores the result therein.
+ // [[codeblock]]
+ using Assembler = FVAssembler<TypeTag, DiffMethod::analytic>;
+ auto assembler = std::make_shared<Assembler>(problem, gridGeometry, gridVariables);
+
+ using LinearSolver = UMFPackBackend;
+ auto linearSolver = std::make_shared<LinearSolver>();
+ LinearPDESolver<Assembler, LinearSolver> solver(assembler, linearSolver);
+ solver.setVerbose(false); // suppress output during solve()
+ // [[/codeblock]]
+
+ // ### Solution of the problem and error computation
+ // The problem is solved by calling `solve` on the instance of `LinearPDESolver`
+ // that we have created above. In the following piece of code, we solve the
+ // problem on the initial refinement and compute the corresponding L2 error.
+ // For a convenient way of computing the L2 error, the function `integrateL2Error`
+ // can be used.
+ // [[codeblock]]
+ solver.solve(p);
+
+ // container to store the L2 errors for the different refinements
+ const int numRefinements = getParam<int>("Grid.RefinementSteps");
+ std::vector<double> l2Errors(numRefinements);
+
+ // use third order error integration
+ constexpr int orderQuadratureRule = 3;
+
+ // compute initial L2 error
+ l2Errors[0] = integrateL2Error(*gridGeometry, p, pExact, orderQuadratureRule);
+ // [[/codeblock]]
+
+ // This procedure is now repeated for the number of refinements as specified
+ // in the input file.
+ // [[codeblock]]
+ for (int stepIdx = 1; stepIdx < numRefinements; stepIdx++)
+ {
+ // Globally refine the grid once
+ gridManager.grid().globalRefine(1);
+
+ // update the grid geometry, the grid variables and
+ // the solution vectors now that the grid has been refined
+ gridGeometry->update();
+ gridVariables->updateAfterGridAdaption(p);
+
+ p.resize(gridGeometry->numDofs());
+ updateAnalyticalSolution(pExact);
+
+ // this recreates the linear system, i.e. the sizes of
+ // the right hand side vector and the Jacobian matrix,
+ // and its sparsity pattern.
+ assembler->setLinearSystem();
+
+ // solve problem on refined grid
+ solver.solve(p);
+ // [[/codeblock]]
+ // #### Post-processing and output
+ // At the end of each refinement step, the convergence
+ // rate is printed to the terminal.
+ // [[codeblock]]
+ // Calculate the L2 error using the numerical solution
+ l2Errors[stepIdx] = integrateL2Error(*gridGeometry, p, pExact, orderQuadratureRule);
+
+ // Print the error and convergence rate
+ const auto rate = std::log(l2Errors[stepIdx]/l2Errors[stepIdx-1])/std::log(0.5);
+ const auto numDofs = gridGeometry->numDofs();
+ std::cout << std::setprecision(8) << std::scientific
+ << "-- L2 error for " << std::setw(5) << numDofs << " dofs: " << l2Errors[stepIdx]
+ << ", rate: " << rate
+ << std::endl;
+ }
+ // [[/codeblock]]
+
+ // After the last refinement, we write the solution to VTK file format on the
+ // finest grid and exit the main function.
+ // [[codeblock]]
+ vtkWriter.write(0.0);
+
+ // program end, return with 0 exit code (success)
+ return 0;
+}
+// [[/codeblock]]
+// ### Exception handling
+// In this part of the main file we catch and print possible exceptions that could
+// occur during the simulation.
+// [[details]] error handler
+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;
+}
+// [[/details]]
+// [[/content]]
diff --git a/examples/1protationsymmetry/params.input b/examples/1protationsymmetry/params.input
new file mode 100644
index 0000000000..8487b511a8
--- /dev/null
+++ b/examples/1protationsymmetry/params.input
@@ -0,0 +1,18 @@
+[Problem]
+EnableGravity = 0 # disable gravity
+Name = rotationsymmetry
+P1 = 1e5 # pressure at the inner boundary at r1
+Q1 = -10.0 # mass flux into the domain at r1 in kg/s/m
+
+[Grid]
+LowerLeft = 0.05
+UpperRight = 1
+Cells = 100
+RefinementSteps = 5
+
+[SpatialParams]
+Permeability = 1e-10 # [m^2]
+
+[Component]
+LiquidKinematicViscosity = 1e-6
+LiquidDensity = 1e3
diff --git a/examples/1protationsymmetry/problem.hh b/examples/1protationsymmetry/problem.hh
new file mode 100644
index 0000000000..f0e532ec90
--- /dev/null
+++ b/examples/1protationsymmetry/problem.hh
@@ -0,0 +1,123 @@
+// -*- 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/>. *
+ *****************************************************************************/
+
+#ifndef DUMUX_ONEP_ROTATION_SYMMETRY_PROBLEM_HH
+#define DUMUX_ONEP_ROTATION_SYMMETRY_PROBLEM_HH
+
+// ## The problem class (`problem.hh`)
+// This file contains the __problem class__ which defines the initial and boundary
+// conditions for the single-phase flow simulation.
+// [[content]]
+// ### Includes
+#include <cmath> // for `std::log`
+#include <dumux/common/properties.hh> // for `GetPropType`
+#include <dumux/common/parameters.hh> // for `getParam`
+#include <dumux/porousmediumflow/problem.hh> // for `PorousMediumFlowProblem`
+
+// ### The problem class
+// We enter the problem class where all necessary boundary conditions and initial conditions are set for our simulation.
+// As this is a porous medium flow problem, we inherit from the base class `PorousMediumFlowProblem`.
+namespace Dumux {
+
+template<class TypeTag>
+class RotSymExampleProblem : public PorousMediumFlowProblem<TypeTag>
+{
+ using ParentType = PorousMediumFlowProblem<TypeTag>;
+ using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+ using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
+ using BoundaryTypes = GetPropType<TypeTag, Properties::BoundaryTypes>;
+ using Element = typename GridGeometry::GridView::template Codim<0>::Entity;
+ using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+public:
+ // In the constructor, we obtain a number of parameters, related to fluid
+ // properties and boundary conditions, from the input file.
+ // [[codeblock]]
+ RotSymExampleProblem(std::shared_ptr<const GridGeometry> gridGeometry)
+ : ParentType(gridGeometry)
+ {
+ // fluid properties
+ k_ = getParam<Scalar>("SpatialParams.Permeability");
+ nu_ = getParam<Scalar>("Component.LiquidKinematicViscosity");
+
+ // The inner radius r1 can be determined from the grid
+ r1_ = gridGeometry->bBoxMin()[0];
+
+ // boundary conditions
+ q1_ = getParam<Scalar>("Problem.Q1"); // mass flux into the domain at r1 in kg/s/m
+ p1_ = getParam<Scalar>("Problem.P1"); // pressure at the inner boundary at r1
+
+ }
+ // [[/codeblock]]
+
+ // We need to specify a constant temperature for our isothermal problem.
+ // Fluid properties that depend on temperature will be calculated with this value.
+ Scalar temperature() const
+ { return 283.15; }
+
+ // #### Specify the types of boundary conditions
+ // This function is used to define the type of boundary conditions used depending on the location.
+ // Two types of boundary conditions can be specified: Dirichlet or Neumann boundary condition.
+ // On a Dirichlet boundary, the values of the primary variables need to be fixed. On a Neumann
+ // boundary condition, values for derivatives need to be fixed. Here, we use Dirichlet boundary
+ // conditions on all boundaries.
+ BoundaryTypes boundaryTypesAtPos(const GlobalPosition& globalPos) const
+ {
+ BoundaryTypes values;
+ values.setAllDirichlet();
+ return values;
+ }
+
+ // #### Specify Dirichlet boundary condition values
+ // This function is used to specify the values of the primary variables at Dirichlet boundaries.
+ // Here, we evaluate the analytical solution (see below) to define the pressures at the boundaries.
+ PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const
+ { return exactSolution(globalPos); }
+
+ // #### Analytical solution
+ // The analytical solution to the problem of this example reads:
+ //
+ // ```math
+ // p = p (r) = p_1 - \frac{q_1 \nu}{2 \pi k} \text{ln} (\frac{r}{r_1}),
+ // ```
+ //
+ // where $`q_1`$ is the mass flux into the domain at the inner radius $`r_1`$
+ // (in kg/s/m) and $`\nu = \mu/\varrho`$ is the kinematic viscosity.
+ // The following function evaluates this solution depending on the
+ // position in the domain. We use this function here both to specify Dirichlet
+ // boundaries and to evaluate the error of the numerical solutions obtained for
+ // different levels of grid refinement.
+ // [[codeblock]]
+ PrimaryVariables exactSolution(const GlobalPosition& globalPos) const
+ {
+ const auto r = globalPos[0];
+ const auto p = p1_ - 1.0/(2*M_PI)*nu_/k_*q1_*std::log(r/r1_);
+ return p;
+ }
+
+private:
+ // private data members required for the analytical solution
+ Scalar q1_, k_, nu_, r1_, p1_;
+};
+
+} // end namespace Dumux
+// [[/codeblock]]
+// [[/content]]
+#endif
diff --git a/examples/1protationsymmetry/properties.hh b/examples/1protationsymmetry/properties.hh
new file mode 100644
index 0000000000..effaea92a7
--- /dev/null
+++ b/examples/1protationsymmetry/properties.hh
@@ -0,0 +1,146 @@
+// -*- 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/>. *
+ *****************************************************************************/
+
+#ifndef DUMUX_ONEP_ROTATION_SYMMETRY_PROPERTIES_HH
+#define DUMUX_ONEP_ROTATION_SYMMETRY_PROPERTIES_HH
+
+// ## Compile-time settings (`properties.hh`)
+// This file defines the `TypeTag` used for the simulation in this example, for
+// which we specialize a number of compile-time `properties`.
+// [[content]]
+// ### Includes
+// [[details]] includes
+#include <dune/grid/yaspgrid.hh> // for `Dune::YaspGrid`
+#include <dumux/discretization/box.hh> // for `TTag::BoxModel`
+
+
+// The `OneP` type tag specializes most of the `properties` required for single-
+// phase flow simulations in DuMu<sup>x</sup>. We will use this in the following to inherit the
+// respective properties, and subsequently specialize those properties for our
+// type tag, which we want to modify or for which no meaningful default can be set.
+#include <dumux/porousmediumflow/1p/model.hh> // for `TTag::OneP`
+
+// The local residual for incompressible flow is included.
+// The one-phase flow model (included above) uses a default implementation of the
+// local residual for single-phase flow. However, in this example we are using an
+// incompressible fluid phase. Therefore, we are including the specialized local
+// residual which contains functionality to analytically compute the entries of
+// the Jacobian matrix. We will use this in the main file.
+#include <dumux/porousmediumflow/1p/incompressiblelocalresidual.hh>
+
+// We will use a single liquid phase consisting of a component with constant fluid properties.
+#include <dumux/material/components/constant.hh>
+#include <dumux/material/fluidsystems/1pliquid.hh>
+
+// As mentioned at the beginning of the documentation of this example, DuMu<sup>x</sup>
+// provides specialized implementations of control volumes and faces for
+// rotation-symmetric problems. These take care of adjusting volume and area
+// computations to account for the extrusion about the symmetry axes.
+// These implementations are exported by the `RotationSymmetricGridGeometryTraits`.
+#include <dumux/discretization/rotationsymmetricgridgeometrytraits.hh>
+
+// The classes that define the problem and parameters used in this simulation
+#include "problem.hh"
+#include "spatialparams.hh"
+// [[/details]]
+//
+// ### `TypeTag` definition
+// A `TypeTag` for our simulation is defined, which inherits properties from the
+// single-phase flow model and the box scheme.
+namespace Dumux::Properties {
+namespace TTag {
+struct OnePRotSym { using InheritsFrom = std::tuple<OneP, BoxModel>; };
+}
+
+// ### Property specializations
+//
+// In the following piece of code, mandatory `properties` for which no meaningful
+// default can be set, are specialized for our type tag `OnePRotSym`.
+// [[codeblock]]
+// We use a structured 1D grid with an offset. This allows us to define the
+// computational domain to be between the radii $`r_1`$ and $`r_2`$ as illustrated
+// in the beginning of the documentation of this example
+template<class TypeTag>
+struct Grid<TypeTag, TTag::OnePRotSym>
+{ using type = Dune::YaspGrid<1, Dune::EquidistantOffsetCoordinates<double, 1>>; };
+
+// The problem class specifying initial and boundary conditions:
+template<class TypeTag>
+struct Problem<TypeTag, TTag::OnePRotSym>
+{ using type = RotSymExampleProblem<TypeTag>; };
+
+// Our spatial parameters class defining the permeability and porosity of the porous medium:
+template<class TypeTag>
+struct SpatialParams<TypeTag, TTag::OnePRotSym>
+{
+private:
+ using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+public:
+ using type = RotSymExampleSpatialParams<GridGeometry, Scalar>;
+};
+
+// We use a single liquid phase consisting of a component with constant fluid properties.
+template<class TypeTag>
+struct FluidSystem<TypeTag, TTag::OnePRotSym>
+{
+private:
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+public:
+ using type = FluidSystems::OnePLiquid<Scalar, Components::Constant<1, Scalar> >;
+};
+// [[/codeblock]]
+
+// As mentioned before, DuMu<sup>x</sup> provides specialized implementations of sub-control
+// volumes and faces for rotation-symmetric problems, which are exported by the
+// `RotationSymmetricGridGeometryTraits`.
+// Here, we pass these traits to the grid geometry of the box scheme (the scheme
+// that we use here) and specialize the `GridGeometry` property accordingly.
+// [[codeblock]]
+template<class TypeTag>
+struct GridGeometry<TypeTag, TTag::OnePRotSym>
+{
+private:
+ static constexpr bool enableCache = getPropValue<TypeTag, Properties::EnableGridGeometryCache>();
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+ using GridView = typename GetPropType<TypeTag, Properties::Grid>::LeafGridView;
+
+ // The default traits for box grid geometries
+ using DefaultTraits = BoxDefaultGridGeometryTraits<GridView>;
+
+ // On the basis of the default traits, define the traits for rotational symmetry.
+ // These will export the corresponding rotation-symmetric sub-control volumes and faces.
+ using GGTraits = RotationSymmetricGridGeometryTraits<DefaultTraits, RotationPolicy::disc>;
+
+public:
+ // Pass the above traits to the box grid geometry such that it uses the
+ // rotation-symmetric sub-control volumes and faces.
+ using type = BoxFVGridGeometry<Scalar, GridView, enableCache, GGTraits>;
+};
+// [[/codeblock]]
+
+// Moreover, here we use a local residual specialized for incompressible flow
+// that contains functionality related to analytic differentiation.
+template<class TypeTag>
+struct LocalResidual<TypeTag, TTag::OnePRotSym>
+{ using type = OnePIncompressibleLocalResidual<TypeTag>; };
+
+} // end namespace Dumux::Properties
+// [[/content]]
+#endif
diff --git a/examples/1protationsymmetry/spatialparams.hh b/examples/1protationsymmetry/spatialparams.hh
new file mode 100644
index 0000000000..cbc60c1904
--- /dev/null
+++ b/examples/1protationsymmetry/spatialparams.hh
@@ -0,0 +1,82 @@
+// -*- 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/>. *
+ *****************************************************************************/
+
+#ifndef DUMUX_ONEP_ROTATION_SYMMETRY_SPATIAL_PARAMS_HH
+#define DUMUX_ONEP_ROTATION_SYMMETRY_SPATIAL_PARAMS_HH
+
+// ## Parameter distributions (`spatialparams.hh`)
+//
+// This file contains the __spatial parameters class__ which defines the
+// distributions for the porous medium parameters permeability and porosity
+// over the computational grid.
+// [[content]]
+// We include the spatial parameters class for single-phase models discretized
+// by finite volume schemes, from which the spatial parameters defined for this
+// example inherit.
+#include <dumux/material/spatialparams/fv1p.hh>
+
+// ### The spatial parameters class
+//
+// In the `RotSymExampleSpatialParams` class, we define the functions needed to describe
+// the porous medium, that is, porosity and permeability.
+// We inherit from the `FVSpatialParamsOneP` class here, which is the base class
+// for spatial parameters in the context of single-phase porous medium flow
+// applications using finite volume discretization schemes.
+// [[codeblock]]
+namespace Dumux {
+
+template<class GridGeometry, class Scalar>
+class RotSymExampleSpatialParams
+: public FVSpatialParamsOneP<GridGeometry, Scalar, RotSymExampleSpatialParams<GridGeometry, Scalar>>
+{
+ using ThisType = RotSymExampleSpatialParams<GridGeometry, Scalar>;
+ using ParentType = FVSpatialParamsOneP<GridGeometry, Scalar, ThisType>;
+ using Element = typename GridGeometry::GridView::template Codim<0>::Entity;
+ using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+public:
+ // Spatial parameter classes for porous medium flow applications need to
+ // export the type used for intrinsic permeabilities.
+ using PermeabilityType = Scalar;
+
+ // In the constructor we obtain the permeability value from the input file.
+ RotSymExampleSpatialParams(std::shared_ptr<const GridGeometry> gridGeometry)
+ : ParentType(gridGeometry)
+ { permeability_ = getParam<Scalar>("SpatialParams.Permeability"); }
+ // [[/codeblock]]
+
+ // #### Porosity distribution
+ // This function is used to define the porosity distribution in the
+ // computational domain. Here, we use a constant porosity of 1.0.
+ Scalar porosityAtPos(const GlobalPosition& globalPos) const
+ { return 1.0; }
+
+ // #### Permeability distribution
+ // This function is used to define the permeability distribution in the
+ // computational domain. Here, we use a constant permeability that is
+ // defined in the input file.
+ PermeabilityType permeabilityAtPos(const GlobalPosition& globalPos) const
+ { return permeability_; }
+
+private:
+ Scalar permeability_;
+};
+
+} // end namespace Dumux
+// [[/content]]
+#endif
diff --git a/examples/CMakeLists.txt b/examples/CMakeLists.txt
index 72da3bd438..058cc9e278 100644
--- a/examples/CMakeLists.txt
+++ b/examples/CMakeLists.txt
@@ -2,3 +2,4 @@ add_subdirectory(2pinfiltration)
add_subdirectory(1ptracer)
add_subdirectory(shallowwaterfriction)
add_subdirectory(freeflowchannel)
+add_subdirectory(1protationsymmetry)
diff --git a/examples/README.md b/examples/README.md
index 1c8d47e7d7..e4e0e646c5 100644
--- a/examples/README.md
+++ b/examples/README.md
@@ -74,3 +74,20 @@ You learn how to
<figure><img src="freeflowchannel/img/setup.png" alt="freeflow result"/></figure></td>
</a></td>
</tr></table>
+
+### [:open_file_folder: Example 5: One-phase flow with rotation-symmetric solution](1protationsymmetry/README.md)
+
+<table><tr><td>
+
+In this example, a rotation-symmetric solution for the single-phase flow equation is discussed.
+You learn how to
+
+* solve a rotation-symmetric problem
+* perform a convergence test against an analytical solution
+* do post-processing in [ParaView](https://www.paraview.org/)
+
+</td>
+<td width="30%"><a href="1protationsymmetry/README.md">
+<figure><img src="1protationsymmetry/img/setup.svg" alt="Rotation-symmetric setup"/></figure></td>
+</a></td>
+</tr></table>
diff --git a/test/references/example_rotationsymmetry-reference.vtp b/test/references/example_rotationsymmetry-reference.vtp
new file mode 100644
index 0000000000..12f4645005
--- /dev/null
+++ b/test/references/example_rotationsymmetry-reference.vtp
@@ -0,0 +1,1231 @@
+<?xml version="1.0"?>
+<VTKFile type="PolyData" version="0.1" byte_order="LittleEndian">
+ <PolyData>
+ <Piece NumberOfLines="1600" NumberOfPoints="1601">
+ <PointData Scalars="p">
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--
GitLab