From aa33ab3d4b71f44f5a2fc27208738d0337976502 Mon Sep 17 00:00:00 2001 From: Timo Koch <timokoch@math.uio.no> Date: Fri, 24 Mar 2023 17:12:06 +0000 Subject: [PATCH] Merge branch 'feature/simple-diffusion' into 'master' [example] Add simple diffusion eqution including full model See merge request dumux-repositories/dumux!3380 (cherry picked from commit 8a7012445cd6a51fe3af0562623016c453bcd823) f334d2ef [common] Add BasicVolumeVariables for reuse in simple models 74f3d6ab [example] Add simple diffusion eqution including full model 369504e8 [doc examples simple-diffusion] first steps for docu of simple-diffusion ddc1161a [example][diffusion][doc] Add documentation 43ed102f [example][diffusion] Test the diffusion example 5164f6f2 [example][diffusion] Document the BaseResidual property 3a9ad1fe [example][diffusion] Fix typos 1f67777d [example][diffusion] Improvements and corrections of the example --- dumux/common/volumevariables.hh | 67 +++ examples/CMakeLists.txt | 1 + examples/README.md | 41 +- examples/diffusion/.doc_config | 27 ++ examples/diffusion/CMakeLists.txt | 29 ++ examples/diffusion/README.md | 161 +++++++ examples/diffusion/doc/_intro.md | 148 ++++++ examples/diffusion/doc/_main.md | 1 + examples/diffusion/doc/_model.md | 1 + examples/diffusion/doc/main.md | 426 ++++++++++++++++++ examples/diffusion/doc/model.md | 245 ++++++++++ examples/diffusion/img/diffusion.gif | Bin 0 -> 1492524 bytes examples/diffusion/main.cc | 339 ++++++++++++++ examples/diffusion/model.hh | 237 ++++++++++ examples/diffusion/params.input | 13 + .../example_diffusion-reference.vtu | 66 +++ ...xample_diffusion_parallel_p0-reference.vtu | 49 ++ ...xample_diffusion_parallel_p1-reference.vtu | 49 ++ 18 files changed, 1890 insertions(+), 10 deletions(-) create mode 100644 dumux/common/volumevariables.hh create mode 100644 examples/diffusion/.doc_config create mode 100644 examples/diffusion/CMakeLists.txt create mode 100644 examples/diffusion/README.md create mode 100644 examples/diffusion/doc/_intro.md create mode 100644 examples/diffusion/doc/_main.md create mode 100644 examples/diffusion/doc/_model.md create mode 100644 examples/diffusion/doc/main.md create mode 100644 examples/diffusion/doc/model.md create mode 100644 examples/diffusion/img/diffusion.gif create mode 100644 examples/diffusion/main.cc create mode 100644 examples/diffusion/model.hh create mode 100644 examples/diffusion/params.input create mode 100644 test/references/example_diffusion-reference.vtu create mode 100644 test/references/example_diffusion_parallel_p0-reference.vtu create mode 100644 test/references/example_diffusion_parallel_p1-reference.vtu diff --git a/dumux/common/volumevariables.hh b/dumux/common/volumevariables.hh new file mode 100644 index 0000000000..2b74ee8f01 --- /dev/null +++ b/dumux/common/volumevariables.hh @@ -0,0 +1,67 @@ +// -*- 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/>. * + *****************************************************************************/ +/*! + * \file + * \ingroup Common + * \brief Basic volume variables for finite volume methods + */ +#ifndef DUMUX_COMMON_BASIC_VOLUME_VARIABLES_HH +#define DUMUX_COMMON_BASIC_VOLUME_VARIABLES_HH + +#include <memory> + +namespace Dumux { + +template <class Traits> +class BasicVolumeVariables +{ + using Scalar = typename Traits::PrimaryVariables::value_type; +public: + //! export the type used for the primary variables + using PrimaryVariables = typename Traits::PrimaryVariables; + + /*! + * \brief Update all quantities for a given control volume + */ + template<class ElementSolution, class Problem, class Element, class SubControlVolume> + void update(const ElementSolution& elemSol, + const Problem& problem, + const Element& element, + const SubControlVolume& scv) + { + priVars_ = elemSol[scv.indexInElement()]; + } + + Scalar priVar(const int pvIdx) const + { return priVars_[pvIdx]; } + + const PrimaryVariables& priVars() const + { return priVars_; } + + // for compatibility with more general models + Scalar extrusionFactor() const + { return 1.0; } + +private: + PrimaryVariables priVars_; +}; + +} // end namespace Dumux + +#endif diff --git a/examples/CMakeLists.txt b/examples/CMakeLists.txt index e6ae059341..fbf20b2458 100644 --- a/examples/CMakeLists.txt +++ b/examples/CMakeLists.txt @@ -1,6 +1,7 @@ add_subdirectory(2pinfiltration) add_subdirectory(1ptracer) add_subdirectory(biomineralization) +add_subdirectory(diffusion) add_subdirectory(embedded_network_1d3d) add_subdirectory(shallowwaterfriction) add_subdirectory(freeflowchannel) diff --git a/examples/README.md b/examples/README.md index 5d73eb799f..beb935118d 100644 --- a/examples/README.md +++ b/examples/README.md @@ -5,7 +5,29 @@ Click on the respective example to get to a detailed documentation of the exampl For each example in this overview, the model equations and discretization method are described in words and the DuMu<sup>x</sup> name of the model is given in parenthesis: e.g. (`OneP`) / (`CCTpfaModel`). -### [:open_file_folder: Example 1: One-phase flow and tracer transport](1ptracer/README.md) +### [:open_file_folder: Example 1: Diffusion equation](diffusion/README.md) +<table><tr><td> + +In this example we create a diffusion equation model and then simulate a diffusive process. + +You learn how to + +* setup a new simple model equation (diffusion equation) +* read parameters from a configuration file +* create a type tag and specialize properties for it +* generate a randomly distributed initial field (with MPI parallelism) +* solve a time-dependent diffusion problem in parallel + +__Model equations:__ A diffusion equation model fully developed and contained within the example<br /> +__Discretization method:__ Vertex-centered finite volumes / control-volume finite elements (Lagrange, P1) (`BoxModel`) + +</td> +<td width="35%"><a href="diffusion/README.md"> +<figure><img src="diffusion/img/diffusion.gif" alt="diffusion"/></figure></td> +</a></td> +</tr></table> + +### [:open_file_folder: Example 2: One-phase flow and tracer transport](1ptracer/README.md) <table><tr><td> @@ -29,7 +51,7 @@ __Discretization method:__ Cell-centered finite volumes with two-point flux appr </a></td> </tr></table> -### [:open_file_folder: Example 2: Two-phase flow with infiltration and adaptive grid](2pinfiltration/README.md) +### [:open_file_folder: Example 3: Two-phase flow with infiltration and adaptive grid](2pinfiltration/README.md) <table><tr><td> @@ -47,14 +69,13 @@ You learn how to __Model equations:__ Immiscible two-phase flow Darcy equations in porous media (`TwoP`)<br /> __Discretization method:__ Cell-centered finite volumes with two-point flux approximation (`CCTpfaModel`) - </td> <td width="35%"><a href="2pinfiltration/README.md"> <figure><img src="2pinfiltration/img/test_2p_pointsource_adaptive.png" alt="2p result"/></figure> </a></td> </tr></table> -### [:open_file_folder: Example 3: Shallow water model](shallowwaterfriction/README.md) +### [:open_file_folder: Example 4: Shallow water model](shallowwaterfriction/README.md) <table><tr><td> @@ -74,7 +95,7 @@ __Discretization method:__ Cell-centered finite volumes with Riemann solver (`CC </a></td> </tr></table> -### [:open_file_folder: Example 4: Freeflow channel](freeflowchannel/README.md) +### [:open_file_folder: Example 5: Freeflow channel](freeflowchannel/README.md) <table><tr><td> @@ -94,7 +115,7 @@ __Discretization method:__ Finite volumes with staggered grid arrangement (`Stag </a></td> </tr></table> -### [:open_file_folder: Example 5: One-phase flow with rotation-symmetric solution](1protationsymmetry/README.md) +### [:open_file_folder: Example 6: One-phase flow with rotation-symmetric solution](1protationsymmetry/README.md) <table><tr><td> @@ -115,7 +136,7 @@ __Discretization method:__ Vertex-centered finite volumes / control-volume finit </a></td> </tr></table> -### [:open_file_folder: Example 6: Biomineralization](biomineralization/README.md) +### [:open_file_folder: Example 7: Biomineralization](biomineralization/README.md) <table><tr><td> @@ -140,7 +161,7 @@ __Discretization method:__ Vertex-centered finite volumes / control-volume finit </a></td> </tr></table> -### [:open_file_folder: Example 7: Lid-driven cavity](liddrivencavity/README.md) +### [:open_file_folder: Example 8: Lid-driven cavity](liddrivencavity/README.md) <table><tr><td> @@ -161,7 +182,7 @@ __Discretization method:__ Finite volumes with staggered grid arrangement (`Stag </a></td> </tr></table> -### [:open_file_folder: Example 8: Permeability estimation using a pore-network model](porenetwork_upscaling/README.md) +### [:open_file_folder: Example 9: Permeability estimation using a pore-network model](porenetwork_upscaling/README.md) <table><tr><td> @@ -182,7 +203,7 @@ __Discretization method:__ Pore-network (`PoreNetworkModel`) </a></td> </tr></table> -### [:open_file_folder: Example 9: Embedded network 1D-3D model (tissue perfusion)](embedded_network_1d3d/README.md) +### [:open_file_folder: Example 10: Embedded network 1D-3D model (tissue perfusion)](embedded_network_1d3d/README.md) <table><tr><td> diff --git a/examples/diffusion/.doc_config b/examples/diffusion/.doc_config new file mode 100644 index 0000000000..41c2bd836b --- /dev/null +++ b/examples/diffusion/.doc_config @@ -0,0 +1,27 @@ +{ + "README.md": [ + "doc/_intro.md" + ], + + "doc/model.md" : [ + "doc/_model.md", + "model.hh" + ], + + "doc/main.md" : [ + "doc/_main.md", + "main.cc" + ], + + "navigation" : { + "mainpage" : "README.md", + "subpages" : [ + "doc/model.md", + "doc/main.md" + ], + "subtitles" : [ + "Model implementation", + "Main program" + ] + } +} diff --git a/examples/diffusion/CMakeLists.txt b/examples/diffusion/CMakeLists.txt new file mode 100644 index 0000000000..cb8baf078e --- /dev/null +++ b/examples/diffusion/CMakeLists.txt @@ -0,0 +1,29 @@ +dune_symlink_to_source_files(FILES "params.input") + +# To add an example it would be enough to have +# dumux_add_test(NAME example_diffusion SOURCES main.cc) +# But we also make sure with automated testing that the example keep compiling +# and produce the same result, so here is a regression test: +dumux_add_test(NAME example_diffusion + LABELS example + SOURCES main.cc + COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py + CMD_ARGS --script fuzzy + --files ${CMAKE_SOURCE_DIR}/test/references/example_diffusion-reference.vtu + ${CMAKE_CURRENT_BINARY_DIR}/diffusion-00050.vtu + --command "${CMAKE_CURRENT_BINARY_DIR}/example_diffusion params.input + -Grid.Cells \"6 6\" -Problem.DiffusionCoefficient 0.001") + +# We also add a parallel test to make sure the parallel version also works +dumux_add_test(NAME example_diffusion_parallel + LABELS example + CMAKE_GUARD MPI_FOUND + TARGET example_diffusion + COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py + CMD_ARGS --script fuzzy + --files ${CMAKE_SOURCE_DIR}/test/references/example_diffusion_parallel_p0-reference.vtu + ${CMAKE_CURRENT_BINARY_DIR}/s0002-p0000-diffusion_parallel-00050.vtu + ${CMAKE_SOURCE_DIR}/test/references/example_diffusion_parallel_p1-reference.vtu + ${CMAKE_CURRENT_BINARY_DIR}/s0002-p0001-diffusion_parallel-00050.vtu + --command "${MPIEXEC} -np 2 ${CMAKE_CURRENT_BINARY_DIR}/example_diffusion params.input + -Grid.Cells \"6 6\" -Problem.DiffusionCoefficient 0.001 -Problem.Name diffusion_parallel") diff --git a/examples/diffusion/README.md b/examples/diffusion/README.md new file mode 100644 index 0000000000..c733e89b42 --- /dev/null +++ b/examples/diffusion/README.md @@ -0,0 +1,161 @@ +<!-- Important: This file has been automatically generated by generate_example_docs.py. Do not edit this file directly! --> + +# Diffusion equation + +In this example, we create an application solving the diffusion equation. +This example is implemented in three files, [`model.hh`](model.hh), [`params.input`](params.input), [`main.cc`](main.cc). +The [`model.hh`](model.hh) header implements a simple self-contained diffusion equation model +to be used with a control-volume finite element discretization like the Box method. +The [`main.cc`](main.cc) source file contains the main program and [`params.input`](params.input) contains +runtime parameters. The executable is configured in [`CMakeLists.txt`](CMakeLists.txt) and created with CMake. +The source code will be discussed in Part 1 and Part 2 after an introduction to the equations and the problem description. + +__The main points illustrated in this example are__ + +* setting up a simple model +* creating a random initial solution in parallel +* solving a time-dependent diffusion problem +* using a linear PDE solver instance +* reusing the Jacobian matrix for all time steps + +__Results__. The simulation result will look something like this: + +<figure> + <center> + <img src="img/diffusion.gif" alt="diffusion"/> + <figcaption> <b> Fig.1 </b> - Evolution of an initially random concentration field according to the diffusion equation.</figcaption> + </center> +</figure> + +__Table of contents__. This description is structured as follows: + +[TOC] + +## Equation and problem description + +The scalar diffusion equation on a domain $\Omega \subset \mathbb{R}^2$ and time interval $(0,T]$ +with boundary $\partial\Omega = \Gamma_D \cup \Gamma_N$ composed of Dirichlet and Neumann boundaries, +where for a position $x \in \Omega$ and time $t$, $c(x,t)$ denotes the unknown evolving concentration field, reads + +```math +\begin{aligned} +\frac{\partial c}{\partial t} - \nabla \cdot (D \nabla c) &= 0 && \mathrm{in}\; \Omega \times (0,T] \\ + c &= c_D && \mathrm{on}\; \Gamma_D \times (0,T] \\ + -D \nabla c \cdot \boldsymbol{n} &= g_N && \mathrm{on}\; \Gamma_N \times (0,T] \\ + c &= c^0 && \mathrm{for}\; t = 0, +\end{aligned} +``` + +with diffusion coefficient $D$, Dirichlet data $c_D$, Neumann data $g_N$, +and $\boldsymbol{n}$ denoting the outward-oriented unit normal vector on $\partial\Omega$. +In this example, we will use homogenenous Neumann boundary conditions +on all of $\partial\Omega$ such that $\Gamma_D = \emptyset$ and $g_N = 0$. +The initial concentration field $c^0$ is a random field (the discrete control volume +averages $c^0_{h,B}$ are sampled from a uniform distribution, $c^0_{h,B} \sim U(0,1)$). + +We partition $\Omega$ into control volumes $B$ (sometimes called "boxes"). +Integrating our equation over a control volume $B$ and applying the divergence theorem yields + +```math +\begin{aligned} +\int_B \frac{\partial c}{\partial t} \,\mathrm{d}V - \int_{\partial B} D \nabla c \cdot \boldsymbol{n} \,\mathrm{d}A &= 0. +\end{aligned} +``` + +We discretize in time using an implicit Euler method + +```math +\begin{aligned} +\int_B \frac{c^{n+1}-c^{n}}{\Delta t} \,\mathrm{d}V - \int_{\partial B} D \nabla c^{n+1} \cdot \boldsymbol{n} \,\mathrm{d}A &= 0. +\end{aligned} +``` + +For the Box method, the control volumes are centered at grid vertices. We partition the control volume boundary +into sub control volume faces $\sigma$ such that each $\sigma$ belongs to exactly one grid element. The discrete solution +$c_{h}$ is a piece-wise linear polynomial, and its restriction on an element $K$, denoted by $c_{h,K}$, +is represented by a linear basis such that + +```math +c_{h,K}(x) = \sum\limits_{B \in \mathcal{B}_K} c_{h,B} N_B(x) +``` + +where $\mathcal{B}_K$ is the set of control volumes intersecting element $K$ and $N_B$ are the basis functions associated +with the vertex corresponding to the center of control volume $B$. Insertion of this ansatz yields the discrete equation + +```math +\begin{aligned} +\vert B \vert \frac{c_B^{n+1}-c_B^{n}}{\Delta t} - \sum_{\sigma \in \Sigma_{B}} \left[ D \nabla c_h^{n+1} \cdot \boldsymbol{n}_{B,\sigma} \vert \sigma \vert \right] &= 0, +\end{aligned} +``` + +for each control volume $B$, where $\Sigma_{B}$ is the set of sub control volume faces on $\partial B$ and $\boldsymbol{n}_{B,\sigma}$ is the outward-oriented +unit normal vector on $\partial B$. When assembling the discrete equation, we take an element-centered view. This means that we iterate +over all elements $K$ in the mesh and for each element add the partial contributions + +```math +\begin{aligned} +\vert B \cap K \vert \frac{c_B^{n+1}-c_B^{n}}{\Delta t} - \sum_{\sigma \in \Sigma_{BK}} \left[ D \sum\limits_{B \in \mathcal{B}_K} \left\lbrace c_{h,B}^{n+1} \nabla N_B(x) \cdot \boldsymbol{n}_{B,\sigma} \vert \sigma \vert \right\rbrace \right] &= 0, +\end{aligned} +``` + +to the control volume residual of control volume $B$, where $B \cap K$ is the sub control volume given by the intersection of $B$ and $K$ +and $\Sigma_{BK} \subset \Sigma_{B}$ is the set of sub control volume faces in $K$ belonging to $\partial B$. +Computing the element-local contributions is described in Part 1. + +### Model parameters + +* $\Omega = [0,1]\times[0,1]$ (unit square) +* End time $T = 5$ and time step size $\Delta t = 0.1$ +* $100 \times 100$ cells (structured Cartesian grid) +* $D = 0.0001$ +* $c^0_{h,B} \sim U(0,1)$ + +### Running the example in parallel + +By default Dumux will try to speed up the assembly by using shared memory parallelism if a suitable +backend has been found on your system (one of TBB, OpenMP, Kokkos, C++ parallel algorithms). +You can limit the number of threads by prepending your executable with `DUMUX_NUM_THREADS=<number>`. +If you also want to use distributed memory parallelism with MPI (works better for solvers at the moment), +run the executable with your MPI environment. Each MPI process will use multi-threading if +`DUMUX_NUM_THREADS` is larger than $1$. + +Running the example with four MPI processes (distribution memory parallelism) +each with two threads (shared memory parallelism): + +```sh +DUMUX_NUM_THREADS=2 mpirun -np 4 ./example_diffusion +``` + +You can set the parameter `Grid.Overlap` to some non-zero integer in [`params.input`](params.input) +to turn the domain decomposition into an overlapping decomposition where +`Grid.Overlap` specifies the number of grid cells in the overlap between processes. +This can help to increase the convergence speed of the linear solver. + +__Tip__: To see the number of linear solver iteration, you can increase the solver verbosity level +by adding to [`params.input`](params.input) the lines: + +```ini +[LinearSolver] +Verbosity = 1 +``` + +or alternatively, run (here for an overlap size of $3$ elements): + +```sh +DUMUX_NUM_THREADS=2 mpirun -np 4 ./example_diffusion -LinearSolver.Verbosity 1 -Grid.Overlap 3 +``` + +# Implementation + +For the code implementation see Part 1 and Part 2. + +## Part 1: Model implementation + +| [:arrow_right: Click to continue with part 1 of the documentation](doc/model.md) | +|---:| + + +## Part 2: Main program + +| [:arrow_right: Click to continue with part 2 of the documentation](doc/main.md) | +|---:| diff --git a/examples/diffusion/doc/_intro.md b/examples/diffusion/doc/_intro.md new file mode 100644 index 0000000000..b899853eb0 --- /dev/null +++ b/examples/diffusion/doc/_intro.md @@ -0,0 +1,148 @@ +# Diffusion equation + +In this example, we create an application solving the diffusion equation. +This example is implemented in three files, [`model.hh`](model.hh), [`params.input`](params.input), [`main.cc`](main.cc). +The [`model.hh`](model.hh) header implements a simple self-contained diffusion equation model +to be used with a control-volume finite element discretization like the Box method. +The [`main.cc`](main.cc) source file contains the main program and [`params.input`](params.input) contains +runtime parameters. The executable is configured in [`CMakeLists.txt`](CMakeLists.txt) and created with CMake. +The source code will be discussed in Part 1 and Part 2 after an introduction to the equations and the problem description. + +__The main points illustrated in this example are__ + +* setting up a simple model +* creating a random initial solution in parallel +* solving a time-dependent diffusion problem +* using a linear PDE solver instance +* reusing the Jacobian matrix for all time steps + +__Results__. The simulation result will look something like this: + +<figure> + <center> + <img src="img/diffusion.gif" alt="diffusion"/> + <figcaption> <b> Fig.1 </b> - Evolution of an initially random concentration field according to the diffusion equation.</figcaption> + </center> +</figure> + +__Table of contents__. This description is structured as follows: + +[TOC] + +## Equation and problem description + +The scalar diffusion equation on a domain $\Omega \subset \mathbb{R}^2$ and time interval $(0,T]$ +with boundary $\partial\Omega = \Gamma_D \cup \Gamma_N$ composed of Dirichlet and Neumann boundaries, +where for a position $x \in \Omega$ and time $t$, $c(x,t)$ denotes the unknown evolving concentration field, reads + +```math +\begin{aligned} +\frac{\partial c}{\partial t} - \nabla \cdot (D \nabla c) &= 0 && \mathrm{in}\; \Omega \times (0,T] \\ + c &= c_D && \mathrm{on}\; \Gamma_D \times (0,T] \\ + -D \nabla c \cdot \boldsymbol{n} &= g_N && \mathrm{on}\; \Gamma_N \times (0,T] \\ + c &= c^0 && \mathrm{for}\; t = 0, +\end{aligned} +``` + +with diffusion coefficient $D$, Dirichlet data $c_D$, Neumann data $g_N$, +and $\boldsymbol{n}$ denoting the outward-oriented unit normal vector on $\partial\Omega$. +In this example, we will use homogenenous Neumann boundary conditions +on all of $\partial\Omega$ such that $\Gamma_D = \emptyset$ and $g_N = 0$. +The initial concentration field $c^0$ is a random field (the discrete control volume +averages $c^0_{h,B}$ are sampled from a uniform distribution, $c^0_{h,B} \sim U(0,1)$). + +We partition $\Omega$ into control volumes $B$ (sometimes called "boxes"). +Integrating our equation over a control volume $B$ and applying the divergence theorem yields + +```math +\begin{aligned} +\int_B \frac{\partial c}{\partial t} \,\mathrm{d}V - \int_{\partial B} D \nabla c \cdot \boldsymbol{n} \,\mathrm{d}A &= 0. +\end{aligned} +``` + +We discretize in time using an implicit Euler method + +```math +\begin{aligned} +\int_B \frac{c^{n+1}-c^{n}}{\Delta t} \,\mathrm{d}V - \int_{\partial B} D \nabla c^{n+1} \cdot \boldsymbol{n} \,\mathrm{d}A &= 0. +\end{aligned} +``` + +For the Box method, the control volumes are centered at grid vertices. We partition the control volume boundary +into sub control volume faces $\sigma$ such that each $\sigma$ belongs to exactly one grid element. The discrete solution +$c_{h}$ is a piece-wise linear polynomial, and its restriction on an element $K$, denoted by $c_{h,K}$, +is represented by a linear basis such that + +```math +c_{h,K}(x) = \sum\limits_{B \in \mathcal{B}_K} c_{h,B} N_B(x) +``` + +where $\mathcal{B}_K$ is the set of control volumes intersecting element $K$ and $N_B$ are the basis functions associated +with the vertex corresponding to the center of control volume $B$. Insertion of this ansatz yields the discrete equation + +```math +\begin{aligned} +\vert B \vert \frac{c_B^{n+1}-c_B^{n}}{\Delta t} - \sum_{\sigma \in \Sigma_{B}} \left[ D \nabla c_h^{n+1} \cdot \boldsymbol{n}_{B,\sigma} \vert \sigma \vert \right] &= 0, +\end{aligned} +``` + +for each control volume $B$, where $\Sigma_{B}$ is the set of sub control volume faces on $\partial B$ and $\boldsymbol{n}_{B,\sigma}$ is the outward-oriented +unit normal vector on $\partial B$. When assembling the discrete equation, we take an element-centered view. This means that we iterate +over all elements $K$ in the mesh and for each element add the partial contributions + +```math +\begin{aligned} +\vert B \cap K \vert \frac{c_B^{n+1}-c_B^{n}}{\Delta t} - \sum_{\sigma \in \Sigma_{BK}} \left[ D \sum\limits_{B \in \mathcal{B}_K} \left\lbrace c_{h,B}^{n+1} \nabla N_B(x) \cdot \boldsymbol{n}_{B,\sigma} \vert \sigma \vert \right\rbrace \right] &= 0, +\end{aligned} +``` + +to the control volume residual of control volume $B$, where $B \cap K$ is the sub control volume given by the intersection of $B$ and $K$ +and $\Sigma_{BK} \subset \Sigma_{B}$ is the set of sub control volume faces in $K$ belonging to $\partial B$. +Computing the element-local contributions is described in Part 1. + +### Model parameters + +* $\Omega = [0,1]\times[0,1]$ (unit square) +* End time $T = 5$ and time step size $\Delta t = 0.1$ +* $100 \times 100$ cells (structured Cartesian grid) +* $D = 0.0001$ +* $c^0_{h,B} \sim U(0,1)$ + +### Running the example in parallel + +By default Dumux will try to speed up the assembly by using shared memory parallelism if a suitable +backend has been found on your system (one of TBB, OpenMP, Kokkos, C++ parallel algorithms). +You can limit the number of threads by prepending your executable with `DUMUX_NUM_THREADS=<number>`. +If you also want to use distributed memory parallelism with MPI (works better for solvers at the moment), +run the executable with your MPI environment. Each MPI process will use multi-threading if +`DUMUX_NUM_THREADS` is larger than $1$. + +Running the example with four MPI processes (distribution memory parallelism) +each with two threads (shared memory parallelism): + +```sh +DUMUX_NUM_THREADS=2 mpirun -np 4 ./example_diffusion +``` + +You can set the parameter `Grid.Overlap` to some non-zero integer in [`params.input`](params.input) +to turn the domain decomposition into an overlapping decomposition where +`Grid.Overlap` specifies the number of grid cells in the overlap between processes. +This can help to increase the convergence speed of the linear solver. + +__Tip__: To see the number of linear solver iteration, you can increase the solver verbosity level +by adding to [`params.input`](params.input) the lines: + +```ini +[LinearSolver] +Verbosity = 1 +``` + +or alternatively, run (here for an overlap size of $3$ elements): + +```sh +DUMUX_NUM_THREADS=2 mpirun -np 4 ./example_diffusion -LinearSolver.Verbosity 1 -Grid.Overlap 3 +``` + +# Implementation + +For the code implementation see Part 1 and Part 2. diff --git a/examples/diffusion/doc/_main.md b/examples/diffusion/doc/_main.md new file mode 100644 index 0000000000..a5e58e7984 --- /dev/null +++ b/examples/diffusion/doc/_main.md @@ -0,0 +1 @@ +# Diffusion equation main program diff --git a/examples/diffusion/doc/_model.md b/examples/diffusion/doc/_model.md new file mode 100644 index 0000000000..6f465c4d97 --- /dev/null +++ b/examples/diffusion/doc/_model.md @@ -0,0 +1 @@ +# Diffusion equation model definition diff --git a/examples/diffusion/doc/main.md b/examples/diffusion/doc/main.md new file mode 100644 index 0000000000..28d3bd539a --- /dev/null +++ b/examples/diffusion/doc/main.md @@ -0,0 +1,426 @@ +<!-- 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](model.md) | +|---|---:| + +# Diffusion equation main program + + +In the file `main.cc`, we use the previously defined model to +setup the simulation. The setup consists of four steps: +1. Define the problem setting boundary conditions and the diffusion coefficient +2. Configure the property system reusing the model defined in Part 1 +3. Define a function for setting the random initial condition +4. The main program defining all steps of the program + +__Table of contents__ + +[TOC] + +We start in `main.cc` with the necessary header includes: +<details><summary> Click to show includes</summary> + +```cpp + +#include <config.h> +``` + +Include the header containing std::true_type and std::false_type + +```cpp +#include <type_traits> +``` + +Include the headers useful for the random initial solution + +```cpp +#include <random> +#include <dumux/common/random.hh> +``` + +As Dune grid interface implementation we will use +the structured parallel grid manager YaspGrid + +```cpp +#include <dune/grid/yaspgrid.hh> +``` + +Common includes for problem and main + +```cpp +#include <dumux/common/initialize.hh> +#include <dumux/common/properties.hh> +#include <dumux/common/parameters.hh> +#include <dumux/common/numeqvector.hh> +#include <dumux/common/boundarytypes.hh> +#include <dumux/common/fvproblem.hh> + +// VTK output functionality +#include <dumux/io/vtkoutputmodule.hh> +#include <dumux/io/grid/gridmanager_yasp.hh> + +// the discretization method +#include <dumux/discretization/box.hh> + +// assembly and solver +#include <dumux/linear/linearsolvertraits.hh> +#include <dumux/linear/linearalgebratraits.hh> +#include <dumux/linear/istlsolvers.hh> +#include <dumux/linear/pdesolver.hh> +#include <dumux/assembly/fvassembler.hh> +``` + + +Finally, we include the model defined in Part 1. + +```cpp +#include "model.hh" +``` + +</details> + +## 1. The problem class + +The problem class implements the boundary conditions. It also provides +an interface that is used by the local residual (see Part 1) to obtain the diffusion +coefficient. The value is read from the parameter configuration tree. + +<details open> +<summary><b>Click to hide/show the file documentation</b> (or inspect the [source code](../main.cc))</summary> + + +```cpp +namespace Dumux { +template<class TypeTag> +class DiffusionTestProblem : public FVProblem<TypeTag> +{ +``` + +<details><summary> Click to show boilerplate code</summary> + +```cpp + + using ParentType = FVProblem<TypeTag>; + using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; + using GlobalPosition = typename GridGeometry::LocalView::Element::Geometry::GlobalCoordinate; + using Scalar = GetPropType<TypeTag, Properties::Scalar>; + using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>; + using NumEqVector = Dumux::NumEqVector<PrimaryVariables>; + using BoundaryTypes = Dumux::BoundaryTypes<GetPropType<TypeTag, Properties::ModelTraits>::numEq()>; +``` + +</details> +In the constructor, we read the diffusion coefficient constant from the +parameter tree (which is initialized with the content of `params.input`). + +```cpp +public: + DiffusionTestProblem(std::shared_ptr<const GridGeometry> gridGeometry) + : ParentType(gridGeometry) + { + diffusionCoefficient_ = getParam<Scalar>("Problem.DiffusionCoefficient"); + } +``` + +As boundary conditions, we specify Neumann everywhere. This means, we +have to prescribe a flux at each boundary sub control volume face + +```cpp + BoundaryTypes boundaryTypesAtPos(const GlobalPosition& globalPos) const + { + BoundaryTypes values; + values.setAllNeumann(); + return values; + } +``` + +We prescribe zero flux over all of the boundary + +```cpp + NumEqVector neumannAtPos(const GlobalPosition& globalPos) const + { return { 0.0 }; } +``` + +The diffusion coefficient interface is used in the local residual (see Part 1). +We can name this interface however we want as long as we adapt the calling site +in the `LocalResidual` class in `model.hh`. + +```cpp + Scalar diffusionCoefficient() const + { return diffusionCoefficient_; } + +private: + Scalar diffusionCoefficient_; +}; +} // end namespace Dumux +``` + + +</details> + +## 2. Property tag and specializations + +We create a new tag `DiffusionTest` that inherits all properties +specialized for the tag `DiffusionModel` (we created this in Part 1) +and the tag `BoxModel` which provides types relevant for the spatial +discretization scheme (see [dumux/discretization/box.hh](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/-/blob/master/dumux/discretization/box.hh)). + +Here we choose a short form of specializing properties. The property +system also recognizes an alias (`using`) with the property name being +a member of the specified type tag. Note that we could also use the same mechanism +as in (Part 1), for example: +```code +template<class TypeTag> +struct Scalar<TypeTag, TTag::DiffusionTest> +{ using type = double; }; +``` +which has the same effect as having an alias `Scalar = double;` +as member of the type tag `DiffusionTest`. +This mechanism allows for a terser code expression. +In case both definitions are present for the same type tag, the explicit +specialization (long form) takes precedence. + + +<details open> +<summary><b>Click to hide/show the file documentation</b> (or inspect the [source code](../main.cc))</summary> + + +```cpp +namespace Dumux::Properties::TTag { + +struct DiffusionTest +{ + using InheritsFrom = std::tuple<DiffusionModel, BoxModel>; + + using Scalar = double; + using Grid = Dune::YaspGrid<2>; + + template<class TypeTag> + using Problem = DiffusionTestProblem<TypeTag>; + + using EnableGridVolumeVariablesCache = std::true_type; + using EnableGridFluxVariablesCache = std::true_type; + using EnableGridGeometryCache = std::true_type; +}; + +} // end namespace Dumux::Properties::TTag +``` + + +</details> + +## 3. Creating the initial solution + +We want to initialize the entries of the solution vector $c_{h,B}$ +with a random field such that $c_{h,B} \sim U(0,1)$. When running +with MPI in parallel this requires communication. With just one +processor (`gg.gridView().comm().size() == 1`), we can just iterate +over all entries of the solution vector and assign a uniformly +distributed random number. However, with multiple processes, the +solution vector only contains a subset of the degrees of freedom +living on the processor. Moreover, some degrees of freedom exist +on multiple processes. Each processor generates their own random +number which means we might generate different numbers for the +same degree of freedom. Therefore, we communicate the number. +The idea is that each process adds its rank number (processes are +numbered starting from 0) to its value. Then we take the minimum +over all processes which will take return the value of the processor +with the lowest rank. Afterwards, we subtract the added rank offset. + + +<details open> +<summary><b>Click to hide/show the file documentation</b> (or inspect the [source code](../main.cc))</summary> + + +```cpp +template<class SolutionVector, class GridGeometry> +SolutionVector createInitialSolution(const GridGeometry& gg) +{ + SolutionVector sol(gg.numDofs()); + + // Generate random number and add processor offset + // For sequential run, `rank` always returns `0`. + std::mt19937 gen(0); // seed is 0 for deterministic results + Dumux::SimpleUniformDistribution<> dis(0.0, 1.0); + + const auto rank = gg.gridView().comm().rank(); + for (int n = 0; n < sol.size(); ++n) + sol[n] = dis(gen) + rank; + + // We, take the value of the processor with the minimum rank + // and subtract the rank offset + if (gg.gridView().comm().size() > 1) + { + Dumux::VectorCommDataHandleMin< + typename GridGeometry::VertexMapper, + SolutionVector, + GridGeometry::GridView::dimension + > minHandle(gg.vertexMapper(), sol); + gg.gridView().communicate(minHandle, Dune::All_All_Interface, Dune::ForwardCommunication); + + // remove processor offset + for (int n = 0; n < sol.size(); ++n) + sol[n][0] -= std::floor(sol[n][0]); + } + + return sol; +} +``` + + +</details> + +## 4. The main program + + +<details open> +<summary><b>Click to hide/show the file documentation</b> (or inspect the [source code](../main.cc))</summary> + + +```cpp +int main(int argc, char** argv) +{ + using namespace Dumux; +``` + +First, we initialize MPI and the multithreading backend. +This convenience function takes care that everything is setup in the right order and +has to be called for every Dumux simulation. `Dumux::initialize` also respects +the environment variable `DUMUX_NUM_THREADS` to restrict to amount of available cores +for multi-threaded code parts (for example the assembly). + +```cpp + Dumux::initialize(argc, argv); +``` + +We initialize parameter tree including command line arguments. +This will, per default, read all parameters from the configuration file `params.input` +if such as file exists. Then it will look for command line arguments. For example +`./example_diffusion -TimeLoop.TEnd 10` will set the end time to $10$ seconds. +Command line arguments overwrite settings in the parameter file. + +```cpp + Parameters::init(argc, argv); +``` + +We specify an alias for the model type tag. +We will configure the assembler with this type tag that +we specialized all these properties for above and in the model definition (Part 1). +We can extract type information through properties specialized for the type tag +using `GetPropType`. + +```cpp + using TypeTag = Properties::TTag::DiffusionTest; + + using Scalar = GetPropType<TypeTag, Properties::Scalar>; + using Grid = GetPropType<TypeTag, Properties::Grid>; + using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; + using Problem = GetPropType<TypeTag, Properties::Problem>; + using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>; + using GridVariables = GetPropType<TypeTag, Properties::GridVariables>; +``` + +First, we initialize the grid. Grid parameters are taken from the input file +from the group `[Grid]` if it exists. You can also pass any other parameter +group (e.g. `"MyGroup"`) to `init` and then it will look in `[MyGroup.Grid]`. + +```cpp + GridManager<Grid> gridManager; + gridManager.init(); +``` + +We, create the finite volume grid geometry from the (leaf) grid view, +the problem for the boundary conditions, a solution vector and a grid variables instance. + +```cpp + auto gridGeometry = std::make_shared<GridGeometry>(gridManager.grid().leafGridView()); + auto problem = std::make_shared<Problem>(gridGeometry); + auto sol = createInitialSolution<SolutionVector>(*gridGeometry); + auto gridVariables = std::make_shared<GridVariables>(problem, gridGeometry); + gridVariables->init(sol); +``` + +Ww initialize the VTK output module and write out the initial concentration field + +```cpp + VtkOutputModule<GridVariables, SolutionVector> vtkWriter(*gridVariables, sol, problem->name()); + vtkWriter.addVolumeVariable([](const auto& vv){ return vv.priVar(0); }, "c"); + vtkWriter.write(0.0); +``` + +We instantiate time loop using start and end time as well as +the time step size from the parameter tree (`params.input`) + +```cpp + auto timeLoop = std::make_shared<CheckPointTimeLoop<Scalar>>( + getParam<Scalar>("TimeLoop.TStart", 0.0), + getParam<Scalar>("TimeLoop.Dt"), + getParam<Scalar>("TimeLoop.TEnd") + ); +``` + +Next, we choose the type of assembler, linear solver and PDE solver +and construct instances of these classes. + +```cpp + using Assembler = FVAssembler<TypeTag, DiffMethod::numeric>; + using LinearSolver = SSORCGIstlSolver<LinearSolverTraits<GridGeometry>, LinearAlgebraTraitsFromAssembler<Assembler>>; + using Solver = Dumux::LinearPDESolver<Assembler, LinearSolver>; + + auto oldSol = sol; // copy the vector to store state of previous time step + auto assembler = std::make_shared<Assembler>(problem, gridGeometry, gridVariables, timeLoop, oldSol); + auto linearSolver = std::make_shared<LinearSolver>(gridGeometry->gridView(), gridGeometry->dofMapper()); + Solver solver(assembler, linearSolver); +``` + +We tell the assembler to create the system matrix and vector objects. Then we +assemble the system matrix once and then tell the solver to reuse in every time step. +Since we have a linear problem, the matrix is not going to change. + +```cpp + assembler->setLinearSystem(); + assembler->assembleJacobian(sol); + solver.reuseMatrix(); +``` + +The time loop is where most of the actual computations happen. +We assemble and solve the linear system of equations, update the solution, +write the solution to a VTK file and continue until the we reach the +final simulation time. + + +```cpp + timeLoop->start(); do + { + // assemble & solve + solver.solve(sol); + + // make the new solution the old solution + oldSol = sol; + gridVariables->advanceTimeStep(); + + // advance to the time loop to the next step + timeLoop->advanceTimeStep(); + + // write VTK output (writes out the concentration field) + vtkWriter.write(timeLoop->time()); + + // report statistics of this time step + timeLoop->reportTimeStep(); + + } while (!timeLoop->finished()); + + timeLoop->finalize(gridGeometry->gridView().comm()); + + return 0; +} +``` + + +</details> + + +| [:arrow_left: Back to the main documentation](../README.md) | [:arrow_left: Go back to part 1](model.md) | +|---|---:| + diff --git a/examples/diffusion/doc/model.md b/examples/diffusion/doc/model.md new file mode 100644 index 0000000000..8bbda20e8a --- /dev/null +++ b/examples/diffusion/doc/model.md @@ -0,0 +1,245 @@ +<!-- 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) | +|---|---:| + +# Diffusion equation model definition + + +In the file `model.hh`, we define the model equations and +set all default model properties. The setup consist of three steps: +1. Create a model type tag (used to specialize properties) +2. Define the local residual class implementing the discrete equation +3. Specialize important properties of the model such that Dumux knows how to assemble the system matrix + +__Table of contents__ + +[TOC] + +We start in `model.hh` with the necessary header includes: +<details><summary> Click to show includes</summary> + +```cpp + +#include <dumux/common/math.hh> +#include <dumux/common/properties.hh> +#include <dumux/common/numeqvector.hh> +#include <dumux/common/volumevariables.hh> +#include <dumux/discretization/method.hh> +``` + +</details> + +## 1. Property Tag + +The property tag is simply an empty struct with the name `DiffusionModel` + + +<details open> +<summary><b>Click to hide/show the file documentation</b> (or inspect the [source code](../model.hh))</summary> + + +```cpp +namespace Dumux::Properties::TTag { +//! The diffusion model tag that we can specialize properties for +struct DiffusionModel {}; +} // end namespace Dumux::Properties::TTag +``` + + +</details> + +## 2. The local (element-wise) residual + +The local residual assembles the contribution to the residual for +all degrees of freedom associated with an element. Here, we use the +Box method which is based on $P_1$ basis functions (piece-wise linears) +and the degrees of freedom are on the nodes. Each node is associate with +exactly one sub control volume (`scv`) per element and several ($2$ in $\mathbb{R}^2$) +sub control volume faces (`scvf`). In the local residual, we can implement the +contribution for one `scv` (storage and source terms) or one `scvf` (flux terms). + +Let's have a look at the class implementation. + + +<details open> +<summary><b>Click to hide/show the file documentation</b> (or inspect the [source code](../model.hh))</summary> + + +The class `DiffusionModelLocalResidual` inherits from something called `BaseLocalResidual`. +This base class differs depending on the chosen discretization scheme. For the box method +(which is a control-volume finite element scheme) used in this example, the property +`BaseLocalResidual` is specialized to `CVFELocalResidual<TypeTag>` +in [dumux/discretization/box.hh](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/-/blob/master/dumux/discretization/box.hh). +Since this local residual only works with control-volume finite element schemes due to +the flux implementation, we could have also chosen to inherit from `public CVFELocalResidual<TypeTag>`. + +```cpp +namespace Dumux { +template<class TypeTag> +class DiffusionModelLocalResidual +: public GetPropType<TypeTag, Properties::BaseLocalResidual> +{ +``` + + +**Storage term:** Evaluate the rate of change of all conserved quantities + +```cpp + NumEqVector computeStorage(const Problem& problem, + const SubControlVolume& scv, + const VolumeVariables& volVars) const + { + NumEqVector storage; + storage[Indices::massBalanceEqIdx] = volVars.priVar(Indices::concentrationIdx); + return storage; + } +``` + +**Flux term:** Evaluate the fluxes over a face of a sub control volume. +Here we evaluate the (integrated) flux + +```math +F_{K,\sigma} = -D \sum_{B \in \mathcal{B}_K} c_{h,B} \nabla N_B \cdot\boldsymbol{n} \vert \sigma \vert +```` + + +```cpp + NumEqVector computeFlux(const Problem& problem, + const Element& element, + const FVElementGeometry& fvGeometry, + const ElementVolumeVariables& elemVolVars, + const SubControlVolumeFace& scvf, + const ElementFluxVariablesCache& elemFluxVarsCache) const + { + static_assert(DiscretizationMethods::isCVFE<typename GridGeometry::DiscretizationMethod>, + "This local residual is hard-coded to control-volume finite element schemes"); + + // Compute ∇c at the integration point of this sub control volume face. + const auto& fluxVarCache = elemFluxVarsCache[scvf]; + Dune::FieldVector<Scalar, dimWorld> gradConcentration(0.0); + for (const auto& scv : scvs(fvGeometry)) + { + const auto& volVars = elemVolVars[scv]; + // v.axpy(a, w) means v <- v + a*w + gradConcentration.axpy( + volVars.priVar(Indices::concentrationIdx), + fluxVarCache.gradN(scv.indexInElement()) + ); + } + + NumEqVector flux; + + // Compute the flux with `vtmv` (vector transposed times matrix times vector) or -n^T D ∇c A. + // The diffusion coefficient comes from the `problem` (see Part 2 of the example). + flux[Indices::massBalanceEqIdx] = -1.0*vtmv( + scvf.unitOuterNormal(), problem.diffusionCoefficient(), gradConcentration + )*scvf.area(); + + return flux; + } +}; +} // end namespace Dumux +``` + + +</details> + +## 3. The model properties + +By specializing properties for our type tag `DiffusionModel`, +every other class that knows about the type tag (this will be +for example the assembler or the problem), can extract the +type information that we specify here. + +Note that these types can be overwritten for specific problem +definitions if this is needed (we will show this on the next page). + + +<details open> +<summary><b>Click to hide/show the file documentation</b> (or inspect the [source code](../model.hh))</summary> + + +```cpp +namespace Dumux::Properties { +``` + +The type of the local residual is the class defined above + +```cpp +template<class TypeTag> +struct LocalResidual<TypeTag, TTag::DiffusionModel> +{ using type = DiffusionModelLocalResidual<TypeTag>; }; +``` + +The default scalar type is double +we compute with double precision floating point numbers + +```cpp +template<class TypeTag> +struct Scalar<TypeTag, TTag::DiffusionModel> +{ using type = double; }; +``` + +The model traits specify some information about our equation system. +Here we have just one equation. We still specify indices so in the +places where we access primary variables, we can do so with a named variable. + +```cpp +template<class TypeTag> +struct ModelTraits<TypeTag, TTag::DiffusionModel> +{ + struct type + { + struct Indices + { + static constexpr int concentrationIdx = 0; + static constexpr int massBalanceEqIdx = 0; + }; + + static constexpr int numEq() { return 1; } + }; +}; +``` + +The primary variable vector has entries of type `Scalar` and is +as large as the number of equations (here 1) but we keep it general. + +```cpp +template<class TypeTag> +struct PrimaryVariables<TypeTag, TTag::DiffusionModel> +{ + using type = Dune::FieldVector< + GetPropType<TypeTag, Properties::Scalar>, + GetPropType<TypeTag, Properties::ModelTraits>::numEq() + >; +}; +``` + +The `BasicVolumeVariables` are the simplest class of volume variables. +They only store one instance of `PrimaryVariables` for the +degree of freedom (here: vertex dof) that they are attached to. + +```cpp +template<class TypeTag> +struct VolumeVariables<TypeTag, TTag::DiffusionModel> +{ + struct Traits + { + using PrimaryVariables + = GetPropType<TypeTag, Properties::PrimaryVariables>; + }; + using type = BasicVolumeVariables<Traits>; +}; + +} // end namespace Dumux::Properties +``` + + +</details> + + +| [:arrow_left: Back to the main documentation](../README.md) | [:arrow_right: Continue with part 2](main.md) | +|---|---:| + diff --git a/examples/diffusion/img/diffusion.gif b/examples/diffusion/img/diffusion.gif new file mode 100644 index 0000000000000000000000000000000000000000..e0aecd597a2e3c7c84b85fae961915ccafb1f6e6 GIT binary patch literal 1492524 zcmd?P_g52W^FEvgDFjGD0t6CBLV!>WMJWO%kU;1Oy(%CgC}==btWOeJ=%IH==tUI7 zf^|a^P;_Z3BD#R6SQnIa(RJm!pZDK*?=$B<bLPiu<~rw^;^yvZYZom6N`QX@0J{`i zY+$ao2sayLcUxr-8#QlRjE{{v&lbnCAq3iL1={F_*y@DrBnR8*N7z!rcN*{Av2(A5 z#onE!(K~FScR0maS;bn|$LarXpYFZ{Gv|Yb-Up354w|y!4Sf=fJQ5824(df7qy{9= zxbfuh1l_oU#H52du?gCT6Esf7X&yhQaVidfHWr^8PmVoEN{k~#$CFcI$>*ZO8=MX{ 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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/>. * + *****************************************************************************/ + +// In the file `main.cc`, we use the previously defined model to +// setup the simulation. The setup consists of four steps: +// 1. Define the problem setting boundary conditions and the diffusion coefficient +// 2. Configure the property system reusing the model defined in Part 1 +// 3. Define a function for setting the random initial condition +// 4. The main program defining all steps of the program +// +// __Table of contents__ +// +// [TOC] +// +// We start in `main.cc` with the necessary header includes: +// [[details]] includes +#include <config.h> + +// Include the header containing std::true_type and std::false_type +#include <type_traits> + +// Include the headers useful for the random initial solution +#include <random> +#include <dumux/common/random.hh> + +// As Dune grid interface implementation we will use +// the structured parallel grid manager YaspGrid +#include <dune/grid/yaspgrid.hh> + +// Common includes for problem and main +// [[codeblock]] +#include <dumux/common/initialize.hh> +#include <dumux/common/properties.hh> +#include <dumux/common/parameters.hh> +#include <dumux/common/numeqvector.hh> +#include <dumux/common/boundarytypes.hh> +#include <dumux/common/fvproblem.hh> + +// VTK output functionality +#include <dumux/io/vtkoutputmodule.hh> +#include <dumux/io/grid/gridmanager_yasp.hh> + +// the discretization method +#include <dumux/discretization/box.hh> + +// assembly and solver +#include <dumux/linear/linearsolvertraits.hh> +#include <dumux/linear/linearalgebratraits.hh> +#include <dumux/linear/istlsolvers.hh> +#include <dumux/linear/pdesolver.hh> +#include <dumux/assembly/fvassembler.hh> +// [[/codeblock]] +// +// Finally, we include the model defined in Part 1. +#include "model.hh" +// [[/details]] + +// +// ## 1. The problem class +// +// The problem class implements the boundary conditions. It also provides +// an interface that is used by the local residual (see Part 1) to obtain the diffusion +// coefficient. The value is read from the parameter configuration tree. +// [[content]] +namespace Dumux { +template<class TypeTag> +class DiffusionTestProblem : public FVProblem<TypeTag> +{ + // [[details]] boilerplate code + using ParentType = FVProblem<TypeTag>; + using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; + using GlobalPosition = typename GridGeometry::LocalView::Element::Geometry::GlobalCoordinate; + using Scalar = GetPropType<TypeTag, Properties::Scalar>; + using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>; + using NumEqVector = Dumux::NumEqVector<PrimaryVariables>; + using BoundaryTypes = Dumux::BoundaryTypes<GetPropType<TypeTag, Properties::ModelTraits>::numEq()>; + // [[/details]] + // In the constructor, we read the diffusion coefficient constant from the + // parameter tree (which is initialized with the content of `params.input`). +public: + DiffusionTestProblem(std::shared_ptr<const GridGeometry> gridGeometry) + : ParentType(gridGeometry) + { + diffusionCoefficient_ = getParam<Scalar>("Problem.DiffusionCoefficient"); + } + + // As boundary conditions, we specify Neumann everywhere. This means, we + // have to prescribe a flux at each boundary sub control volume face + BoundaryTypes boundaryTypesAtPos(const GlobalPosition& globalPos) const + { + BoundaryTypes values; + values.setAllNeumann(); + return values; + } + + // We prescribe zero flux over all of the boundary + NumEqVector neumannAtPos(const GlobalPosition& globalPos) const + { return { 0.0 }; } + + // The diffusion coefficient interface is used in the local residual (see Part 1). + // We can name this interface however we want as long as we adapt the calling site + // in the `LocalResidual` class in `model.hh`. + Scalar diffusionCoefficient() const + { return diffusionCoefficient_; } + +private: + Scalar diffusionCoefficient_; +}; +} // end namespace Dumux +// [[/content]] + +// +// ## 2. Property tag and specializations +// +// We create a new tag `DiffusionTest` that inherits all properties +// specialized for the tag `DiffusionModel` (we created this in Part 1) +// and the tag `BoxModel` which provides types relevant for the spatial +// discretization scheme (see [dumux/discretization/box.hh](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/-/blob/master/dumux/discretization/box.hh)). +// +// Here we choose a short form of specializing properties. The property +// system also recognizes an alias (`using`) with the property name being +// a member of the specified type tag. Note that we could also use the same mechanism +// as in (Part 1), for example: +// ```code +// template<class TypeTag> +// struct Scalar<TypeTag, TTag::DiffusionTest> +// { using type = double; }; +//``` +// which has the same effect as having an alias `Scalar = double;` +// as member of the type tag `DiffusionTest`. +// This mechanism allows for a terser code expression. +// In case both definitions are present for the same type tag, the explicit +// specialization (long form) takes precedence. +// +// [[content]] +namespace Dumux::Properties::TTag { + +struct DiffusionTest +{ + using InheritsFrom = std::tuple<DiffusionModel, BoxModel>; + + using Scalar = double; + using Grid = Dune::YaspGrid<2>; + + template<class TypeTag> + using Problem = DiffusionTestProblem<TypeTag>; + + using EnableGridVolumeVariablesCache = std::true_type; + using EnableGridFluxVariablesCache = std::true_type; + using EnableGridGeometryCache = std::true_type; +}; + +} // end namespace Dumux::Properties::TTag +// [[/content]] + +// +// ## 3. Creating the initial solution +// +// We want to initialize the entries of the solution vector $c_{h,B}$ +// with a random field such that $c_{h,B} \sim U(0,1)$. When running +// with MPI in parallel this requires communication. With just one +// processor (`gg.gridView().comm().size() == 1`), we can just iterate +// over all entries of the solution vector and assign a uniformly +// distributed random number. However, with multiple processes, the +// solution vector only contains a subset of the degrees of freedom +// living on the processor. Moreover, some degrees of freedom exist +// on multiple processes. Each processor generates their own random +// number which means we might generate different numbers for the +// same degree of freedom. Therefore, we communicate the number. +// The idea is that each process adds its rank number (processes are +// numbered starting from 0) to its value. Then we take the minimum +// over all processes which will take return the value of the processor +// with the lowest rank. Afterwards, we subtract the added rank offset. +// +// [[content]] +// [[codeblock]] +template<class SolutionVector, class GridGeometry> +SolutionVector createInitialSolution(const GridGeometry& gg) +{ + SolutionVector sol(gg.numDofs()); + + // Generate random number and add processor offset + // For sequential run, `rank` always returns `0`. + std::mt19937 gen(0); // seed is 0 for deterministic results + Dumux::SimpleUniformDistribution<> dis(0.0, 1.0); + + const auto rank = gg.gridView().comm().rank(); + for (int n = 0; n < sol.size(); ++n) + sol[n] = dis(gen) + rank; + + // We, take the value of the processor with the minimum rank + // and subtract the rank offset + if (gg.gridView().comm().size() > 1) + { + Dumux::VectorCommDataHandleMin< + typename GridGeometry::VertexMapper, + SolutionVector, + GridGeometry::GridView::dimension + > minHandle(gg.vertexMapper(), sol); + gg.gridView().communicate(minHandle, Dune::All_All_Interface, Dune::ForwardCommunication); + + // remove processor offset + for (int n = 0; n < sol.size(); ++n) + sol[n][0] -= std::floor(sol[n][0]); + } + + return sol; +} +// [[/codeblock]] +// [[/content]] +// +// ## 4. The main program +// +// [[content]] +int main(int argc, char** argv) +{ + using namespace Dumux; + + // First, we initialize MPI and the multithreading backend. + // This convenience function takes care that everything is setup in the right order and + // has to be called for every Dumux simulation. `Dumux::initialize` also respects + // the environment variable `DUMUX_NUM_THREADS` to restrict to amount of available cores + // for multi-threaded code parts (for example the assembly). + Dumux::initialize(argc, argv); + + // We initialize parameter tree including command line arguments. + // This will, per default, read all parameters from the configuration file `params.input` + // if such as file exists. Then it will look for command line arguments. For example + // `./example_diffusion -TimeLoop.TEnd 10` will set the end time to $10$ seconds. + // Command line arguments overwrite settings in the parameter file. + Parameters::init(argc, argv); + + // We specify an alias for the model type tag. + // We will configure the assembler with this type tag that + // we specialized all these properties for above and in the model definition (Part 1). + // We can extract type information through properties specialized for the type tag + // using `GetPropType`. + using TypeTag = Properties::TTag::DiffusionTest; + + using Scalar = GetPropType<TypeTag, Properties::Scalar>; + using Grid = GetPropType<TypeTag, Properties::Grid>; + using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; + using Problem = GetPropType<TypeTag, Properties::Problem>; + using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>; + using GridVariables = GetPropType<TypeTag, Properties::GridVariables>; + + // First, we initialize the grid. Grid parameters are taken from the input file + // from the group `[Grid]` if it exists. You can also pass any other parameter + // group (e.g. `"MyGroup"`) to `init` and then it will look in `[MyGroup.Grid]`. + GridManager<Grid> gridManager; + gridManager.init(); + + // We, create the finite volume grid geometry from the (leaf) grid view, + // the problem for the boundary conditions, a solution vector and a grid variables instance. + auto gridGeometry = std::make_shared<GridGeometry>(gridManager.grid().leafGridView()); + auto problem = std::make_shared<Problem>(gridGeometry); + auto sol = createInitialSolution<SolutionVector>(*gridGeometry); + auto gridVariables = std::make_shared<GridVariables>(problem, gridGeometry); + gridVariables->init(sol); + + // Ww initialize the VTK output module and write out the initial concentration field + VtkOutputModule<GridVariables, SolutionVector> vtkWriter(*gridVariables, sol, problem->name()); + vtkWriter.addVolumeVariable([](const auto& vv){ return vv.priVar(0); }, "c"); + vtkWriter.write(0.0); + + // We instantiate time loop using start and end time as well as + // the time step size from the parameter tree (`params.input`) + auto timeLoop = std::make_shared<CheckPointTimeLoop<Scalar>>( + getParam<Scalar>("TimeLoop.TStart", 0.0), + getParam<Scalar>("TimeLoop.Dt"), + getParam<Scalar>("TimeLoop.TEnd") + ); + + // Next, we choose the type of assembler, linear solver and PDE solver + // and construct instances of these classes. + using Assembler = FVAssembler<TypeTag, DiffMethod::numeric>; + using LinearSolver = SSORCGIstlSolver<LinearSolverTraits<GridGeometry>, LinearAlgebraTraitsFromAssembler<Assembler>>; + using Solver = Dumux::LinearPDESolver<Assembler, LinearSolver>; + + auto oldSol = sol; // copy the vector to store state of previous time step + auto assembler = std::make_shared<Assembler>(problem, gridGeometry, gridVariables, timeLoop, oldSol); + auto linearSolver = std::make_shared<LinearSolver>(gridGeometry->gridView(), gridGeometry->dofMapper()); + Solver solver(assembler, linearSolver); + + // We tell the assembler to create the system matrix and vector objects. Then we + // assemble the system matrix once and then tell the solver to reuse in every time step. + // Since we have a linear problem, the matrix is not going to change. + assembler->setLinearSystem(); + assembler->assembleJacobian(sol); + solver.reuseMatrix(); + + // The time loop is where most of the actual computations happen. + // We assemble and solve the linear system of equations, update the solution, + // write the solution to a VTK file and continue until the we reach the + // final simulation time. + // + // [[codeblock]] + timeLoop->start(); do + { + // assemble & solve + solver.solve(sol); + + // make the new solution the old solution + oldSol = sol; + gridVariables->advanceTimeStep(); + + // advance to the time loop to the next step + timeLoop->advanceTimeStep(); + + // write VTK output (writes out the concentration field) + vtkWriter.write(timeLoop->time()); + + // report statistics of this time step + timeLoop->reportTimeStep(); + + } while (!timeLoop->finished()); + + timeLoop->finalize(gridGeometry->gridView().comm()); + + return 0; +} +// [[/codeblock]] +// [[/content]] diff --git a/examples/diffusion/model.hh b/examples/diffusion/model.hh new file mode 100644 index 0000000000..fcf7220f72 --- /dev/null +++ b/examples/diffusion/model.hh @@ -0,0 +1,237 @@ +// -*- 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_EXAMPLES_DIFFUSION_MODEL_HH +#define DUMUX_EXAMPLES_DIFFUSION_MODEL_HH + +// In the file `model.hh`, we define the model equations and +// set all default model properties. The setup consist of three steps: +// 1. Create a model type tag (used to specialize properties) +// 2. Define the local residual class implementing the discrete equation +// 3. Specialize important properties of the model such that Dumux knows how to assemble the system matrix +// +// __Table of contents__ +// +// [TOC] +// +// We start in `model.hh` with the necessary header includes: +// [[details]] includes +#include <dumux/common/math.hh> +#include <dumux/common/properties.hh> +#include <dumux/common/numeqvector.hh> +#include <dumux/common/volumevariables.hh> +#include <dumux/discretization/method.hh> +// [[/details]] +// +// ## 1. Property Tag +// +// The property tag is simply an empty struct with the name `DiffusionModel` +// +// [[content]] +// [[codeblock]] +namespace Dumux::Properties::TTag { +//! The diffusion model tag that we can specialize properties for +struct DiffusionModel {}; +} // end namespace Dumux::Properties::TTag +// [[/codeblock]] +// [[/content]] +// +// ## 2. The local (element-wise) residual +// +// The local residual assembles the contribution to the residual for +// all degrees of freedom associated with an element. Here, we use the +// Box method which is based on $P_1$ basis functions (piece-wise linears) +// and the degrees of freedom are on the nodes. Each node is associate with +// exactly one sub control volume (`scv`) per element and several ($2$ in $\mathbb{R}^2$) +// sub control volume faces (`scvf`). In the local residual, we can implement the +// contribution for one `scv` (storage and source terms) or one `scvf` (flux terms). +// +// Let's have a look at the class implementation. +// +// [[content]] +// +// The class `DiffusionModelLocalResidual` inherits from something called `BaseLocalResidual`. +// This base class differs depending on the chosen discretization scheme. For the box method +// (which is a control-volume finite element scheme) used in this example, the property +// `BaseLocalResidual` is specialized to `CVFELocalResidual<TypeTag>` +// in [dumux/discretization/box.hh](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/-/blob/master/dumux/discretization/box.hh). +// Since this local residual only works with control-volume finite element schemes due to +// the flux implementation, we could have also chosen to inherit from `public CVFELocalResidual<TypeTag>`. +namespace Dumux { +template<class TypeTag> +class DiffusionModelLocalResidual +: public GetPropType<TypeTag, Properties::BaseLocalResidual> +{ + // [[exclude]] + // the base local residual is selected depending on the chosen discretization scheme + using ParentType = GetPropType<TypeTag, Properties::BaseLocalResidual>; + using Scalar = GetPropType<TypeTag, Properties::Scalar>; + using Problem = GetPropType<TypeTag, Properties::Problem>; + using NumEqVector = Dumux::NumEqVector<GetPropType<TypeTag, Properties::PrimaryVariables>>; + + using GridVariables = GetPropType<TypeTag, Properties::GridVariables>; + using VolumeVariables = typename GridVariables::GridVolumeVariables::VolumeVariables; + using ElementVolumeVariables = typename GridVariables::GridVolumeVariables::LocalView; + using ElementFluxVariablesCache = typename GridVariables::GridFluxVariablesCache::LocalView; + + using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; + using FVElementGeometry = typename GridGeometry::LocalView; + using SubControlVolume = typename GridGeometry::SubControlVolume; + using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace; + using GridView = typename GridGeometry::GridView; + using Element = typename GridView::template Codim<0>::Entity; + + using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>; + using Indices = typename ModelTraits::Indices; + static constexpr int dimWorld = GridView::dimensionworld; + +public: + using ParentType::ParentType; + // [[/exclude]] + // + // **Storage term:** Evaluate the rate of change of all conserved quantities + // [[codeblock]] + NumEqVector computeStorage(const Problem& problem, + const SubControlVolume& scv, + const VolumeVariables& volVars) const + { + NumEqVector storage; + storage[Indices::massBalanceEqIdx] = volVars.priVar(Indices::concentrationIdx); + return storage; + } + // [[/codeblock]] + + // **Flux term:** Evaluate the fluxes over a face of a sub control volume. + // Here we evaluate the (integrated) flux + // + // ```math + // F_{K,\sigma} = -D \sum_{B \in \mathcal{B}_K} c_{h,B} \nabla N_B \cdot\boldsymbol{n} \vert \sigma \vert + // ```` + // + // [[codeblock]] + NumEqVector computeFlux(const Problem& problem, + const Element& element, + const FVElementGeometry& fvGeometry, + const ElementVolumeVariables& elemVolVars, + const SubControlVolumeFace& scvf, + const ElementFluxVariablesCache& elemFluxVarsCache) const + { + static_assert(DiscretizationMethods::isCVFE<typename GridGeometry::DiscretizationMethod>, + "This local residual is hard-coded to control-volume finite element schemes"); + + // Compute ∇c at the integration point of this sub control volume face. + const auto& fluxVarCache = elemFluxVarsCache[scvf]; + Dune::FieldVector<Scalar, dimWorld> gradConcentration(0.0); + for (const auto& scv : scvs(fvGeometry)) + { + const auto& volVars = elemVolVars[scv]; + // v.axpy(a, w) means v <- v + a*w + gradConcentration.axpy( + volVars.priVar(Indices::concentrationIdx), + fluxVarCache.gradN(scv.indexInElement()) + ); + } + + NumEqVector flux; + + // Compute the flux with `vtmv` (vector transposed times matrix times vector) or -n^T D ∇c A. + // The diffusion coefficient comes from the `problem` (see Part 2 of the example). + flux[Indices::massBalanceEqIdx] = -1.0*vtmv( + scvf.unitOuterNormal(), problem.diffusionCoefficient(), gradConcentration + )*scvf.area(); + + return flux; + } +}; +} // end namespace Dumux +// [[/codeblock]] +// [[/content]] +// +// ## 3. The model properties +// +// By specializing properties for our type tag `DiffusionModel`, +// every other class that knows about the type tag (this will be +// for example the assembler or the problem), can extract the +// type information that we specify here. +// +// Note that these types can be overwritten for specific problem +// definitions if this is needed (we will show this on the next page). +// +// [[content]] +namespace Dumux::Properties { + +// The type of the local residual is the class defined above +template<class TypeTag> +struct LocalResidual<TypeTag, TTag::DiffusionModel> +{ using type = DiffusionModelLocalResidual<TypeTag>; }; + +// The default scalar type is double +// we compute with double precision floating point numbers +template<class TypeTag> +struct Scalar<TypeTag, TTag::DiffusionModel> +{ using type = double; }; + +// The model traits specify some information about our equation system. +// Here we have just one equation. We still specify indices so in the +// places where we access primary variables, we can do so with a named variable. +template<class TypeTag> +struct ModelTraits<TypeTag, TTag::DiffusionModel> +{ + struct type + { + struct Indices + { + static constexpr int concentrationIdx = 0; + static constexpr int massBalanceEqIdx = 0; + }; + + static constexpr int numEq() { return 1; } + }; +}; + +// The primary variable vector has entries of type `Scalar` and is +// as large as the number of equations (here 1) but we keep it general. +template<class TypeTag> +struct PrimaryVariables<TypeTag, TTag::DiffusionModel> +{ + using type = Dune::FieldVector< + GetPropType<TypeTag, Properties::Scalar>, + GetPropType<TypeTag, Properties::ModelTraits>::numEq() + >; +}; + +// The `BasicVolumeVariables` are the simplest class of volume variables. +// They only store one instance of `PrimaryVariables` for the +// degree of freedom (here: vertex dof) that they are attached to. +template<class TypeTag> +struct VolumeVariables<TypeTag, TTag::DiffusionModel> +{ + struct Traits + { + using PrimaryVariables + = GetPropType<TypeTag, Properties::PrimaryVariables>; + }; + using type = BasicVolumeVariables<Traits>; +}; + +} // end namespace Dumux::Properties +// [[/content]] +// [[exclude]] +#endif +// [[/exclude]] diff --git a/examples/diffusion/params.input b/examples/diffusion/params.input new file mode 100644 index 0000000000..7fb645d26a --- /dev/null +++ b/examples/diffusion/params.input @@ -0,0 +1,13 @@ +[TimeLoop] +TEnd = 5.0 +Dt = 0.1 + +[Grid] +LowerLeft = 0 0 +UpperRight = 1 1 +Cells = 100 100 +Overlap = 0 + +[Problem] +Name = diffusion +DiffusionCoefficient = 0.0001 diff --git a/test/references/example_diffusion-reference.vtu b/test/references/example_diffusion-reference.vtu new file mode 100644 index 0000000000..169c52e3c6 --- /dev/null +++ b/test/references/example_diffusion-reference.vtu @@ -0,0 +1,66 @@ +<?xml version="1.0"?> +<VTKFile type="UnstructuredGrid" version="0.1" 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