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fenicsR13: A Tensorial Mixed Finite Element Solver for the Linear R13 Equations Using the FEniCS Computing Platform

Pipeline status Test coverage Documentation Website Zenodo Link with DOI Documentation Website

Paper / Documentation

See the following paper for a detailed description of the solver!

Lambert Theisen, Manuel Torrilhon. 2021. fenicsR13: A Tensorial Mixed Finite Element Solver for theLinear R13 Equations Using the FEniCS Computing Platform. ACM Trans. Math. Softw. 47, 2, Article 17 (April 2021), 29 pages, 10.1145/3442378. Preprint @ arXiv (Free PDF).

Main Features

  • Solving Steady 2D Linear R13 Equations in Normalized Form
  • Stabilization with: Continous Interior Penalty (CIP) or Galerkin Least Squares (GLS)
  • Option for convergence study with input for exact solution
  • Output in XDMF/HDF5 and PDF
  • Arbitray finite element combinations (thanks to FEniCS)
  • Easy setup of parameter studies
  • Structured/Documented YAML input file format
  • Rarefied gas flow effects predictable: Knudsen paradox, Knudsen pump, ...
  • Interface for Gmsh meshes

Installation

  1. Install Git (if not shipped with you OS).
  2. Install Git LFS (needed to download the meshes from the repository).
  3. Clone and open the repository:
# Clone Repository and open main folder
git clone git@git.rwth-aachen.de:lamBOO/fenicsR13.git
cd fenicsR13

Alternatively: download the repository, unpack and open it.

Docker

It is recommended to use the program with Docker, a virtualization software available (with free docker account) for `download`_ for most operating systems. Our repository provides a Docker container based on the official FEniCS Docker image which contains all necessities for FEniCS and has been adjusted to solve the R13 equations. The program docker-compose is also required.

Starting the Environment

Make sure you installed Docker and it is running on your system. You can start the fenicsR13 compute environment from the root-directory of the repository using the command-line

## 1) FOR USERS:
## - Pulls and runs "fenicsr13_release" service
## - Uses preinstalled latest version of fenicsR13
docker-compose pull fenicsr13_release
docker-compose run --rm fenicsr13_release

## 2) FOR DEVELOPERS (uncommend the last 3 lines of this block):
## - Builds the "fenicsr13_debug"
## - Install an editable version of fenicsR13
## - The "pip"-command install an editable version of fenicsR13
## - This allows a modification of the source files which can be directly
##   executed within the debug container
# docker-compose build fenicsr13_debug
# docker-compose run fenicsr13_debug
# sudo pip install -e .

When you run this for the first time, docker will pull (download and extract) the container image from our repository which is roughly 800MB and the download may require some patience. After the initial download the docker image will be stored (2-3 GB) on your system and any new run will start the container immediately.

The above docker command will start a RedHat-based bash environment. The repository is mounted as a volume under /home/fenics/shared in the container and should be the default folder on startup. What ever is changed in this folder or its sub-folders will change in the folder on your original system as well. However, any changes outside this folder will be gone after you exit the docker environment.

Running a Simulation

To execute a simulation case, go to to the case folder (e.g. examples/lid_driven_cavity)

# [It might be required to install the package inside the Docker container]
pip install --user -e .
# Move to folder:
cd examples/lid_driven_cavity

We provide a script to utilize gmsh and generate a H5 mesh-file from a local geometry file by

# Create mesh:
./create_mesh.sh

To run a simulation execute the solver main program fenicsR13.py (which is located in the src-directory in the top level) while specifying an input file as first command line argument.

# Run program with given input file:
fenicsR13 input.yml

Output files will be written to a folder which is named after the output_folder keyword of the input.yml. For immediate inspection the output folder contains simple visualizations in PDF files for each of the fields (temperature, pressure,...).

The numerical results for each field is ouput into h5-files, including mesh data and with corresponding xdmf-file. The XDMF-files can be opened in Paraview to perform visualization, e.g., with Paraview > File > Open > u_0.xdmf > Apply filters

# Leave directory:
cd ../..

Channel Flow Example

We provide a simple example of a flow through a finite-length channel in 2D.

# Move to folder:
cd examples/channel_flow_force
# Create mesh:
./create_mesh.sh
# Run program with given input file:
fenicsR13 input.yml

In the output folder the results can be post-processed to demonstrate the Knudsen paradox in a simple table.

# Go to folder with simulation results (=casename in input.yml)
cd channel_flow_force
# Generate correlation data between Knudsen number and massflow
bash postprocessing.sh
cat table.csv
# Leave directory:
cd ../..

Convergence Study

We can test the convergence of the R13 discretization on a simple double-cylindrical geometry.

# Move to folder:
cd tests/2d_r13
# Meshes are already in Git:
ls ../2d_mesh
# Run program with given input file:
fenicsR13 inputs/r13_1_coeffs_nosources_norot_inflow_p1p1p1p1p1_stab.yml
# Go to folder with simulation results (=casename in input.yml)
cd r13_1_coeffs_nosources_norot_inflow_p1p1p1p1p1_stab
# Open errors:
cat errors.csv

Additional information

Parallel Execution

FEniCS allows simple parallelization using MPI

# Parallel execution ("-u" to flash stdout)
# Usage: mpirun -n <numberOfProcesses> <serialCommand>
# E.g.: mpirun -n 4 fenicsR13 input.yml

Building the Docker Image Locally

The main folder of this repository contains a Dockerfile defining the used environment. Here, we used the optimized and official FEniCS Docker image and include Gmsh and install some requirements from the requirements.txt. This can take a while, especially the Gmsh mirror can be quite slow. To avoid very long execution commands (docker run <..> -v <volume share> <etc..>), a docker-compose.yml is used to store all these parameters. docker-compose acts as an wrapper for the Docker execution.

The fenics environment (also called service in the docker-compose.yml) first has to be build and can be executed afterwards. The command to build the container is

# build fenics service
docker-compose build fenicsr13_release

Interactive Docker Sessions

It is possible to use a Jupyter sever or a X11 forwarding but this is not recommended anymore. All relevant plots are now written by default without the need for the tricky X11 forwarding or interactive usage with Jupyter.

Documentation

Documentation using Sphinx is available.

Pre-Build Version

Visit the hosted version on Gitlab Pages or download the artifacts from Gitlab's CI pages-pipeline.

Manual Generation

# cat .gitlab-ci.yml
cd docs
sphinx-apidoc -o source/src ../src
sphinx-apidoc -o source/tests/2d_heat ../tests/2d_heat
sphinx-apidoc -o source/tests/2d_stress ../tests/2d_stress
sphinx-apidoc -o source/tests/2d_r13 ../tests/2d_r13
sphinx-apidoc -o source/tests/3d_heat ../tests/3d_heat
sphinx-apidoc -o source/tests/3d_stress ../tests/3d_stress
sphinx-apidoc -o source/tests/3d_r13 ../tests/3d_r13
sphinx-apidoc -o source/examples ../examples
make html
make latex

Developer Legacy Notes

Developer Tips

  • Monitor the performance of the program with e.g.:

    htop -p `{ fenicsR13 inputs/1_coeffs_nosources_norot_inflow_p1p1p1p1p1_stab.yml > /dev/null & } && echo $!`

  • Use doctest with python3 -m doctest -v src/meshes.py

  • Run pydocstyle once in a while

  • Matplotbib fails when having wrong backend on macOS
    • Fix: Add backend: TkAgg to ~/.matplotlib/matplotlibrc file

  • Performance in Docker is way better than conda build, especially JIT compilation is faster

  • Get C++ inlcude paths: echo | gcc -E -Wp,-v -

  • Bessel functions in DOLFIN:

    • C++17 functions cannpot be used. Boost functions also not per default. Expression("boost::math::cyl_bessel_i(0,atan2(x[1], x[0]))", degree=2) is allowed if one changes in file /usr/local/lib/python3.6/dist-packages/dolfin/jit/jit.py

      _math_header = """
// cmath functions
#include <boost/math/special_functions/bessel.hpp> // Added
%s
"""

Python notes

  • Get current work directory:

    import os
cwd = os.getcwd()
print(cwd)

  • Latex font for matplotlib:

    # LaTeX text fonts:
# Use with raw strings: r"$\mathcal{O}(h^1)$"
plt.rc('text', usetex=True)
plt.rc('font', family='serif')

  • Get system path where modules are searched:

    import sys
print(sys.path)

Create new version tag

  1. Add CHANGELOG entry
  2. Adapt version in conf.py for docs and setup.py for package
  3. Change badge in README.rst
  4. Change version in program information printing
  5. Build new Docker container

Gitlab CI Setup

  • The build stage has to be triggered manually when something in the setup changes. This is because it takes a fair amount of time.
  • In ~/.gitlab-runner/config.toml (for the runner):
  • Run local: gitlab-runner exec docker --docker-privileged build or with build replaced by job name
    • maybe local vars have to be change to use local Docker images because CI_REGISTRY,... are not set

An example gitlab runner config/toml in ~/.gitlab-runner can look like:

concurrent = 1
check_interval = 0

[[runners]]
name = "190716-macbookpro"
url = "https://git.rwth-aachen.de/"
token = "<PRIVATE_TOKEN>"
executor = "docker"
environment = ["DOCKER_TLS_CERTDIR="]
[runners.docker]
    tls_verify = false
    image = "docker:stable"
    privileged = true
    disable_cache = false
    volumes = ["/cache"]
    shm_size = 0
    pull_policy = "if-not-present"
[runners.cache]

macOS Native FEniCS Installation (not recommended)

  1. Install miniconda from here
    1. If using zsh, add miniconda bins to PATH: export PATH="$HOME/ miniconda3/bin:$PATH" to ~/.zshrc
    2. Maybe, activation has to be done with executing <path to miniconda>/bin/activate
    3. Optional: Create separate coda environment: conda creafenics-env
  2. Install FEniCS using conda: conda install -c conda-forge fenics
    1. Optional: Install matplobib: conda install -c conda-forge matplotlib
    2. Optional: Install meshio: conda install -c mrossi meshio
    3. Optional (for linting): conda install pylint
    4. Install mshr with conda install -c conda-forge mshr
    5. Fix macOS bug in matplotbib: mkdir -p ~/.matplotlib; echo "backend: TkAgg" > ~/.matplotlib/matplotlibrc
    6. XCode and command line developer tools msut be installed!
    7. Optional: Install Jupyter: conda install -c anaconda jupyter
    8. Optional: Install documentation system: conda install -c anaconda sphinx
    9. Optional: conda install -c anaconda sympy

Further Installation Tips

Interactive Jupyter Notebooks with Microsoft's Visual Studio Code

This is may be a convenient solution. Run a file with %run ../../fenicsr13/fenicsr13.py

X11 Window Forwarding on OSX

See guide for the programs to install. Then source the open-macos-gui-tunnel.sh with . open-macos-gui-tunnel. Afterwards, start the container and run the change-matplotbib-backend-tkagg.sh script to set the right matplotlib's output.

X11 Window Forwarding on Windows

A nice guide can be found here on Dev.to.

The steps can be summarized as:

  1. Install the package manager Chocolatey.

    REM comment: open cmd.exe as admin
@"%SystemRoot%\System32\WindowsPowerShell\v1.0\powershell.exe" -NoProfile -InputFormat None -ExecutionPolicy Bypass -Command "iex ((New-Object System.Net.WebClient).DownloadString('https://chocolatey.org/install.ps1'))" && SET "PATH=%PATH%;%ALLUSERSPROFILE%\chocolatey\bin"

  2. Open cmd.exe as admin and install VcXsrv Windows X Server.

    choco install vcxsrv

  3. Open a X11 server and set the ip variable (that is used in the docker-compose.yml when starting the Docker container to set export DISPLAY=${ip}:0).

    # home of this repo
source sripts/open-windows-gui-tunnel.sh

Contact

Author:
Supervisor:
Prof. Dr. Manuel Torrilhon
Lehrstuhl für Mathematik (MathCCES)
RWTH Aachen University