Commit 8939208b authored by Lambert Theisen's avatar Lambert Theisen 🔥

Imrpove Readme

parent 81645e33
......@@ -11,10 +11,43 @@ fenicsR13: A Tensorial Mixed Finite Element Solver for the Linear R13 Equations
``#extendedGasDynamics`` ``#using`` ``#FEniCS``
Installation
.. math::
\scriptsize \nabla \cdot u \, & \scriptsize = \dot{m}
\\
\scriptsize \nabla p + \nabla \cdot \sigma \, & \scriptsize = b
\\
\scriptsize \nabla \cdot u + \nabla \cdot s \, & \scriptsize = r
\\
\scriptsize \frac{4}{5} {(\nabla s)}_{\text{stf}} + 2 {(\nabla u)}_{\text{stf}} + \nabla \cdot m \, & \scriptsize = - \frac{1}{\mathbb{K}} \sigma
\\
\scriptsize \frac{5}{2} \nabla \theta + \nabla \cdot \sigma + \frac{1}{2} \nabla \cdot R + \frac{1}{6} \nabla \Delta \, & \scriptsize = - \frac{1}{\mathbb{K}} \frac{2}{3} s
\\
\scriptsize m \, & \scriptsize = - 2 \mathbb{K} {(\nabla\sigma)}_{\text{stf}}
\\
\scriptsize R \, & \scriptsize = - \frac{24}{5} \mathbb{K} {(\nabla s)}_{\text{stf}}
\\
\scriptsize \Delta \, & \scriptsize = - 12 \mathbb{K} \left( \nabla \cdot s \right)
Main Features
--------------------------------------------------------------------------------
This repository contains all main and auxiliary scripts to solve the linear R13 equations for rarefied gas flows with the `FEniCS`_ software in 2D, including examples and some convergence tests.
- 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
.. _FEniCS: https://fenicsproject.org/
.. _YAML: https://de.wikipedia.org/wiki/YAML
.. _XDMF: http://www.xdmf.org/index.php/XDMF_Model_and_Format
.. _Gmsh: http://gmsh.info/
Installation
--------------------------------------------------------------------------------
Download the repository as a `zip-file`_ and un-zip, or use `git`_ with
......
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