Commit 8939208b by Lambert Theisen 🔥

 ... ... @@ -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 ... ...