Hierarchical Boltzmann Simulations

This is a very basic proof-of-concept research code that solves the linear steady Boltzmann equation with Hermite-discretizations and an implicit discontinuous Galerkin method in two dimensions on unstructured grids. The hierarchical nature allows to produce both accurate and very efficient solutions of classical fluid dynamics and precisely resolved Boltzmann simulations.

The code comes with rather limited documentation and user friendliness. For questions please contact

Manuel Torrilhon  - [email protected]
Neeraj Sarna      - [email protected]

Requirements

The code has been tested on Unix- and OSX-systems using recent Gnu- and Intel- compilers. The following additional libraries are required for compilation:

• C++-template library for linear algebra Eigen, see http://eigen.tuxfamily.org
• The Mesh-oriented Database MOAB, see http://sigma.mcs.anl.gov/moab-library

The linear system solution is based on the sparse-direct-solver pardiso which can be used in two versions:

• Intel's math kernel library Intel MKL, see https://software.intel.com/en-us/node/470282
• original Pardiso Solver Project, see http://www.pardiso-project.org

Some of the analytical solutions require Bessel functions provided by

• C++ libraries Boost, see http://www.boost.org

Some basic evaluation and visualization of the results is based on scripts using

• Mathematica, see https://www.wolfram.com/mathematica

Basic Usage

1. Download the repository
2. Install the required libraries
3. Consult and modify the directory definitions in MakefileMKL.def or MakefilePARDISO.def depending on your installation.
4. Change into one of the application folders System*, the most general is SystemGxy, and compile with make
5. Check out the Readme.md of the application for instructions how to run the code

Alternatively, open the mathematica notebooks provided in the Evaluation folders to explore precomputed results.

Reference

This repository supplements the publication

• M. Torrilhon and N. Sarna, Hierarchical Boltzmann Simulations and Model Error Estimation, (2016), submitted

which also contains additional details of the methods used in the code.