Fast Boltzmann : solving the Boltzmann equation in N log N

This software was developed (or is under development) within the higher education and research community. Its stability can vary (see fields below) and its working state is not guaranteed.
Higher Edu - Research dev card
  • Creation or important update: 17/05/10
  • Minor correction: 17/05/10
  • Index card author: Francis Filbet (ICJ)
  • Theme leader: Violaine Louvet (Institut Camille Jordan)
General software features

We propose fast deterministic algorithms based on spectral methods derived for the Boltzmann collision operator for a class of interactions including the hard spheres model in dimension 3. These algorithms are implemented for the solution of the Boltzmann equation in dimension 2 and 3, first for homogeneous solutions, then for general non homogeneous solutions. The results are compared to explicit solutions, when available, and to Monte-Carlo methods.

Context in which the software is used

The construction of approximate methods of solution for the
Boltzmann equation has a long history tracing back to D. Hilbert, S. Chapmann and D. Enskog [see Cercignani's book] at the beginning of the last century. The mathematical difficulties related to the Boltzmann equation make it extremely difficult, if not impossible, the determination of analytic solutions in most physically relevant situations.

Publications related to software
  • High order Numerical Methods for the Space Non Homogeneous Boltzmann Equation, J. Comput. Physics, 186 (2003), no. 2, 457--480, with G. Russo.
  • Solving the Boltzmann Equation in N log(N) with Deterministic Methods, SIAM J. Scientific Computing, vol. 28, no. 3 (2006) 1029--1053 with C. Mouhot and L. Pareschi.