A mixed spectral-difference method for the steady state Boltzmann-Poisson system

Christian Ringhofer

doi:10.1137/S003614290138958X

A mixed spectral-difference method for the steady state Boltzmann-Poisson system

Christian Ringhofer

CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

The approximate solution of the Boltzmann transport equation via Galerkin-type series expansion methods leads to a system of conservation laws in space and time for the expansion coefficients. In this paper, we derive discretization methods for these equations in the mean field approximation, which are based on the entropy principles of the underlying Boltzmann equation, and discuss the performance of these discretizations and the series expansion approach in nonequilibrium regimes.

Original language	English (US)
Pages (from-to)	64-89
Number of pages	26
Journal	SIAM Journal on Numerical Analysis
Volume	41
Issue number	1
DOIs	https://doi.org/10.1137/S003614290138958X
State	Published - Feb 2003

Keywords

Boltzmann equation
Finite differences
Galerkin methods

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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KW - Galerkin methods

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