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

Research output: Contribution to journalArticle

14 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)64-89
Number of pages26
JournalSIAM Journal on Numerical Analysis
Volume41
Issue number1
DOIs
StatePublished - Feb 2003

Fingerprint

Spectral Methods
Series Expansion
Ludwig Boltzmann
Difference Method
Siméon Denis Poisson
Boltzmann Transport Equation
Systems of Conservation Laws
Discretization Method
Mean-field Approximation
Boltzmann Equation
Galerkin
Non-equilibrium
Approximate Solution
Boltzmann equation
Discretization
Entropy
Conservation
Coefficient

Keywords

  • Boltzmann equation
  • Finite differences
  • Galerkin methods

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

A mixed spectral-difference method for the steady state Boltzmann-Poisson system. / Ringhofer, Christian.

In: SIAM Journal on Numerical Analysis, Vol. 41, No. 1, 02.2003, p. 64-89.

Research output: Contribution to journalArticle

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