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 | |
| State | Published - Feb 2003 |
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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 journal › Article
}
TY - JOUR
T1 - A mixed spectral-difference method for the steady state Boltzmann-Poisson system
AU - Ringhofer, Christian
PY - 2003/2
Y1 - 2003/2
N2 - 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.
AB - 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.
KW - Boltzmann equation
KW - Finite differences
KW - Galerkin methods
UR - http://www.scopus.com/inward/record.url?scp=1842563943&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=1842563943&partnerID=8YFLogxK
U2 - 10.1137/S003614290138958X
DO - 10.1137/S003614290138958X
M3 - Article
AN - SCOPUS:1842563943
VL - 41
SP - 64
EP - 89
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
SN - 0036-1429
IS - 1
ER -