TY - JOUR
T1 - Dissipative discretization methods for approximations to the Boltzmann equation
AU - Ringhofer, Christian
N1 - Funding Information:
∗E-mail: ringhofer@asu.edu; supported by NSF grant Nos. DMS 9706792 and INT 9603253.
Copyright:
Copyright 2005 Elsevier Science B.V., Amsterdam. All rights reserved.
PY - 2001/2
Y1 - 2001/2
N2 - This paper deals with the spatial discretization of partial differential equations arising from Galerkin approximations to the Boltzmann equation, which preserves the entropy properties of the original collision operator. A general condition on finite difference methods is derived, which guarantees that the discrete system satisfies the appropriate equivalent of the entropy condition. As an application of this concept, entropy producing difference methods for the hydrodynamic model equations and for spherical harmonics expansions are presented.
AB - This paper deals with the spatial discretization of partial differential equations arising from Galerkin approximations to the Boltzmann equation, which preserves the entropy properties of the original collision operator. A general condition on finite difference methods is derived, which guarantees that the discrete system satisfies the appropriate equivalent of the entropy condition. As an application of this concept, entropy producing difference methods for the hydrodynamic model equations and for spherical harmonics expansions are presented.
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U2 - 10.1142/S0218202501000799
DO - 10.1142/S0218202501000799
M3 - Article
AN - SCOPUS:0035582407
VL - 11
SP - 133
EP - 148
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
SN - 0218-2025
IS - 1
ER -