Geodesic
On the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws
Kröger, Tim ; Noelle, Sebastian ; Zimmermann, Susanne1
1 ETH Zentrum, Seminar für Angewandte Mathematik, 8092 Zürich, Switzerland.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 6, pp. 989-1009

Voir la notice de l'article provenant de la source Numdam

In this paper, we present some interesting connections between a number of Riemann-solver free approaches to the numerical solution of multi-dimensional systems of conservation laws. As a main part, we present a new and elementary derivation of Fey's Method of Transport (MoT) (respectively the second author's ICE version of the scheme) and the state decompositions which form the basis of it. The only tools that we use are quadrature rules applied to the moment integral used in the gas kinetic derivation of the Euler equations from the Boltzmann equation, to the integration in time along characteristics and to space integrals occurring in the finite volume formulation. Thus, we establish a connection between the MoT approach and the kinetic approach. Furthermore, Ostkamp's equivalence result between her evolution Galerkin scheme and the method of transport is lifted up from the level of discretizations to the level of exact evolution operators, introducing a new connection between the MoT and the evolution Galerkin approach. At the same time, we clarify some important differences between these two approaches.

DOI : 10.1051/m2an:2004047
Classification : 35C15, 35L65, 65D32, 65M25, 76M12, 76N15, 76P05
Keywords: systems of conservation laws, Fey's method of transport, Euler equations, Boltzmann equation, kinetic schemes, bicharacteristic theory, state decompositions, flux decompositions, exact and approximate integral representations, quadrature rules

Kröger, Tim  ; Noelle, Sebastian  ; Zimmermann, Susanne 1

1 ETH Zentrum, Seminar für Angewandte Mathematik, 8092 Zürich, Switzerland. 
@article{M2AN_2004__38_6_989_0,
     author = {Kr\"oger, Tim and Noelle, Sebastian and Zimmermann, Susanne},
     title = {On the connection between some {Riemann-solver} free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {989--1009},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {6},
     year = {2004},
     doi = {10.1051/m2an:2004047},
     mrnumber = {2108941},
     zbl = {1083.35063},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004047/}
}
TY  - JOUR
AU  - Kröger, Tim
AU  - Noelle, Sebastian
AU  - Zimmermann, Susanne
TI  - On the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2004
SP  - 989
EP  - 1009
VL  - 38
IS  - 6
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004047/
DO  - 10.1051/m2an:2004047
LA  - en
ID  - M2AN_2004__38_6_989_0
ER  - 
%0 Journal Article
%A Kröger, Tim
%A Noelle, Sebastian
%A Zimmermann, Susanne
%T On the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2004
%P 989-1009
%V 38
%N 6
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004047/
%R 10.1051/m2an:2004047
%G en
%F M2AN_2004__38_6_989_0
Kröger, Tim; Noelle, Sebastian; Zimmermann, Susanne. On the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 6, pp. 989-1009. doi: 10.1051/m2an:2004047

Cité par Sources :