228 IGPM228.pdf        May 2003
TITLE On the Connection between some Riemann-Solver Free Approaches to the Approximation of Multi-Dimensional Systems of Hyperbolic Conservation Laws
AUTHORS Tim Kröger, Sebastian Noelle, Susanne Zimmermann
ABSTRACT 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 occuring in the finite volume formulation. Thus, we establish a connection between the MoT approach and the kinetic approach. Further more, 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.
KEYWORDS systems of conservation laws, Fey's Method of Transport, Euler equations, Boltzmann equation, kinetic schemes, bicharacteristic theory, state decompositions, decompositions, exact and approximate evolution operators, quadrature rules
DOI 10.1051/m2an:2004047
PUBLICATION Mathematical modelling and numerical analysis = Modélisation mathématique et analyse numérique
38, 989-1009 (2004)