6533b7d6fe1ef96bd126648b

RESEARCH PRODUCT

A Second Order Accurate Kinetic Relaxation Scheme for Inviscid Compressible Flows

S. V. Raghurama RaoMaria Lukacova-medvidovaK. R. ArunPhoolan Prasad

subject

Physicssymbols.namesakeConservation lawDistribution functionInviscid flowEntropy (statistical thermodynamics)Mathematical analysissymbolsKinetic schemeRelaxation (approximation)Boltzmann equationEuler equations

description

In this paper we present a kinetic relaxation scheme for the Euler equations of gas dynamics in one space dimension. The method is easily applicable to solve any complex system of conservation laws. The numerical scheme is based on a relaxation approximation for conservation laws viewed as a discrete velocity model of the Boltzmann equation of kinetic theory. The discrete kinetic equation is solved by a splitting method consisting of a convection phase and a collision phase. The convection phase involves only the solution of linear transport equations and the collision phase instantaneously relaxes the distribution function to an equilibrium distribution. We prove that the first order accurate method is conservative, preserves the positivity of mass density and pressure and entropy stable. An anti-diffusive Chapman-Enskog distribution is used to derive a second order accurate method. The results of numerical experiments on some benchmark problems confirm the efficiency and robustness of the proposed scheme.

yearjournalcountryeditionlanguage
2013-01-01
https://doi.org/10.1007/978-3-642-33221-0_1