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A Second Order Accurate Kinetic Relaxation Scheme for Inviscid Compressible Flows

  • K. R. ArunEmail author
  • M. Lukáčová-Medvidová
  • Phoolan Prasad
  • S. V. Raghurama Rao
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 120)

Abstract

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.

Keywords

Boltzmann Equation Euler Equation Kinetic Scheme Order Scheme Relaxation Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • K. R. Arun
    • 1
    Email author
  • M. Lukáčová-Medvidová
    • 2
  • Phoolan Prasad
    • 3
  • S. V. Raghurama Rao
    • 4
  1. 1.Institut für Geometrie und Praktische MathematikRWTH-AachenAachenGermany
  2. 2.Institut für MathematikJohannes Gutenberg Universität MainzMainzGermany
  3. 3.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  4. 4.Department of Aerospace EngineeringIndian Institute of ScienceBangaloreIndia

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