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A Characteristics Based Genuinely Multidimensional Discrete Kinetic Scheme for the Euler Equations

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Abstract

In this paper we present the results of a kinetic relaxation scheme for an arbitrary hyperbolic system of conservation laws in two space dimensions. We propose a new discrete velocity Boltzmann equation, which is an improvement over the previous models in terms of the isotropic coverage of the multidimensional domain by the foot of the characteristic. The discrete kinetic equation is solved by a splitting method consisting of a convection step and a collision step. The convection step involves only the solution of linear transport equations whereas the collision step instantaneously relaxes the distribution function to a local Maxwellian. An anti-diffusive Chapman-Enskog distribution is used to derive a second order accurate method. Finally some numerical results are presented which confirm the robustness and correct multidimensional behaviour of the proposed scheme.

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Acknowledgements

The authors thank Professors Sebastian Noelle and Phoolan Prasad for their constant encouragement and support. They also wish to thank the anonymous reviewers for their valuable suggestions to improve the quality of the paper. K.R.A. is supported by the Alexander von Humboldt Foundation through a postdoctoral fellowship.

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  1. Institut für Geometrie und Praktische Mathematik, RWTH-Aachen, Templergraben 55, 52056, Aachen, Germany

    K. R. Arun

  2. Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55099, Mainz, Germany

    M. Lukáčová-Medviďová

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  1. K. R. Arun
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Correspondence to K. R. Arun.

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Arun, K.R., Lukáčová-Medviďová, M. A Characteristics Based Genuinely Multidimensional Discrete Kinetic Scheme for the Euler Equations. J Sci Comput 55, 40–64 (2013). https://doi.org/10.1007/s10915-012-9623-6

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