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Simulation of strong nonlinear waves with vectorial lattice Boltzmann schemes

Author

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  • François Dubois

    (Conservatoire National des Arts et Métiers, Laboratoire de Mécanique des Structures et des Systèmes Couplés, F-75003, Paris, France;
    Department of Mathematics, University Paris-Sud, Bât. 425, F-91405 Orsay Cedex, France)

Abstract

We show that a hyperbolic system with a mathematical entropy can be discretized with vectorial lattice Boltzmann schemes using the methodology of kinetic representation of the dual entropy. We test this approach for the shallow water equations in one and two spatial dimensions. We obtain interesting results for a shock tube, reflection of a shock wave and nonstationary two-dimensional propagation. This contribution shows the ability of vectorial lattice Boltzmann schemes to simulate strong nonlinear waves in nonstationary situations.

Suggested Citation

  • François Dubois, 2014. "Simulation of strong nonlinear waves with vectorial lattice Boltzmann schemes," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 25(12), pages 1-9.
    • Handle: RePEc:wsi:ijmpcx:v:25:y:2014:i:12:n:s0129183114410149
    DOI: 10.1142/S0129183114410149
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    Cited by:

    1. Yeoh, Chin Vern & Ooi, Ean Hin & Foo, Ji Jinn, 2021. "Utilization of pressure wave-dynamics in accelerating convergence of the lattice-Boltzmann method for steady and unsteady flows," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    2. Baty, Hubert & Drui, Florence & Helluy, Philippe & Franck, Emmanuel & Klingenberg, Christian & Thanhäuser, Lukas, 2023. "A robust and efficient solver based on kinetic schemes for Magnetohydrodynamics (MHD) equations," Applied Mathematics and Computation, Elsevier, vol. 440(C).

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