Simulation of strong nonlinear waves with vectorial lattice Boltzmann schemes

François Dubois (1, 2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 LMSSC - Laboratoire de Mécanique des Structures et des Systèmes Couplés

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 non-stationary two-dimensional propagation. This contribution shows the ability of vectorial lattice Boltzmann schemes to simulate strong nonlinear waves in non-stationary situations.

Mots clés: hyperbolic conservation laws; entropy; shock wave; shallow water equations

Domaines: Analyse numérique [math.NA]; Automates cellulaires et gaz sur réseau [nlin.CG]; Mécanique des fluides [physics.class-ph]

François Dubois. Simulation of strong nonlinear waves with vectorial lattice Boltzmann schemes. International Journal of Modern Physics C, 2014, 25 (12), pp.1441014. ⟨10.1142/S0129183114410149⟩. ⟨hal-00923281v2⟩