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We show that an hyperbolic system with a mathematical entropy can bediscretized with vectorial lattice Boltzmann schemes with the methodology ofkinetic representation of the dual entropy. We test this approach for theshallow water equations in one and two space dimensions. We obtain interestingresults for a shock tube, reflection of a shock wave and unstationarytwo-dimensional propagation. This contribution shows the ability of vectoriallattice Boltzmann schemes to simulate strong nonlinear waves in unstationarysituations.

Simulation of strong nonlinear waves with vectorial lattice Boltzmann schemes