François Dubois
Published 2014-01-02Version 1
We show that an hyperbolic system with a mathematical entropy can be discretized with vectorial lattice Boltzmann schemes with the methodology of kinetic representation of the dual entropy. We test this approach for the shallow water equations in one and two space dimensions. We obtain interesting results for a shock tube, reflection of a shock wave and unstationary two-dimensional propagation. This contribution shows the ability of vectorial lattice Boltzmann schemes to simulate strong nonlinear waves in unstationary situations.
A two-dimensional high-order well-balanced scheme for the shallow water equations with topography and Manning friction
Parallel-in-time integration of the shallow water equations on the rotating sphere using Parareal and MGRIT
On the advantage of well-balanced schemes for moving-water equilibria of the shallow water equations
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