Le système d'Euler bi-température non conservatif : propriétés entropiques et approximation numérique.

International audienc

Numerical approximation of Kerr-Debye equations

We investigate finite volume schemes for the one-dimensional Kerr-Debye model of electromagnetic propagation in nonlinear media. In this relaxation quasilinear hyperbolic system, the relaxation parameter is the response time of the media. When it tends to zero, the relaxed limit is known as the Kerr system. We show that basic explicit splitting methods fail to preserve this asymptotic. Following two different viewpoints, we construct splitting implicit and well-balanced explicit approximations which are stable, entropic and own the correct asymptotic behavior. Various numerical experiments are performed

The Riemann problem for Kerr equations and non-uniqueness of selfsimilar entropy solutions

We solve the Riemann problem for a nonlinear full wave Maxwell system arising in nonlinear optics. This system is hyperbolic, some eigenvalues have non-constant multiplicity and are neither genuinely nonlinear, nor linearly degenerate. In a particular 2x2 reduced case, we are able to exhibit two distinct selfsimilar entropy solutions. We compute the amounts of entropy dissipation and compare them