AREGBA-DRIOLLET, Denise; BERTHON, Christophe

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AREGBA-DRIOLLET, Denise
Institut de Mathématiques de Bordeaux [IMB]

BERTHON, Christophe
Laboratoire de Mathématiques Jean Leray [LMJL]

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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.< Réduire

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Finite volume methods

hyperbolic problems

asymptotic preserving schemes

relaxation

linearly degenerate

well-balanced

splitting

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Numerical approximation of Kerr-Debye equations

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Résumé en anglais

Mots clés en anglais

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