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Preprint 2008-004

A relaxation method via the Born–Infeld system

Michaël Baudin, Frédéric Coquel and Quang Huy Tran

Abstract: We propose an original relaxation scheme for scalar conservation laws of the form tu+∂x(u(1−u)g(u))=0. Those scalar conservation laws come from a drift-flux model for two-phase flows. Unlike Jin and Xin's approach, the new relaxation strategy does not involve any tuning parameter, but makes use of the Born-Infeld system. The advantage of this new method is that it enables us to achieve a maximum principle on the velocities w=(1−u)g and z=−ug, and to control the sign of the numerical flux. Stability is established for a wide class of eligible functions g. This method can be plugged into a scheme for two-phase fluids, for which numerical experiments are shown.

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Michaël Baudin
Frédéric Coquel
Quang Huy Tran,
Publishing information:
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; 2008-01-26.