A relaxation method via the Born-Infeld system


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Abstract: We propose an original relaxation scheme for scalar conservation laws of the formt u + ∂x(u(1 − u)g(u)) = 0, where g C1 ([0, 1]; ℝ). Those scalar conservation laws come from a drift-flux model for two-phase flows [16]. Unlike Jin and Xin's approach [12], the new relaxation strategy does not involve any tuning parameter, but makes use of the Born-Infeld system [5, 18]. 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.

Mots Clés: Two-phase flow; Drift-flux model; Multi-component fluid; Relaxation methods; Born-Infeld system; Chapman-Enskog analysis; Whitham condition

Date: 2008-04-28