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Article Dans Une Revue Mathematical Models and Methods in Applied Sciences Année : 2003

Analysis and approximation of a scalar conservation law with a flux function with discontinuous coefficients

Nicolas Seguin
Julien Vovelle

Résumé

We study here a model of conservative nonlinear conservation law with a flux function with discontinuous coefficients, namely the equation ut + (k(x)u(1 - u))x = 0. It is a particular entropy condition on the line of discontinuity of the coefficient k which ensures the uniqueness of the entropy solution. This condition is discussed and justified. On the other hand, we perform a numerical analysis of the problem. Two finite volume schemes, the Godunov scheme and the VFRoe-ncv scheme, are proposed to simulate the conservation law. They are compared with two finite volume methods classically used in an industrial context. Several tests confirm the good behavior of both new schemes, especially through the discontinuity of permeability k (whereas a loss of accuracy may be detected when industrial methods are performed). Moreover, a modified MUSCL method which accounts for stationary states is introduced.
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Dates et versions

hal-01376535 , version 1 (20-11-2018)

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Nicolas Seguin, Julien Vovelle. Analysis and approximation of a scalar conservation law with a flux function with discontinuous coefficients. Mathematical Models and Methods in Applied Sciences, 2003, 13 (2), pp.221-257. ⟨10.1142/S0218202503002477⟩. ⟨hal-01376535⟩
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