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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-01376535
Contributor : Julien Vovelle Connect in order to contact the contributor
Submitted on : Tuesday, November 20, 2018 - 12:39:11 PM
Last modification on : Monday, June 28, 2021 - 2:26:03 PM

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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, World Scientific Publishing, 2003, 13 (2), pp.221-257. ⟨10.1142/S0218202503002477⟩. ⟨hal-01376535⟩

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