Choice of measure source terms in interface coupling for a model problem in gas dynamics

Coquel, Frédéric; Godlewski, Edwige; Haddaoui, Khalil; Marmignon, Claude; Renac, Florent

doi:10.1090/mcom/3063

Choice of measure source terms in interface coupling for a model problem in gas dynamics
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by Frédéric Coquel, Edwige Godlewski, Khalil Haddaoui, Claude Marmignon and Florent Renac PDF

Math. Comp. 85 (2016), 2305-2339 Request permission

Abstract:

This paper is devoted to the mathematical and numerical analysis of a coupling procedure for one-dimensional Euler systems. The two systems have different closure laws and are coupled through a thin fixed interface. Following the work of Ambroso, Chalons, Coquel and Galié (2004), we propose to couple these systems by a bounded vector-valued Dirac measure, concentrated at the coupling interface, which in the applications may have a physical meaning. We show that the proposed framework allows the control of the coupling conditions and we propose an approximate Riemann solver based on a relaxation approach preserving equilibrium solutions of the coupled problem. Numerical experiments in constrained optimization problems are then presented to assess the performances of the present method.

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