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


Authors: Frédéric Coquel, Edwige Godlewski, Khalil Haddaoui, Claude Marmignon and Florent Renac
Journal: Math. Comp. 85 (2016), 2305-2339
MSC (2010): Primary 35L04, 76M12, 76N15
DOI: https://doi.org/10.1090/mcom/3063
Published electronically: February 1, 2016
MathSciNet review: 3511283
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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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Additional Information

Frédéric Coquel
Affiliation: CNRS and CMAP, Ecole polytechnique, 91128 Palaiseau Cedex, France
Email: frederic.coquel@cmap.polytechnique.fr

Edwige Godlewski
Affiliation: Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France — and —CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France, INRIA-Paris, EPC Ange, F-75012, Paris, France
Email: edwige.godlewski@upmc.fr

Khalil Haddaoui
Affiliation: ONERA The French Aerospace Lab, 92320 Châtillon Cedex, France — and — UPMC Université Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France
Email: khalil.haddaoui.edu@gmail.com

Claude Marmignon
Affiliation: ONERA The French Aerospace Lab, 92320 Châtillon Cedex, France
Email: claude.marmignon@onera.fr

Florent Renac
Affiliation: ONERA The French Aerospace Lab, 92320 Châtillon Cedex, France
Email: florent.renac@onera.fr

DOI: https://doi.org/10.1090/mcom/3063
Keywords: Model coupling, hyperbolic systems of conservation laws, measure source term, Riemann solver, relaxation, constrained optimization
Received by editor(s): April 25, 2014
Received by editor(s) in revised form: November 21, 2014, and January 23, 2015
Published electronically: February 1, 2016
Article copyright: © Copyright 2016 American Mathematical Society