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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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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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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
  • MR Author ID: 266191
  • 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
  • MR Author ID: 652914
  • Email: claude.marmignon@onera.fr
  • Florent Renac
  • Affiliation: ONERA The French Aerospace Lab, 92320 Châtillon Cedex, France
  • MR Author ID: 938391
  • Email: florent.renac@onera.fr
  • 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
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 85 (2016), 2305-2339
  • MSC (2010): Primary 35L04, 76M12, 76N15
  • DOI: https://doi.org/10.1090/mcom/3063
  • MathSciNet review: 3511283