A well-balanced approximate Riemann solver for compressible flows in variable cross-section ducts

Authors:
Philippe Helluy;Jean-Marc HéRard;HéLèNe Mathis
Affiliations:
IRMA, Université de Strasbourg, 7 rue Descartes, 67084 Strasbourg, France;EDF, R&D, Fluid Dynamics, Power Generation and Environment, 6 quai Watier, 78400 Chatou, France;IRMA, Université de Strasbourg, 7 rue Descartes, 67084 Strasbourg, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

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Abstract

A well-balanced approximate Riemann solver is introduced in this paper in order to compute approximations of one-dimensional Euler equations in variable cross-section ducts. The interface Riemann solver is grounded on the VFRoe-ncv scheme, and it enforces the preservation of Riemann invariants of the steady wave. The main properties of the scheme are detailed. We provide numerical results to assess the validity of the scheme, even when the cross-section is discontinuous. A first series is devoted to analytical test cases, and the last results correspond to the simulation of a bubble collapse.