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

Philippe Helluy (1, 2) , Jean-Marc Hérard (3, 4) , Hélène Mathis (5)

1 IRMA - Institut de Recherche Mathématique Avancée
2 TONUS - TOkamaks and NUmerical Simulations
3 I2M - Institut de Mathématiques de Marseille
4 EDF R&D - EDF R&D
5 LMJL - Laboratoire de Mathématiques Jean Leray

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 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.

Mots clés: Well-balanced scheme; Approximate Riemann solver; Compressible flows; Riemann problem

Domaines: Mathématiques [math]

Philippe Helluy, Jean-Marc Hérard, Hélène Mathis. A well-balanced approximate Riemann solver for compressible flows in variable cross-section ducts. Journal of Computational and Applied Mathematics, 2012, 236, pp.1976-1992. ⟨10.1016/j.cam.2011.11.008⟩. ⟨hal-01265318⟩