A Relaxation Approach for Simulating Fluid Flows in a Nozzle
We present here a Godunov-type scheme to simulate one-dimensional flows in a nozzle with variable cross-section. The method relies on the construction of a relaxation Riemann solver designed to handle all types of flow regimes, from subsonic to supersonic flows, as well as resonant transonic flows. Some computational results are also provided, in which this relaxation method is compared with the classical Rusanov scheme and a modified Rusanov scheme.
KeywordsRelaxation scheme Godunov-type scheme resonant transonic flows
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The second author receives a financial support by ANRT through an EDF-CIFRE contract 529/2009. Computational facilities were provided by EDF. The third author is partially supported by the LRC Manon (Modélisation et Approximation Numérique Orientées pour l’énergie Nucléaire – CEA/DM2S-LJLL).
- 1.F. Bouchut. Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws. Birkhauser. Frontiers in Mathematics. 2004.Google Scholar
- 2.F. Coquel, K. Saleh, N. Seguin. Relaxation and numerical approximation for fluid flows in a nozzle. Preprint to be published. Google Scholar
- 3.C.M. Dafermos. Hyperbolic Conservation Laws in Continuum Physics. Springer-Verlag. Grundlehren der mathematischen Wissenschaften. Vol 325. 2000.Google Scholar
- 4.L. Girault, J-M. Hérard. A two-fluid hyperbolic model in a porous medium. M2AN, Vol 44(6), pp 1319-1348, 2010.Google Scholar
- 5.P. Goatin, P.G. LeFloch. The Riemann problem for a class of resonant hyperbolic systems of balance laws. Ann. Inst. H. Poincaré Anal. Non Linéaire 21, no 6, pp 881-902, 2004.Google Scholar
- 6.E. Godlewski, P-A. Raviart. Numerical Approximation of Hyperbolic Systems ofConservation Laws. Springer-Verlag. Applied Mathematical Sciences. Vol 118. 1996.Google Scholar
- 7.A. Harten, P.D. Lax & B. Van Leer. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. Comm. Math. Sci. Vol 1. pp 763-796. 2003.Google Scholar
- 8.D. Kröner, M.D. Thanh. Numerical solution to compressible flows in a nozzle with variable cross-section. SIAM J. Numer. Anal., Vol 43(2), pp 796-824, 2006.Google Scholar
- 9.P.G. LeFloch, M.D. Thanh. The Riemann problem for fluid flows in a nozzle with discontinuous cross-section. Comm. Math. Sci. Vol 1, pp 763-796, 2003.Google Scholar