A hybrid pressure–densitybased algorithm for （一个混合pressuredensitybased算法）.pdf

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 2012; 70:961–976 Published online 4 Nov 2011 in Wiley Online Library (/journal/nmf). DOI: 10.1002/fld.2722 A hybrid pressure–density-based algorithm for the Euler equations at all Mach number regimes 1,*,† 1 1 2 C. M. Xisto , J. C. Páscoa , P. J. Oliveira and D. A. Nicolini 1Dep. de Eng. Electromecânica, Universidade da Beira Interior, R. Mq.s D Ávila e Bolama, 6201-001 Covilhã, Portugal 2Directorate of Science and Robotic Exploration, European Space Agency, ESTEC, Keplerlaan 1, 2201AZ Noordwijk, The Netherlands SUMMARY In the present work, we propose a reformulation of the fluxes and interpolation calculations in the PISO method, a well-known pressure-correction solver. This new reformulation introduces the AUSMC up flux definition as a replacement for the standard Rhie and Chow method of obtaining fluxes and central inter- polation of pressure at the control volume faces. This algorithm tries to compatibilize the good efficiency of a pressure based method for low Mach number applications with the advantages of AUSMC up at high Mach number flows. The algorithm is carefully validated using exact solutions. Results for subsonic, transonic and supersonic axisymmetric flows in a nozzle are presented and compared with exact analyti- cal solutions. Further, we also present and discuss subsonic, transonic and supersonic results for the well known bump test-case. The code is also benchmarked against a very tough test-case for the supersonic and hypersonic flow over a cylinder. Copyright © 2011 John Wiley Sons, Ltd. Received 29 July 2011; Revised 8 October 2011; Accepted 16 October 2011 KEY WORDS: finite volume; Eul