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An algorithm for unsteady viscous flows at all speeds. (English) Zbl 1003.76057
Summary: We present an algorithm for simulation of unsteady viscous stratified compressible flows, which remains valid at all speeds. The method is second-order accurate in both space and time, and is independent of Mach number. In order to remove the stiffness of numerical problem due to large disparity between flow speed and acoustic wave speed at low Mach number, we propose an approximate Newton method based on artificial compressibility. Additionally, a modified advection upstream splitting method (AUSM+) is used, which permits accurate computations of both compressible and incompressible flows. We give a detailed comparison with other approximate Newton methods described in the literature. Furthermore, through computations of various benchmark test cases it is shown that the accuracy of algorithm does not depend on Mach number.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
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[1] Choi, Journal of Computational Physics 105 pp 207– (1993)
[2] Turkel, Journal of Computational Physics 72 pp 277– (1987)
[3] A preconditioned Navier-Stokes solver for low Mach number flows. In Proceedings of Computational Fluid Dynamics ’96, (eds). Wiley: Chichester, 1996; 199-205.
[4] Lee, Journal of Computational Physics 144 pp 423– (1998)
[5] Strang, SIAM Journal of Numerical Analysis 5 pp 506– (1968)
[6] The analysis and simulation of compressible turbulence. ICASE Report 90-15, Hampton, VA, 1990. · Zbl 0722.76068
[7] Codina, International Journal of Numerical Methods in Fluids 27 pp 13– (1998)
[8] Karki, AIAA Journal 27 pp 1167– (1989)
[9] Demirdzic, International Journal of Numerical Methods in Fluids 16 pp 1029– (1993)
[10] Bijl, Journal of Computational Physics 141 pp 153– (1998)
[11] Shuen, Journal of Computational Physics 106 pp 306– (1993)
[12] On solving the compressible Navier-Stokes equation for unsteady flows at very low Mach numbers. AIAA Paper No. 93-3368, 1993.
[13] Coupled compressible and incompressible finite volume formulations for LES of turbulent flow with and without heat transfer. PhD thesis, Iowa State University, Ames, IA, 1995.
[14] Dual time stepping and preconditioning for unsteady computations. AIAA Paper No. 95-0078, 1995.
[15] Dailey, Computers and Fluids 25 pp 791– (1996)
[16] A preconditioned dual-time, diagonalized ADI scheme for unsteady computations. AIAA Paper No. 97-2101, 1997.
[17] Mary, Computers and Fluids 29 pp 119– (2000)
[18] Preconditioning and the limit to the incompressible flow equations. ICASE Report No. 93-42, 1993.
[19] Edwards, AIAA Journal 36 pp 1610– (1998)
[20] Guillard, Computers and Fluids 28 pp 63– (1999)
[21] Turkel, Computers and Fluids 26 pp 613– (1997)
[22] van der Vorst, SIAM Journal of Scientific and Statistical Computing 13 pp 631– (1992)
[23] Chorin, Journal of Computational Physics 2 pp 12– (1967)
[24] An assessment of some algorithm for steady and unsteady low Mach number flows. In Proceedings of ICFD 6th International Conference on Numerical Methods for Fluid Dynamics, (ed.). Will Print: Oxford, 1998; 403-409.
[25] Liou, Journal of Computational Physics 129 pp 364– (1996)
[26] Luo, Journal of Computational Physics 146 pp 664– (1998)
[27] Sesterhenn, Journal of Computational Physics 151 pp 597– (1999)
[28] Spiegel, Astrophysics Journal 141 pp 1068– (1965)
[29] On the use and accuracy of compressible flow codes at low Mach numbers. AIAA Paper No. 91-1662, 1991.
[30] A fast flux-splitting for all speed flow. In Proceedings of 15th International Conference on Numerical Methods in Fluid Dynamics, (ed.). Springer: New York, Monterey, CA, 1996; 141-146.
[31] Yee, Journal of Computational Physics 68 pp 664– (1987)
[32] Time-accurate Navier-Stokes calculations with multigrid acceleration. In Proceedings of the 6th Copper Mountain Conference on Multigrid Methods, Copper Mountain, CO, (ed.). 1993; 423-437.
[33] Time accuracy and the use of implicit methods. AIAA Paper No. 93-3360, 1993.
[34] Analyse num?rique matricielle appliqu?e ? l’art de l’ing?nieur (tome 2). Masson: Paris, 1987.
[35] Choice of implicit and explicit operator for the upwinding differencing method. AIAA Paper No. 88-0624, 1988.
[36] Orkwis, AIAA Journal 31 pp 832– (1993)
[37] Computational Methods for Fluid Flow. Springer: New York, 1983. · Zbl 0514.76001
[38] Time-accurate unsteady incompressible flow algorithms based on artificial compressibility. AIAA Paper No. 87-1137, 1987.
[39] Fr?hlich, European Journal of Mechanics, B Fluids 12 pp 141– (1993)
[40] Rehm, Journal of Research of the National Bureau of Standards 83 pp 297– (1978) · Zbl 0433.76072
[41] Sohankar, International Journal of Numerical Methods in Fluids 26 pp 39– (1998)
[42] Franke, Journal of Wind Engineering and Industrial Aerodynamics 35 pp 237– (1990)
[43] Davis, Journal of Fluid Mechanics 116 pp 475– (1982)
[44] Sohankar, Physics and Fluids 11 pp 288– (1999)
[45] A numerical study of a class of TVD schemes for compressible mixing layers. NASA TM-102194, 1989.
[46] Lele, Journal of Computational Physics 103 pp 16– (1992)
[47] Shu, Journal of Computational Physics 77 pp 439– (1988)
[48] ENO and PPM schemes for direct numerical simulation of compressible flows. In Advances in DNS/LES, (eds). Greyden Press: Ruston, USA, 1997; 589-596.
[49] Liu, Journal of Computational Physics 115 pp 200– (1994)
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