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A collocated finite volume method for predicting flows at all speeds. (English) Zbl 0774.76066
Summary: An existing two-dimensional method for the prediction of steady-state incompressible flows in complex geometry is extended to treat also compressible flows at all speeds. The primary variables are the Cartesian velocity components, pressure and temperature. Density is linked to pressure via an equation of state. The influence of pressure on density in the case of compressible flows is implicitly incorporated into the extended SIMPLE algorithm, which in the limit of incompressible flow reduces to its well-known form. Special attention is paid to the numerical treatment of boundary conditions. The method is verified on a number of test cases (inviscid and viscous flows), and both the results and convergence properties compare favourably with other numerical results available in the literature.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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[1] and , ’Numerical solutions to the Euler equations by finite volume methods using Runge-Kutta time stepping’, AIAA Paper 81-1259, 1981.
[2] Beam, AIAA J. 16 pp 393– (1978)
[3] and , ’Computational efficiency achieved by time splitting of finite difference operators’, AIAA Paper 72-154, 1972.
[4] Ni, AIAA J. 28 pp 1565– (1982)
[5] and , ’Transfinite mesh generation and damped Euler equation algorithm for transonic flow around wing-body configuration’, AIAA Paper 81-0999, 1981.
[6] Sahu, AIAA J. 23 pp 1348– (1985)
[7] Soh, J. Comput. Phys. 79 pp 113– (1988)
[8] Numerical Heat Transfer and Fluid Flow, Hemisphere, New York, 1980. · Zbl 0521.76003
[9] Rhie, AIAA J. 21 pp 1525– (1983)
[10] ’A finite volume method for the prediction of three-dimensional fluid flow in complex ducts’, Ph.D. Thesis, University of London, London, 1985.
[11] Demirdžić, Comput. Fluids 15 pp 251– (1987)
[12] Demirdžić, Int. j. numer. methods fluids 10 pp 771– (1990)
[13] Hirt, J. Comput Phys. 14 pp 226– (1974)
[14] Karki, AIAA J. 27 pp 1167– (1989)
[15] and , ’Solution method for viscous flows at all speeds in complex domains’, in (ed.), Notes on Numerical Fluid Mechanics, Vol. 29, Vieweg, Braunschweig, 1990.
[16] Issa, AIAA J. 27 pp 182– (1977)
[17] Patankar, Int. J. Heat Mass Transfer 15 pp 1787– (1972)
[18] Momentum, Energy and Mass Transfer in Continua, McGraw-Hill, New York, 1972.
[19] The Dynamics and Thermodynamics of Compressible Fluid Flow, Wiley, New York, 1953.
[20] Perić, Numer. Heat Transfer 17 pp 63– (1990)
[21] Numerical Computation of Internal and External Flows, Wiley, New York, 1991.
[22] Stone, SIAM J. Numer. Anal. 5 pp 530– (1968)
[23] ’Comparison of cell centred and cell vertex finite volume schemes’, in (ed.), Notes on Numerical Fluid Mechanics, Vol. 20, Vieweg, Braunschweig, 1988. · Zbl 0684.76014
[24] Demirdžić, Int. j. numer. methods fluids 15 pp 329– (1992)
[25] Technische Thermodynamik, Steinkopff, Dresden, 1972.
[26] and (eds), ’Numerical methods for the computation of inviscid transonic flows with shock waves’, in Notes on Numerical Fluid Mechanics, Vol. 3, Vieweg, Braunschweig, 1981. · Zbl 0445.76044
[27] Eidelman, AIAA J. 22 pp 1609– (1984)
[28] Morton, J. Comput. Phys. 80 pp 168– (1989)
[29] , , , and , ’Solution procedures for accurate numerical simulations of flow in turbomachinery’, AIAA Paper 83-0257, 1983.
[30] (ed.), ’Numercial simulation of compressible Navier-Stokes flows’, in Notes on Numerical Fluid Mechanics, Vol. 18, Vieweg, Braunschweig, 1987.
[31] Chang, J. Comput. Phys. 80 pp 334– (1989)
[32] and , ’Euler solvers for hypersonic aerothermodinamic problems’, in (ed.), Notes on Numerical Fluid Mechanics, Vol. 20, Vieweg, Braunschweig, 1988.
[33] Hortmann, Int. j. numer. methods fluids 11 pp 189– (1990)
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