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Cancellation problem of preconditioning method at low Mach numbers. (English) Zbl 1343.76047
Summary: The effects of cancellation errors on the convergence characteristics of preconditioned Navier-Stokes equations at low Mach numbers are analyzed. Laminar viscous flows around a circular cylinder are calculated at different Mach numbers. It is shown that the cancellation error in the energy equation grows faster than those in the other equations, as the Mach number decreases. It is also shown that the cancellation problem of the energy equation is due to the off-diagonal element that is related to a pressure change in the preconditioner.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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[1] Turkel, E., Annu. rev. fluid mech., 31, 385, (1999)
[2] Turkel, E., J. comput. phys., 72, 277, (1987)
[3] Turkel, E., Appl. numer. math., 12, 257, (1993)
[4] B. van Leer, W-T. Lee, P. Roe, AIAA paper 91-1552-CP, 1991.
[5] Choi, Y.H.; Merkle, C.L., J. comput. phys., 105, 207, (1993)
[6] Weiss, J.M.; Smith, W.A., Aiaa j., 33, 2050, (1995)
[7] Merkle, C.J., Aiaa j., 36, 515, (1998)
[8] Sabanca, M.; Brenner, G.; Alemdaroglu, N., Int. J. numer. methods fluids, 34, 167, (2000)
[9] Sabanca, M.; Durst, F., Phys. fluids, 15, 1821, (2003)
[10] Shuen, J.S.; Chen, K.H., J. comput. phys., 106, 306, (1993)
[11] K.H. Chen, J.S. Shuen, AIAA paper 94-3047, 1994.
[12] K.H. Chen, J.S. Shuen, E. Mularz, AIAA paper 95-0800, 1995.
[13] L.D. Dailey, R.H. Pletcher, AIAA paper 95-1668, 1995.
[14] Hsieh, S.; Yang, V., Int. J. CFD, 8, 31, (1997)
[15] P. Buelow, D.A. Schwer, J. Feng, C.L. Merkle, AIAA paper 97-2101, 1997.
[16] Lee, S.-H., J. comput. phys., 208, 266, (2005)
[17] Sesterhenn, J.; Muller, B.; Thomann, H., J. comput. phys., 151, 597, (1999)
[18] Conte, S.D.; de Boor, C., Elementary numerical analysis, (1988), McGraw-Hill New York
[19] Guillard, S.; Viozat, C., Comput. fluid, 28, 63, (1999)
[20] Arminjon, P.; St-Cyr, A.; Madrane, A., Appl. numer. math., 40, 367, (2002)
[21] Darmofal, D.L.; Moinier, P.; Giles, M.B., J. comput. phys., 160, 369, (2000)
[22] Okong’o, N.; Bellan, J., J. comput. phys., 176, 330, (2002)
[23] Dennis, S.C.R.; Chang, G.-Z., J. fluid mech., 42, 471, (1970)
[24] Fornberg, B., J. fluid mech., 98, 819, (1980)
[25] Linnick, M.N.; Fasel, H.F., J. comput. phys., 204, 157, (2005)
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