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A high order accurate difference scheme for complex flow fields. (English) Zbl 0882.76054
Summary: A high order accurate finite difference method for direct numerical simulation of coherent structure in the mixing layers is presented. The reason for oscillation production in numerical solutions is analyzed. It is caused by a nonuniform group velocity of wavepackets. A method of group velocity control for the improvement of the shock resolution is presented. In numerical simulation the fifth-order accurate upwind compact difference relation is used to approximate the derivatives in the convective terms of the compressible Navier-Stokes equations, a sixth-order accurate symmetric compact difference relation is used to approximate the viscous terms, and a three-stage Runge-Kutta method is used to advance in time. In order to improve the shock resolution, the scheme is reconstructed with the method of diffusion analogy which is used to control the group velocity of wavepackets.

76M20 Finite difference methods applied to problems in fluid mechanics
76F10 Shear flows and turbulence
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
Full Text: DOI
[1] S. K. Lele, 1989
[2] Lee, S.; Lele, S.K.; Moin, P., Phys. fluids A, 3, (1991)
[3] Sandham, N.D.; Reynolds, W.C., J. fluid mech., 224, 133, (1991)
[4] Papamoschou, D.; Roshko, A., J. fluid mech., 197, 453, (1988)
[5] Bogdanoff, D.W., Aiaa j., 21, 926, (1983)
[6] Ragab, S.A.; Wu, J.L., Phys. fluids A, 1, 957, (1989)
[7] Sandham, N.D.; Reynolds, W.C., Aiaa j., 28, 618, (1990)
[8] Tam, C.K.W.; Hu, F.Q., J. fluid mech., 203, 51, (1986)
[9] D. Fu, Y. Ma, H. Liu, 1993, Proceedings, 5th International Symposium on CFD, Sendai, 1993, 1, 184
[10] Lele, S.K., J. comput. phys., 103, 16, (1992)
[11] Chi-Wang, Shu; Osher, S., J. comput. phys., 77, 439, (1988)
[12] Ma, Y.; Fu, D., Sci. China ser. A, 35, 1090, (1992)
[13] J. L. Steger, R. F. Warming
[14] D. Papamoschou, A. Roshko, 1986
[15] Michalke, A., J. fluid mech., 19, 543, (1964)
[16] Moser, R.D.; Rogers, M.M., J. fluid mech., 247, 265, (1993)
[17] L. Trefethen, SIAM Rev. 24, 136
[18] A. Harten, 1986, Proceedings, International Conference on Hyperbolic Problems, Saint-Etieme, 1986
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