×

zbMATH — the first resource for mathematics

Developing high-order weighted compact nonlinear schemes. (English) Zbl 0988.76060
The authors consider compact high-order nonlinear schemes and three fourth- and fifth-order weighted compact nonlinear schemes (WCNS). Using Fourier analysis, the authors discuss dissipative and dispersive features of WCNS. In view of the modified wave number, the WCNS are equivalent to fifth-order upwind biased explicit schemes in smooth regions, and both flux difference splitting and flux vector splitting methods can be applied to them, though they are finite difference schemes. Numerical results show a good performance of WCNS for discontinuity capture, high accuracy for boundary-layer calculations, and also a good convergence rate.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
76L05 Shock waves and blast waves in fluid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Lele, S.K., Compact finite difference schemes with spectral-like resolution, J. comput. phys., 103, 16, (1992) · Zbl 0759.65006
[2] R. V. Wilson, A. Q. Demuren, and, M. H. Carpenter, High-order compact schemes for numerical simulations of incompressible flows, ICASE Report 98-13 ICASE, Langley Research Center, 1998.
[3] Leslie, L.M.; Purser, R.J., Three-dimensional mass-conserving semi-Lagrangian scheme employing forward tajectories, Mon. weather rev., 123, 2551, (1995)
[4] Garanzha, V.A.; Konshin, Numerical algorithms for viscous incompressible fluid flows based on the high-order conservative compact schemes, Comput. math. math. phys., 8, 1321, (1999) · Zbl 1083.76558
[5] Gaitonde, D.; Shang, J.S., Optimized compact-difference-based finite-volume schemes for linear wave phenomena, J. comput. phys., 138, 617, (1997) · Zbl 0898.65055
[6] Kobayashi, M.H., On a class of pade finite volume methods, J. comput. phys., 156, 137, (1999) · Zbl 0940.65092
[7] Cockburn, B.; Shu, C.W., Nonlinearly stable compact schemes for shock calculations, SIAM J. numer. anal., 31, 607, (1994) · Zbl 0805.65085
[8] Deng, X.G.; Maekawa, H., Compact high-order accurate nonlinear schemes, J. comput. phys., 130, 77, (1997) · Zbl 0870.65075
[9] Deng, X.G.; Maekawa, H., An uniform fourth-order nonlinear compact schemes for discontinuities capturing, AIAA paper 96-1974, 27th AIAA fluid dynamics meeting, (1996)
[10] Deng, X.G.; Maekawa, H.; Shen, Q., A class of high-order dissipative compact schemes, AIAA paper 96-1972, 27th AIAA fluid dynamics meeting, (1996)
[11] X. G. Deng, and, M. L. Mao, Weighted compact high-order nonlinear schemes for the Euler equations, AIAA Paper 97-1941, presented of the 13th AIAA Computational Fluid Dynamic Conference (Snowmass).
[12] Liu, X.D.; Osher, S.; Chan, T., Weighted essentially non-oscillatory schemes, J. comput. phys., 115, 200, (1994) · Zbl 0811.65076
[13] G. S. Jiang, and, C. W. Shu, Efficient implementation of weighted ENO schemes, ICASE Report, No. 95-73, 1995; also NASA CR 198228, 1995.
[14] Shu, C.W.; Osher, S., Efficient implementation of essentially non-oscillatory shock-capturing schemes II, J. comput. phys., 83, 32, (1989) · Zbl 0674.65061
[15] Huynh, H.T., Accurate upwind methods for the Euler equations, SIAM J. numer. anal., 32, 1565, (1995) · Zbl 0847.76052
[16] Gustaffson, B., The convergence rate for difference approximations to mixed initial boundary value problems, Math. comput., 49, 396, (1975)
[17] Roberts, G.O., Computational meshes for the boundary problems, Proc. second international conf. numerical methods fluid dyn., 171, (1971)
[18] Gaitonde, D.; Shang, J.S., Accuracy of flux-split algorithms in high-speed viscous flows, Aiaa j., 31, 1215, (1993) · Zbl 0782.76065
[19] Woodward, P.; Collela, P., The numerical simulation of two-dimensional fluid flow with strong shocks, J. comput. phys., 54, 115, (1984)
[20] Kopriva, D.A., Spectral solution of the viscous blunt-body problem, Aiaa j., 31, 1235, (1993) · Zbl 0781.76067
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.