Hybrid finite compact-WENO schemes for shock calculation

International Journal for Numerical Methods in Fluids

Volumn 53, Issue 4, 2007, Pages 531-560

  Shen, Yiqing ^a   Yang, Guowei ^a  

^a INSTITUTE OF MECHANICS   (China)

Author keywords

ACM filter scheme; ENO scheme; Finite compact difference scheme; Shock calculation; WENO scheme

Indexed keywords

BOUNDARY CONDITIONS; FINITE DIFFERENCE METHOD; MATHEMATICAL MODELS; MATRIX ALGEBRA; WAVEFORM ANALYSIS;

ARTIFICIAL COMPRESSION METHOD (ACM); FINITE COMPACT DIFFERENCE SCHEME; HYBRID SCHEMES; NUMERICAL FLUX FUNCTION; SHOCK CALCULATION;

SHOCK WAVES;

BOUNDARY CONDITIONS; FINITE DIFFERENCE METHOD; MATHEMATICAL MODELS; MATRIX ALGEBRA; SHOCK WAVES; WAVEFORM ANALYSIS;

EID: 33846428802     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1286     Document Type: Article

References (28)

1. Harten A. High resolution schemes for hyperbolic conservation laws. Journal of Computational Physics 1983; 49:357-393.
2. Harten A, Engquist B, Osher S, Chakravarthy SR. Uniformly high order accuracy essentially non-oscillatory schemes. III. Journal of Computational Physics 1987; 71:231-303.
3. Shu CW, Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes. II. Journal of Computational Physics 1989; 83:32-78.
4. Liu XD, Osher S, Chan T. Weighted essentially non-oscillatory schemes. Journal of Computational Physics 1994; 115:200-212.
5. Jiang GS, Shu CW. Efficient implementation of weighted ENO schemes. Journal of Computational Physics 1996; 126:202-228.
6. Kim D, Kwon JH. A high-order accurate hybrid scheme using a central flux scheme and a WENO scheme for compressible flowfield analysis. Journal of Computational Physics 2005; 210:554-583.
7. Yee HC, Sandham ND, Djomehri MJ. Low-dissipative high-order shock capturing methods using characteristic-based filters. Journal of Computational Physics 1999; 150:199-238.
8. Sjogreen B, Yee HC. Grid convergence of high order methods for multiscale complex unsteady viscous compressible flows. Journal of Computational Physics 2003; 185:1-26.
9. Wang ZJ, Chen RF. Optimized weighted essentially non-oscillatory schemes for linear waves with discontinuity. Journal of Computational Physics 2001; 174:381-404.
10. Balsara D, Shu CW. Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. Journal of Computational Physics 2000; 160:405-452.
11. Jiang Z. On dispersion-controlled principles for non-oscillatory shock-capturing schemes. Acta Mechanica Sinica 2004; 20(1):1-15.
12. Lele SK. Compact finite difference schemes with spectral-like resolution. Journal of Computational Physics 1992;103:16-42.
13. Cockburn B, Shu CW. Nonlinearly stable compact schemes for shock calculations. SIAM Journal on Numerical Analysis 1994; 31(3):607-627.
14. Ravichandran KS. Higher order KFVS algorithms using compact upwind difference operators. Journal of Computational Physics 1997; 130:161-173.
15. Deng XG, Zhang HX. Developing high-order weighted compact nonlinear schemes. Journal of Computational Physics 2000; 165:22-44.
16. Zhu QY, Chan CK. An upwind compact approach with group velocity control for compressible flow fields. International Journal for Numerical Methods in Fluids 2004; 44:463-482.
17. Fu DX, Ma YW. A high order accurate finite difference scheme for complex flow fields. Journal of Computational Physics 1997; 134:1-15.
18. Adams NA, Shariff K. A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems. Journal of Computational Physics 1996; 127:27-51.
19. Pirozzoli S. Conservative hybrid compact-WENO schemes for shock-turbulence interaction. Journal of Computational Physics 2002; 178:81-117.
20. Ren YX, Liu M, Zhang HX. A characteristic-wise hybrid compact-WENO scheme for solving hyperbolic conservation laws. Journal of Computational Physics 2003; 192:365-386.
21. Tolstykh AI, Lipavskii MV. On performance of methods with third- and fifth-order compact upwind differencing. Journal of Computational Physics 1998; 140:205-232.
22. Shen YQ, Yang GW, Gao Z. High-resolution finite compact difference schemes for hyperbolic conservation laws. Journal of Computational Physics 2006; 216:114-137.
23. Yee HC, Sjogreen B. Designing adaptive low dissipative high order schemes for long-time integrations. RIACS Technical Report TR01-28, December 2001; In Turbulent Flow Computation, Drikakis D, Geurts B (eds). Kluwer Academic Publishers: Dordrecht, MA, 2002; 141-198.
24. Yee HC, Sjogreen B. Nonlinear filtering in compact high order schemes. International Conference on Numerical Simulation of Plasma, 12-15 July, 2005, Nara, Japan; Journal of Plasma Physics, in press.
25. Carpenter MH, Gottlieb D, Abarbanel S. The stability of numerical boundary treatments for compact high-order finite-difference schemes. Journal of Computational Physics 1993; 108:272-295.
26. Ma YW, Fu DX, Kobayashi T, Taniguchi N. Numerical solution of the incompressible Navier-Stokes equations with an upwind compact difference scheme. International Journal for Numerical Methods in Fluids 1999; 30:509-521.
27. Steger JL, Warming RF. Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods. Journal of Computational Physics 1981; 40:263-293.
28. Shu CW, Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes. Journal of Computational Physics 1988; 77:439-471.