High resolution conjugate filters for the simulation of flows

Journal of Computational Physics

Volumn 189, Issue 1, 2003, Pages 159-179

  Zhou, Y C ^a   Wei, G W ^a  

^a MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

Conjugate filters; Discrete singular convolution; Hermite kernel; High resolution; Hyperbolic conservation laws

Indexed keywords

CONVOLUTION; FOURIER ANALYSIS; HIGH PASS FILTERS; INCOMPRESSIBLE FLOW; OSCILLATING FLOW;

CONJUGATE FILTER; CONVOLUTION ALGORITHM; DISCRETE SINGULAR CONVOLUTION; HERMITE; HERMITE KERNEL; HIGH RESOLUTION; HIGH-PASS FILTER; HYPERBOLIC CONSERVATION LAWS; LOW-PASS FILTERS; OSCILLATIONS REDUCTION;

LOW PASS FILTERS;

EID: 0038454600     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(03)00206-7     Document Type: Article

References (40)

1. S. Ghosal, An analysis of numerical errors in large-eddy simulations of turbulence, J. Comput. Phys. 125 (1996) 187-206.
2. G.L. Browning, H.-O. Kreiss, Comparison of numerical methods for the calculation of two-dimensional turbulence, Math. Comput. 186 (1989) 389-410.
3. C.K.W. Tam, Computational aeroacoustics: issues and methods, AIAA J. 13 (10) (1995) 1788-1796.
4. S.Y. Yang, Y.C. Zhou, G.W. Wei, Comparison of the discrete singular convolution algorithm and the Fourier pseudospectral method for solving partial differential equations, Comput. Phys. Commun. 143 (2002) 113-135.
5. S.K. Lele, Compact finite difference scheme with spectral-like resolution, J. Comput. Phys. 103 (1992) 16-42.
6. C.K.W. Tam, J.C. Webb, Dispersion-relation-preserving finite difference schemes for computational acoustics, J. Comput. Phys. 107 (1993) 262-281.
7. B. Engquist, B. Sjögreen, Examples of error propagation from discontinuities, in: V. Venkatakrishnan, M.D. Salas, S.R. Chakravarthy (Eds.), Barriers and Challenges in Computational Fluid Dynamics, Kluwer Academic Publishers, Boston, MA, 1998, p. 27.
8. A. Harten, B. Engquist, S. Osher, S. Chakravarthy, Uniform high-order accurate essentially non-oscillatory schemes, III, J. Comput. Phys. 71 (1987) 231-303.
9. C.-W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, ICASE Report, No. 97-65, 1997.
10. W. E, C.-W. Shu, A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow, J. Comput. Phys. 110 (1994) 39-46.
11. X.-D. Liu, S. Osher, T. Chan, Weighted essentially non-oscillatory schemes, J. Comput. Phys. 115 (1994) 200-212.
12. X.-D. Liu, E. Tadmor, Third order non-oscillatory central scheme for hyperbolic conservation laws, Numer. Math. 79 (1998) 397-425.
13. A. Kurganov, D. Levy, A third-order semidiscrete central scheme for conservation laws and convention diffusion equations, SIAM J. Sci. Comput. 22 (2000) 1461.
14. E.F. Toro, R.C. Millington, V.A. Titarev, ADER: arbitrary-order non-oscillatory advection scheme, in: Proceedings of the 8th International Conference on Non-linear Hyperbolic Problems, Magdeburg, Germany, 2000.
15. D.S. Balsara, C.-W. Shu, Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy, J. Comput. Phys. 160 (2000) 405-452.
16. S. Lee, S.K. Lele, P. Moin, Interaction of isotropic turbulence with shock waves: effect of shock strength, J. Fluid Mech. 340 (1997) 225-247.
17. E. Garnier, M. Mossi, P. Sagaut, P. Comet, M. Deville, On the use of shock-capturing scheme for large-eddy simulation, J. Comput. Phys. 153 (2001) 273-311.
18. G.W. Wei, Oscillation reduction by anisotropic diffusions, Comput. Phys. Commun. 144 (2002) 317-342.
19. G.W. Wei, Synchronization of single-side averaged coupling and its application to shock capturing, Phys. Rev. Lett, 86 (2001) 3542-3545.
20. H.C. Yee, N.D. Sandham, M.J. Djomehri, Low-dissipative high-order shock-capturing methods using characteristic-based filters, J. Comput. Phys. 150 (1999) 199-238.
21. E. Garnier, P. Sagaut, M. Deville, A class of explicit ENO filters with application to unsteady flows, J. Comput. Phys. 170 (2001) 184-204.
22. W.S. Don, Numerical study of pseudospectral methods in shock wave applications, J. Comput. Phys. 110 (1994) 103-111.
23. D. Gottlieb, C.-W. Shu, On the Gibbs phenomenon and its resolution, SIAM Rev. 39 (1997) 644-668.
24. G.W. Wei, Y. Gu, Conjugated filter approach for solving Burgers' equation, J. Comput. Appl. Math. 149 (2002) 439-456; arXiv:math.SC/0009125, September 13, 2000.
25. Y. Gu, G.W. Wei, Conjugated filter approach for shock capturing, Commun. Numer. Meth. Eng. 19 (2003) 99-110.
26. G.W. Wei, Discrete singular convolution for the solution for the Fokker-Planck equations, J. Chem. Phys. 110 (1999) 8930-8942.
27. L. Schwartz, Théore des Distributions, Hermann, Paris, 1951.
28. A.I. Zayed, Advances in Shannon's Sampling Theory, CRC Press, London, 1993.
29. G.W. Wei, Y.B. Zhao, Y. Xiang, Discrete singular convolution and its application to the analysis of plates with internal supports. I. Theory and algorithm, Int. J. Numer. Meth. Eng. 55 (2002) 913-946.
30. G. Bao, G.W. Wei, A.H. Zhou, Analysis of regularized Whittaker-Kotel'nikov Shannon sampling expansion, preprint.
31. J. Koreevar, Pansions and the theory of Fourier transforms, Am. Math. Soc. Trans. 91 (1959) 53-101.
32. D.K. Hoffman, N. Nayar. O.A. Sharafeddin, D.J. Kouri, Analytic banded approximation for the discretized free propagator, J. Phys. Chem. 95 (1991) 8299-8305.
33. G.W. Wei, Wavelets generated by using discrete singular convolution kernels, J. Phys. A: Math. General 33 (2000) 8577-8596.
34. G.W. Wei, A new algorithm for solving some mechanical problems, Comput. Methods Appl. Mech. Eng. 190 (2001) 2017-2030.
35. D.C. Wan, B.S.V. Patnaik, G.W. Wei, A new benchmark quality solution for the buoyancy driven cavity by discrete singular convolution, Numer. Heat Transfer B - Fundamentals 40 (2001) 199-228.
36. D.C. Wan, Y.C. Zhou, G.W. Wei, Numerical solution of incompressible flows by discrete singular convolution, Int. J. Numer. Meth. Fluid 38 (2002) 789-810.
37. D.C. Wan, B.S.V. Patnaik, G.W. Wei, Discrete singular convolution-finite subdomain method for the solution of incompressible viscous flows, J. Comput. Phys. 180 (2002) 229-255.
38. F.Q. Hu, M.Y. Hussaini, J. Manthey, Low-dissipation and -dispersion Runge-Kutta schemes for computational acoustics, NASA TR-94-102.
39. J.B. Bell, P. Colella, H.M. Glaz, A 2nd-order projection method for the incompressible Navier Stokes equations, J. Comput. Phys. 85 (1989) 257-283.
40. J.-G. Liu, C.-W. Shu, A high-order discontinuous Galerkin method for 2D incompressible flows, J. Comput. Phys. 160 (2000) 577-596.