Wavenumber-extended high-order upwind-biased finite-difference schemes for convective scalar transport

Journal of Computational Physics

Volumn 133, Issue 2, 1997, Pages 235-255

  Li, Yuguo ^a  

^a CSIRO   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE DIFFERENCE METHOD;

DIFFERENCING SCHEME; DISPERSION ERROR; DISSIPATION ERROR; FINITE DIFFERENCE SCHEME; FOURIER'S ANALYSIS; HIGH-ORDER; HIGHER-ORDER; SCALAR-TRANSPORT; WAVE NUMBERS;

FOURIER ANALYSIS;

EID: 0031570254     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1997.5649     Document Type: Article

References (27)

1. 1. R. F. Warming and R. M. Beam, Upwind second-order difference schemes and applications in aerodynamics flows, AIAA J. 14, 1241 (1976).
2. 2. W. Shyy, A study of finite difference approximations to steady-state, convection-dominated flow problems, J. Comput. Phys. 57, 415 (1985).
3. 3. B. P. Leonard, A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Comput. Methods Appl. Mech. Eng. 19, 59 (1979).
4. 4. A. Harten, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys. 49, 357 (1983).
5. 5. B. P. Leonard, Simple high-accuracy resolution program for convective modeling of discontinuities, Int. J. Numer. Methods Fluids 8, 1291 (1988).
6. 6. M. N. Rai and P. Moin, Direct simulations of turbulent flow using finite-difference schemes, J. Comput. Phys. 96, 15 (1991).
7. 7. S. K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys. 103, 16 (1992).
8. 8. M. N. Rai, Navier-Stokes simulations of blade-vortex interaction using high-order accurate upwind schemes, AIAA Paper 87-0543 (1987) (unpublished).
9. 9. P. Tamamidis and D. N. Assanis, Three-dimensional incompressible flow calculations with alternative discretization schemes, Numer. Heat Transfer B 24, 57 (1993).
10. 10. T. Kawamura and K. Kuwahara, Computation of high Reynolds number flow around a circular cylinder with surface roughness, AIAA Paper 84-0340 (1984).
11. 11. R. Vichnevetsky and F. De Schutter, in Advances in Computer Methods for Partial Differential Equations, edited by R. Vichnevetsky (AICA/IMACS, Rutgers University, NJ, 1975), p. 46.
12. 12. D. W. Zingg and H. Lomax, Finite-difference schemes on regular triangular grids, J. Comput. Phys. 108, 306 (1993).
13. 13. T. Hayase, A. C. Humphfrey, and R. Grief, A consistently formulated QUICK scheme for fast and stable convergence using finite-volume iterative calculation procedures, J. Comput. Phys. 98, 108 (1992).
14. 14. P. K. Khosla and S. G. Rubin, A diagonally dominant second-order accurate implicit scheme, Comput. Fluids 2, 207 (1974).
15. 15. Y. Li and L. Baldacchino, Implementation of some higher-order convection schemes on non-uniform grids, Int. J. Numer. Methods Fluids 21, 1201 (1995).
16. 16. B. Gustafsson, The convergence rate for difference approximations to mixed initial boundary value problems, Math. Comput. 29, 396 (1975).
17. 17. M. H. Carpenter, D. Gottlieb, and S. Abarbanel, The stability of numerical boundary treatments for compact high-order finite-difference schemes, J. Comput. Phys. 108, 272 (1993).
18. 18. J. C. Strikwerda, Initial boundary value problems for the method of lines, J. Comput. Phys. 34, 94 (1980).
19. 19. S. T. Zalesak, Fully multidimensional flux-corrected transport algorithms for fluids, J. Comput. Phys. 31, 335 (1979).
20. 20. Y. Li and M. Rudman, Assessment of higher-order upwind schemes incorporating FCT for convection-dominated problems, Numer. Heat Transfer B 27, 1 (1995).
21. 21. C. K. W. Tam and J. C. Webb, Dispersion-relation-preserving finite difference schemes for computational acoustics, J. Comput. Phys. 107, 262 (1993).
22. 22. C. A. J. Fletcher, Computational Techniques for Fluid Dynamics (Springer-Verlag, Berlin, 1991), Vol. 1.
23. 23. R. Vichnevetsky and J. B. Bowles, Fourier Analysis of Numerical Approximations of Hyperbolic Equations (SIAM, Philadelphia, 1982).
24. 24. L. N. Trefethen, Stability of hyperbolic finite-difference models with one or two boundaries, in Large-Scale Computations in Fluid Mechanics, edited by B. E. Engquist, S. Osher and R. C. Somerville, Lectures in Applied Mathematics, Vol. 22 (Am. Math Soc., Providence, RI, 1985), p. 311 (1985).
25. 25. G. de Vahl Davis and G. D. Mallinson, An evaluation of upwind and central difference approximations by a study of recirculating flow, Computers and Fluids 4, 29 (1976).
26. 26. A. O. Demuren, False diffusion in three-dimensional flow calculations, Computer and Fluids 13, 411 (1985).
27. 27. G. D. Raithby, Skew upstream differencing schemes for problems involving fluid flow, Comp. Meths. Appl. Mech. Eng. 9, 153 (1976).