A three-point sixth-order staggered combined compact difference scheme

Mathematical and Computer Modelling

Volumn 32, Issue 3-4, 2000, Pages 323-340

  Chu, Peter C ^a   Fan, Chenwu ^a  

^a NAVAL POSTGRADUATE SCHOOL   (United States)

Author keywords

Blasius equation; Combined compact difference scheme; Computational stability; Sigma coordinate ocean model; Staggered grid

Indexed keywords

EID: 0034254497     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(00)00138-2     Document Type: Article

References (24)

1. Y. Adam, Highly accurate compact implicit methods and boundary conditions, J. Comput. Phys. 24, 10-22, (1977).
2. S.K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys. 103, 16-42, (1992).
3. M.H. Carpenter, D.G. Gottlieb and S. Abarbanel, The stability of numerical boundary treatments for compact high-order finite-difference schemes, J. Comput. Phys. 108, 227-295, (1993).
4. M.H. Carpenter, D.G. Gottlieb and S. Abarbanel, Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes, J. Comput. Phys. 111, 220-236, (1994).
5. P.C. Chu and C. Fan, Sixth-order difference scheme for sigma coordinate ocean models, J. Phys. Oceanogr. 27, 2064-2071, (1997).
6. R.S. Hirsh, Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique, J. Comput. Phys. 19, 90-109, (1975).
7. S.G. Rubin and P.K. Khosla, Polynomial interpolation methods for viscous flow calculations, J. Comput. Phys. 24, 217-244, (1977).
8. I.M. Navon and H.A. Riphagen, An implicit compact fourth-order algorithm for solving the shallow-water equations in conservation-law form, Mon. Wea. Rev. 107, 1107-1127, (1979).
9. P.C. Chu and C. Fan, A three-point combined compact difference scheme, J. Comput. Phys. 140, 370-399, (1998).
10. P.C. Chu and C. Fan, A three-point sixth-order nonuniform combined compact difference scheme, J. Comput. Phys. 148, 663-674, (1999).
11. M.H. Carpenter, D.G. Gottlieb and S. Abarbanel, Stable and accurate boundary treatments for compact high-order finite difference schemes, Appl. Num. Math. 12, 55-87, (1993).
12. B. Gustsfsson, H.-O. Kreiss and A. Sundstrom, Stability theory of difference approximations for mixed initial boundary value problems. II, Math. Comput. 26 (119), 649-686, (1972).
13. MATLAB, Reference Guide, Math Works, Natick, MA, (1992).
14. F.M. White, Viscous Fluid Flow, pp. 712, McGraw-Hill, New York, (1974).
15. J.M. Gary, Estimate of truncation error in transformed coordinate primitive equation atmospheric models, J. Atmos. Sci. 30, 223-233, (1973).
16. R.L. Haney, On the pressure gradient force over steep topography in sigma coordinate ocean models, J. Phys. Oceanogr. 21, 610-619, (1991).
17. G.L. Mellor, T. Ezer and L.-Y. Oey, The pressure gradient conundrum of sigma coordinate ocean models, J. Atmos. Oceanic Technol. 11, 1126-1134, (1994).
18. D.B. Haidvogel, J.L. Wikin and R. Young, A semi-spectral primitive equation model using vertical sigma and orthogonal curvilinear coordinates, J. Comput. Phys. 94, 151-185, (1991).
19. K. Hedstrom, User's Manual for a Semi-Spectral Primitive Equation Ocean Circulation Model Version 3.9, pp. 131, Rutgers University, New Jersey, (1994).
20. J.D. McCalpin, A comparison of second-order and fourth-order pressure gradient algorithms in a σ-coordinate ocean model, Int. J. Numer. Methods Fluids 18, 361-383, (1994).
21. A. Beckmann and D.B. Haidvogel, Numerical simulation of flow around a tall isolated seamount. Part 1: Problem formulation and model accuracy, J. Phys. Oceanogr. 23, 1736-1753, (1993).
22. W.J. Goedheer and J.H.M. Potters, A compact finite difference scheme on a non-equidistance mesh, J. Comput. Phys. 61, 269-279, (1985).
23. P.M. Prenter, Splines and Variational Method, pp. 100-101, Wiley-Intersci., New York, (1974).
24. J.C. Strikwerda, Initial boundary value problems for the method of lines, J. Comput. Phys. 34, 94-107, (1980).