Completely Conservative and Oscillationless Semi-Lagrangian Schemes for Advection Transportation

Journal of Computational Physics

Volumn 170, Issue 2, 2001, Pages 498-522

  Xiao, Feng ^a,b   Yabe, Takashi ^a  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b JAPAN AGENCY FOR MARINE EARTH SCIENCE AND TECHNOLOGY   (Japan)

Author keywords

Atmospheric modeling; Computational algorithm; Linear and nonlinear transportation equations; Mass conservation; Semi Lagrangian scheme; Shock wave

Indexed keywords

ADVECTION; CELLS; CYTOLOGY; INTERPOLATION; LAGRANGE MULTIPLIERS; NONLINEAR EQUATIONS;

ATMOSPHERIC MODELING; COMPUTATIONAL ALGORITHM; CUBIC POLYNOMIALS; GRID CELLS; INTERPOLATION FUNCTION; LINEAR AND NONLINEAR TRANSPORTATION EQUATION; MASS CONSERVATION; SEMI-LAGRANGIAN SCHEME; SHOCK-WAVES; SPATIAL INTEGRATIONS;

SHOCK WAVES;

EID: 0037655394     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2001.6746     Document Type: Article

References (37)

1. H. Akima, A new method of interpolation and smooth curve fitting based on local procedures, J. Assoc. Comput. Mach. 17, 589 (1970).
2. R. Bermejo and A. Staniforth, The conversion of semi-Lagrangian advection schemes to quasi-monotone schemes, Mon. Weather Rev. 120, 2622 (1992).
3. J. P. Boris and D. L. Book, Flux corrected transport. I. SHASTA: A fluid transport algorithm that works, J. Comput. Phys. 11, 38 (1973).
4. P. Collela and P. R. Woodward, The piecewise parabolic method (PPM) for gas-dynamical simulations, J. Comput. Phys. 54, 174 (1984).
5. D. R. Durran, Numerical Methods for Wave Equations in Geophysical Fluid Dynamics (Springer-Verlag, New York, 1999).
6. F. N. Fritsch and J. Butland, An Improved Monote Piecewise Cubic Interpolation Algorithm, Lawrence Livermore National Laboratory preprint UCRL-85104, 1980.
7. A. Harten, B. Engquist, S. Osher, and S. R. Chakravarthy, Uniformly highorder accuracy essentially nonoscillatory schemes, III, J. Comput. Phys. 71, 231 (1987).
8. A. Harten and S. Osher, Uniformly high order accurate non-oscillatory schemes, I, SIAM J. Numer. Anal. 24, 279 (1987).
9. P. Holnicki, A piecewise-quintic interpolation scheme, J. Comput. Phys. 127, 316 (1996).
10. J. H. Hyman, Accurate monotonicity preserving cubic interpolations, SIAM J. Sci. Stat. Comput. 4, 645 (1983).
11. G. S. Jiang and C. W. Shu, Efficient implementation of ENO schemes, J. Comput. Phys. 126, 202 (1996).
12. P. D. Lax and B. Wendroff, Systems of conservation laws, Commun. Pure Appl. Math. 13, 217 (1960).
13. S. J. Lin and R. B. Rood, Multidimensional flux-form semi-Lagrangian transportation schemes, Mon. Weather Rev. 124, 2046 (1996).
14. X. D. Liu, S. Osher, and T. Chan, Weighted essentially non-oscillatory schemes, J. Comput. Phys. 115, 200 (1994).
15. A. McDonald, Accuracy of multiply-upstream, semi-Lagrangian advection schemes, Mon. Weather Rev. 112, 1267 (1984).
16. A. McDonald, Accuracy of multiply-upstream, semi-Lagrangian advection schemes, II, Mon. Weather Rev. 115, 1446 (1987).
17. A. McDonald and J. R. Bates, Improving the estimate of the departure point position in a two-time-level semi-Lagrangian and semi-implicit model, Mon. Weather Rev. 115, 737 (1987).
18. J. L. McGregor, Economical determination of departure points for semi-Lagrangian models, Mon. Weather Rev. 121, 221 (1992).
19. G. Moretti, A technique for integrating two-dimensional Euler equations, Comput. Fluids 15, 59 (1987).
20. S. Osher, Riemann solvers, the entropy condition, and difference approximations. SIAM J. Numer. Anal. 31, 217 (1984).
21. A. Priestley, A quasi-conservation version of the semi-Lagrangian advection scheme, Mon. Weather Rev. 121, 621 (1993).
22. D. K. Purnell, Solution of the advective equation by upstream interpolation with a cubic spline, Mon. Weather Rev. 104, 42 (1975).
23. K. Sakurai, T. Aoki, and T. Yabe, A semi-Lagrangian cubic interpolated propagation scheme for long parcel trajectories, CFD J. in press.
24. P. K. Smolarkiewicz and J. A. Pudykiewicz, A class of semi-Lagrangian approximations for fluids, J. Atmos. Sci. 49, 2082 (1992).
25. A. Staniforth and J. Côté, Semi-Lagrangian integration scheme for atmospheric model - A review, Mon. Weather Rev. 119, 2206 (1991).
26. L. L. Takacs, A two-step scheme for advection equation with minimized dissipation and dispersion errors, Mon. Weather Rev. 113, 1050 (1985).
27. R. Tanaka, T. Nakamura, and T. Yabe, Constructing exactly conservative scheme in a non-conservative form. Comput. Phys. Commun. 126, 232 (2000).
28. B. van Leer, Toward the ultimate conservative difference scheme. Part IV. A new approach to numerical convection, J. Comput. Phys. 23, 276 (1977).
29. B. van Leer, Toward the ultimate conservative difference scheme. Part V. A second order sequel to Godunov's method, J. Comput. Phys. 32, 101 (1979).
30. D. L. Williamson and P. J. Rasch, Two-dimensional semi-Lagrangian transport with shape-preserving interpolation, Mon. Weather Rev. 117, 102 (1989).
31. F. Xiao, A class of single-cell high order semi-Lagrangian advection schemes, Mon. Weather Rev. 128, 1165 (2000).
32. F. Xiao, T. Yabe, and T. Ito, Constructing oscillation preventing scheme for advection equation by rational function, Comput. Phys. Commun. 93, 1 (1996).
33. T. Yabe and T. Aoki, A universal solver for hyperbolic-equations by cubic-polynomial interpolation. 1. One-dimensional solver, Comput. Phys. Commun. 66, 219 (1991).
34. T. Yabe, T. Ishikawa, P. Y. Wang, T. Aoki, Y Kadota, and F. Ikeda, A universal solver for hyperbolic-equations by cubic-polynomial interpolation. 2. 2-dimensional and 3-dimensional solvers, Comput. Phys. Commun. 66, 233 (1991).
35. T. Yabe, R. Tanaka, T. Nakamura, and F. Xiao, Exactly conservative semi-Lagrangian scheme (CIP-CSL) in one dimension, Mon. Wea. Rev. 129, 332 (2001).
36. H. Q. Yang and A. J. Przekwas, A comparative study of advanced shock-capturing schemes applied to Burger's equation, J. Comput. Phys. 102, 139 (1992).
37. S. T. Zalesak, Fully multidimensional flux corrected transport algorithm for fluids, J. Comput. Phys. 31, 335 (1979).