Numerical solution of the reaction-advection-diffusion equation on the sphere

Journal of Computational Physics

Volumn 213, Issue 1, 2006, Pages 358-390

  Pudykiewicz, Janusz A ^a  

^a ENVIRONMENT CANADA   (Canada)

Author keywords

Advection on the sphere; Atmospheric transport; Finite volume method; Icosahedral grid; Reaction diffusion waves

Indexed keywords

ADVECTION; ATMOSPHERIC MOVEMENTS; CLIMATE MODELS; DIFFUSION IN LIQUIDS; LINEAR EQUATIONS; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; SPHERES; WEATHER FORECASTING;

ADVECTION ON THE SPHERE; ADVECTION-DIFFUSION PROBLEM; ATMOSPHERIC TRANSPORT; FINITE-VOLUME; FINITE-VOLUME METHOD; ICOSAHEDRAL GRID; NUMERICAL SOLUTION; PERFORMANCE; REACTION ADVECTION-DIFFUSION EQUATIONS; REACTION-DIFFUSION WAVES;

FINITE VOLUME METHOD;

EID: 31744448654     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.08.021     Document Type: Article

References (47)

1. V.I. Arnold Ordinary Differential Equations 1998 MIT Press Cambridge, MA and London, England
2. J.P. Boris D.L. Book Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works J. Comput. Phys. 11 1972 397-431
3. L. Cesari Asymptotic Behavior and Stability Problems in Ordinary Differential Equations 1963 Academic Press New York
4. P. Colella P.R. Woodward The Piecewise Parabolic Method (PPM) for gas-dynamics simulation J. Comput. Phys. 54 1984 174-201
5. H. Flanders Differential Forms with Applications to the Physical Sciences 1963 Academic Press New York, London
6. F.X. Giraldo Lagrange-Galerkin methods on spherical geodesic grids J. Comput. Phys. 136 1997 197-213
7. S.K. Godunov A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics Math. Sb. 47 1959 271-306
8. F. Harary Graph Theory 1969 Perseus Books Reading, MA
9. M.E. Hubbard Multidimensional slope limiters for MUSCL-type finite volume schemes on unstructured grids J. Comput. Phys. 155 1999 54-74
10. O. Knoth R. Wolke Implicit-explicit Runge-Kutta methods for computing atmospheric reactive flows Appl. Numer. Math. 28 1998 327-341
11. H.O. Kreiss J. Oliger Comparison of accurate methods for the integration of hyperbolic equations Tellus 24 1972 199-215
12. J.D. Lambert Computational Methods in Ordinary Differential Equations 1973 Wiley New York
13. R.J. Leveque Finite Volume Methods for Hyperbolic Problems 2002 Cambridge University Press Cambridge
14. X. Liu D.S. Osher T. Chan Weighted essentially non-oscillatory schemes J. Comput. Phys. 115 1994 200-212
15. D. Majewski D. Liermann P. Prohl B. Ritter M. Buchhold T. Hannish G. Paul W. Wergen The operational global icosahedral-hexagonal gridpoint model gme: Description and high resolution tests Mon. Weather Rev. 130 2002 319-338
16. C.R. Molenkamp Accuracy of finite difference methods applied to the advection equation J. Appl. Metall. 7 1968 160-167
17. G. Nicolis Introduction to Nonlinear Science 1995 Cambridge University Press Cambridge
18. G. Nicolis J. Auchmuty Dissipative structures, catastrophes and pattern formation: A bifurcation analysis Proc. Natl. Acad. Sci. USA 71 1977 2748-2751
19. G. Nicolis I. Prigogine Self-organization in Nonequilibrium Systems 1977 Wiley New York
20. E.S. Oran J.P. Boris Numerical Simulation of Reactive Flow 1987 Elsevier New York, Amsterdam, London
21. E.S. Oran J.P. Boris Numerical Simulation of Reactive Flow second ed. 2001 Cambridge University Press Cambridge
22. I. Prigogine R. Lefever Symmetry-breaking instabilities in dissipative systems J. Chem. Phys. 48 1968 1695-1700
23. I. Prigogine From Being to Becoming 1980 Freeman San Francisco
24. J. Pudykiewicz A predictive tracer model J. Met. Soc. Jpn. 68 1990 213-225
25. P.J. Rash D.L. Williamson Computational aspects of moisture transport in global models Quart. J. Roy. Meteorol. Soc. 116 1990 1071-1090
26. T.D. Ringler R.H. Heikes D.A. Randall Modelling the atmospheric general circulation using a spherical geodesic grid: A new class of dynamical cores Mon. Weather Rev. 128 2000 2471-2490
27. H. Ritchie Application of a semi-Lagrangian integration scheme to the moisture equation in a regional forecast model Mon. Weather Rev. 113 1985 424-435
28. R. Sadourny A. Arakawa Y. Mintz Integration of the nondivergent barotropic vorticity equation with an icosahedral hexagonal grid for the sphere Mon. Weather Rev. 96 1968 351-356
29. A. Sandu J.G. Verwer M. Van Loon G.R. Carmichael F.A. Potra D. Dabdub J.H. Seinfeld Benchmarking stiff ODE solvers for atmospheric chemistry problems - I. Implicit vs. explicit Atmos. Environ. 31 1997 3151-3166
30. A. Shchepetkin J.C. McWilliams Quasi-monotone advection schemes based on explicit locally adaptive dissipation Mon. Weather Rev. 126 1998 1541-1580
31. P.K. Smolarkiewicz A fully multidimensional advection transport algorithm with small implicit diffusion J. Comput. Phys. 67 1984 396
32. P.K. Smolarkiewicz W.W. Grabowski The multidimensional positive definite advection transport algorithm: Nonoscillatory option J. Comput. Phys. 86 1990 355-375
33. P.K. Smolarkiewicz P.J. Rash Monotone advection on the sphere: An Eulerian versus semi-Lagrangian approach J. Atmos. Sci. 48 1991 793-810
34. P.K. Smolarkiewicz J. Szmelter MPDATA: An edge based unstructured-grid formulation J. Comput. Phys. 206 2005 624-649
35. H. Tomita M. Satoh K. Goto An optimization of the icosahedral grid modified by spring dynamics J. Comput. Phys. 183 2002 307-331
36. H. Tomita M. Satoh A new dynamical framework of nonhydrostatic global model using the icosahedral grid Fluid Dyn. Res. 34 2004 357-400
37. H. Tomita M. Tsugawa M. Satoh K. Goto Shallow water model on a modified icosahedral geodesic grid by using spring dynamics J. Comput. Phys. 174 2001 579-613
38. A.M. Turing The chemical basis of morphogenesis Philos. Trans. R. Soc. Lond. B 237 1952 37-72
39. A. Quarteroni R. Sacco F. Saleri Numerical Mathematics 2000 Springer New York
40. B. van Leer Towards the ultimate conservative difference scheme J. Comput. Phys. 135 1997 229-248
41. D.L. Williamson Integration of the barotropic vorticity equation on a spherical geodesic grid Tellus 20 1968 642-653
42. D.L. Williamson P.J. Rash Two-dimensional semi-Lagrangian transport with shape-preserving interpolation Mon. Weather Rev. 117 1989 102-129
43. D.L. Williamson J.B. Drake J.J. Hack R. Jakob P.N. Shwartzrauber A standard test set for numerical approximations to the shallow water equations in spherical geometry J. Comput. Phys. 102 1992 211
44. C.B. Vreugdenhill Linear central-difference methods C.B. Vreugdenhill B. Koren Notes on Numerical Fluid Mechanics Numerical Methods for Advection-Diffusion Problems vol. 45 1993 Braunschweig Viesbaden 27-54
45. N.A. Yanenko The Method of Fractional Steps 1971 Springer Berlin 160p
46. S.T. Zalesak Fully multidimensional flux-corrected transport algorithms for fluids J. Comput. Phys. 31 1979 335-362
47. X. Zhong Additive semi-implicit Runge-Kutta methods for computing high-speed nonequilibrium reactive flows J. Comput. Phys. 128 1996 19-31