Conservative transport schemes for spherical geodesic grids: High-order flux operators for ODE-based time integration

Monthly Weather Review

Volumn 139, Issue 9, 2011, Pages 2962-2975

  Skamarock, William C ^a   Gassmann, Almut ^b  

^a NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

^b MAX PLANCK INSTITUTE FOR METEOROLOGY   (Germany)

Author keywords

Numerical analysis modeling; Transport

Indexed keywords

ATMOSPHERIC MODEL; BAROCLINIC WAVES; COURANT NUMBERS; FINITE-VOLUME; FOURTH-ORDER; HIGH-ORDER; HIGHER ORDER; HIGHER-ORDER SCHEME; LEADING-ORDER TRUNCATION ERRORS; LEAST SQUARES FIT; MONOTONIC BEHAVIOR; NONHYDROSTATIC MODEL; OPTIMAL VALUES; POSITIVE DEFINITE; QUALITATIVE EVALUATIONS; RECTANGULAR MESH; RUNGE-KUTTA; SECOND ORDERS; SECOND-ORDER SCHEME; SPATIAL DERIVATIVES; SPHERICAL GEODESIC GRID; THIRD-ORDER; TIME INTEGRATION; TIME STEP; TIME-INTEGRATION SCHEME; TRANSPORT; TRANSPORT ALGORITHMS; TRANSPORT SCHEMES; VORONOI;

RUNGE KUTTA METHODS; SPHERES; STANDARDS; THREE DIMENSIONAL;

QUALITY CONTROL;

ALGORITHM; ATMOSPHERIC MODELING; ATMOSPHERIC TRANSPORT; BAROCLINIC WAVE; COMPUTER SIMULATION; ERROR ANALYSIS; LEAST SQUARES METHOD; NUMERICAL MODEL; TWO-DIMENSIONAL MODELING;

EID: 80053206719     PISSN: 00270644     EISSN: None     Source Type: Journal    
DOI: 10.1175/MWR-D-10-05056.1     Document Type: Article

References (28)

1. Blossey, P. N., and D. R. Durran, 2008: Selective monotonicity preservation in scalar advection. J. Comput. Phys., 227, 5160-5183.
2. Durran, D. R., 2010: Numerical Methods for Fluid Dynamics: With Applications to Geophysics. 2nd ed. Texts in Applied Mathematics, No. 32, Springer, 516 pp.
3. Gassmann, A., 2010: Nonhydrostatic modelling with ICON. Proc. Workshop on Nonhydrostatic Modelling, Reading, United Kingdom, ECMWF. [Available online at http://www.ecmwf.int.]
4. Gassmann, A., and H.-J. Herzog, 2008: Towards a consistent numerical compressible non-hydrostatic model using generalized Hamiltonian tools. Quart. J. Roy. Meteor. Soc., 134, 1597-1613.
5. Hundsdorfer, W. B., B. Koren, M. van Loon, and J. G. Verwer, 1995: A positive finite difference advection scheme. J. Comput. Phys., 117, 35-46.
6. Ii, S., and F. Xiao, 2010: A global shallow water model using high order multi-moment constrained finite volume method and icosahedral grid. J. Comput. Phys., 229, 1774-1796.
7. Jablonowski, C., and D. L. Williamson, 2006: A baroclinic instability test case for atmospheric model dynamical cores. Quart. J. Roy. Meteor. Soc., 132, 2943-2975.
8. Lashley, R. K., 2002: Automatic generation of accurate advection schemes on unstructured grids and their application to meteorological problems. Ph.D. thesis, University of Reading, Reading, United Kingdom, 223 pp. [Available online at http://www.reading.ac.uk/maths/research/maths-phdtheses.aspx.]
9. Lipscomb, W. H., and T. Ringler, 2005: An incremental remapping transport scheme on a spherical geodesic grid. Mon. Wea. Rev., 133, 2235-2250.
10. Majewski, D., and Coauthors, 2002: The operational global icosahedral-hexagonal gridpoint model GME: Description and high-resolution tests. Mon. Wea. Rev., 130, 319-338.
11. Miura, H., 2007: An upwind-biased conservative advection scheme for spherical hexagonal-pentagonal grids. Mon. Wea. Rev., 135, 4038-4044.
12. Nair, R. D., and P. H. Lauritzen, 2010: A class of deformational flow test cases for linear transport problems on the sphere. J. Comput. Phys., 229, 8868-8887.
13. Purser, R. J., 2007: Accuracy considerations of time-splitting methods for models using two-time-level schemes. Mon. Wea. Rev., 135, 1158-1164.
14. Ringler, T., L. Ju, and M. Gunzburger, 2008: A multiresolution method for climate system modeling: Application of spherical centroidal Voronoi tessellations. Ocean Dyn., 58, 475-498.
15. Ringler, T., J. Thuburn, J. B. Klemp, and W. C. Skamarock, 2010: A unified approach to energy conservation and potential vorticity dynamics for arbitrarily-structured C-grids. J. Comput. Phys., 229, 3065-3090.
16. Rípodas, P., and Coauthors, 2009: Icosahedral shallow water model (ICOSWM) results of shallow water test cases and sensitivity to model parameters. Geosci. Model Dev., 2, 231-251.
17. Skamarock, W. C., and J. B. Klemp, 2008: A time-split nonhydrostatic atmospheric model for weather research and forecasting applications. J. Comput. Phys., 227, 3465-3485.
18. Skamarock, W. C., and M. Menchaca, 2010: Conservative transport schemes for spherical geodesic grids: High-order reconstructions for forward-in-time schemes. Mon. Wea. Rev., 138, 4497-4508.
19. Skamarock, W. C., and Coauthors, 2010: Global nonhydrostatic modeling using Voronoi meshes: The MPAS model. Proc. Workshop on Nonhydrostatic Modelling, Reading, United Kingdom, ECMWF. [Available online at http://www.ecmwf.int/newsevents/meetings/workshops/2010/Non_hydrostatic_Modelling/presentations/Skamarock.pdf.]
20. Strang, G., 1980: Linear Algebra and Its Applications. 2nd ed. Academic Press, 414 pp.
21. Tomita, H., M. Tsugawa, M. Satoh, and K. Goto, 2001: Shallow water model on a modified icosahedral geodesic grid by using spring dynamics. J. Comput. Phys., 174, 579-613.
22. Walko, R. L., and R. Avissar, 2008: The ocean-land-atmosphere model (OLAM). Part II: Formulation and tests of the nonhydrostatic dynamic core. Mon. Wea. Rev., 136, 4045-4062.
23. Wang, H., W. C. Skamarock, and G. Feingold, 2009: Evaluation of scalar advection schemes in the Advanced Research WRF model using large-eddy simulations of aerosol-cloud interactions. Mon. Wea. Rev., 137, 2547-2558.
24. Weller, H., H.G. Weller, and A. Fournier, 2009: Voronoi, Delaunay, and block-structured mesh refinement for solution of the shallow-water equations on the sphere. Mon. Wea. Rev., 137, 4208-4224.
25. Wicker, L. J., and W. C. Skamarock, 2002: Time-splitting methods for elastic models using forward time schemes. Mon. Wea. Rev., 130, 2088-2097.
26. Williamson, D. L., J. Drake, J. J. Hack, R. Jakob, and P. N. Swarztrauber, 1992: A standard test set for numerical approximations to the shallow-water equations in spherical geometry. J. Comput. Phys., 102, 211-224.
27. Yeh, K.-Y., 2007: The streamline subgrid integration method: I. Quasi-monotonic second-order transport schemes. J. Comput. Phys., 225, 1632-1652.
28. Zalesak, S. T., 1979: Fully multidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys., 31, 335-362.