Predicting mesh density for adaptive modelling of the global atmosphere

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 367, Issue 1907, 2009, Pages 4523-4542

  Weller, Hilary ^a  

^a UNIVERSITY OF READING   (United Kingdom)

Author keywords

AtmosFOAM; Finite volume; OpenFOAM; Unstructured; Voronoi

Indexed keywords

ACCURATE MAPPING; COARSE MESHES; FINITE VOLUME; HIGHER RESOLUTION; LARGE-SCALE DYNAMICS; LOAD-BALANCING; MESH ADAPTATION; MESH DENSITY; RESOLVING FEATURES; SHALLOW WATER EQUATIONS; TEST CASE; UNIFORM MESH; VORONOI;

EID: 73249134764     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2009.0151     Document Type: Article

References (23)

1. Arakawa, A. &Lamb, V. 1977 Computational design of the basic dynamical processes of the UCLA general circulation model. Methods Comput. Phys. 17, 173-265.
2. Bacon, D. et al. 2000 A dynamically adapting weather and dispersion model: the Operational Multiscale Environment Model with Grid Adaptivity (OMEGA). Mon. Weather Rev. 128, 2044-2076. (doi:10.1175/1520-0493(2000) 128<2044:ADAWAD>2.0.CO;2)
3. Behrens, J. 2006 Adaptive atmospheric modelling. Lecture Notes in Computational Science and Engineering, no. 54. Berlin, Germany: Springer.
4. Berger, M. &Oliger, J. 1984 Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys. 53,484-512. (doi:10.1016/0021-9991(84)90073-1)
5. Côt́, J. 1988 A Lagrange multiplier approach for the metric terms of semi-Lagrangian models on the sphere. Q. J. R. Meteorol. Soc. 114, 1347-1352.
6. Dietachmayer, G. &Droegemeier, K. 1992 Application of continuous dynamic grid adaption techniques to meteorological modeling. Part I: Basic formulation and accuracy. Mon. Weather Rev. 120, 1675-1706. (doi:10.1175/1520- 0493(1992)120<1675:AOCDGA>2.0.CO;2) (Pubitemid 23375508)
7. Fiedler, B. &Trapp, R. J. 1993 A fast dynamic grid adaption scheme for meteorological flows. Mon. Weather Rev. 121, 2879-2888. (doi:10.1175/1520- 0493(1993)121<2879:AFDGAS>2.0.CO;2)
8. Galewsky, J., Scott, R. &Polvani, L. 2004 An initial-value problem for testing numerical models of the global shallow-water equations. Tellus A 56, 429-440. (doi:10.1111/j.1600-0870.2004.00071.x) (Pubitemid 39526823)
9. Iske, A. &Kaser, M. 2004 Conservative semi-Lagrangian advection on adaptive unstructured meshes. Numer. Methods Partial Diff. Equat. 20, 388-411. (doi:10.1002/num.10100)
10. Jablonowski, C., Herzog, M., Penner, J., Oehmke, R., Stout, Q., van Leer, B. &Powell, K. 2006 Block-structured adaptive grids on the sphere: advection experiments. Mon. Weather Rev. 134, 3691-3713. (doi:10.1175/MWR3223.1) (Pubitemid 46091970)
11. L̈uter, M., Handorf, D., Rakowsky, N., Behrens, J., Frickenhaus, S., Best, M., Dethloff, K. &Hiller, W. 2007 A parallel adaptive barotropic model of the atmosphere. J. Comput. Phys. 223, 609-628. (doi:10.1016/j.jcp.2006.09. 029)
12. L̈uter, M., Giraldo, F., Handorf, D. &Dethloff, K. 2008 A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates. J. Comput. Phys. 227, 10226-10242 (doi:10.1016/j.jcp. 2008.08.019)
13. O'Rourke, J., Chien, C.-B., Olson, T. &Naddor, D. 1982 A new linear algorithm for intersecting convex polygons. Comput. Graph. Image Process. 19, 384-391. (doi:10.1016/0146-664X(82)90023-5)
14. Power, P., Piggott, M., Fang, F., Gorman, G., Pain, C., Marshall, D., Goddard, A. &Navon, I. 2006 Adjoint goal-based error norms for adaptive mesh ocean modelling. Ocean Modell. 15, 3-38. (doi:10.1016/j.ocemod.2006.05.001) (Pubitemid 44161162)
15. Rhie, C. &Chow, W. 1983 Numerical study of the turbulent-flow past an airfoil with trailing edge separation. AIAA J. 21, 1525-1532. (doi:10.2514/3.8284)
16. Ringler, T., Ju, L. &Gunzburger, M. 2008 A multiresolution method for climate system modeling: applications of spherical centroidal Voronoi tessellations. Ocean Dyn. 58, 475-498.(doi:10.1007/s10236-008-0157-2)
17. Skamarock, W. &Klemp, J. 1993 Adaptive grid refinement for two-dimensional and three-dimensional non-hydrostatic atmospheric flow. Mon. Weather Rev. 121, 788-804. (doi:10.1175/1520-0493(1993)121<0788:AGRFTD>2. 0.CO;2)
18. Skamarock, W., Oliger, J. &Street, R. 1989 Adaptive grid refinement for numerical weather prediction. J. Comput. Phys. 80, 27-60. (doi:10.1016/0021-9991(89)90089-2)
19. St-Cyr, A., Jablonowski, C., Dennis, J., Tufo, H. &Thomas, S. 2008 A comparison of two shallow-water models with nonconforming adaptive grids. Mon. Weather Rev. 136, 1898-1922. (doi:10.1175/2007MWR2108.1)
20. Staniforth, A. &Mitchell, H. 1978 Variable-resolution finite-element technique for regional forecasting with primitive equations. Mon. Weather Rev. 106, 439-447. (doi:10.1175/1520-0493(1978)106<0439:AVRFET>2.0.CO;2)
21. Tomita, H., Satoh, M. &Goto. K. 2002 An optimization of the icosahedral grid modified by spring dynamics. J. Comput. Phys. 183, 307-331. (doi:10.1006/jcph.2002.7193) (Pubitemid 36100559)
22. Weller, H. &Weller, H. 2008 A high-order arbitrarily unstructured finite-volume model of the global atmosphere: tests solving the shallow-water equations. Int. J. Numer. Meth. Fluids 56, 1589-1596. (doi:10.1002/fld.1595)
23. Weller, H., Weller, H. G. &Fournier, A. In press. Voronoi, Delaunay and block structured mesh refinement for solution of the shallow water equations on the sphere. Mon. Weather Rev.(doi:10.1175/2009MWR2917.1)