Continuous and discontinuous Galerkin methods for a scalable three-dimensional nonhydrostatic atmospheric model: Limited-area mode

Journal of Computational Physics

Volumn 231, Issue 24, 2012, Pages 7988-8008

  Kelly, James F ^a   Giraldo, Francis X ^a  

^a NAVAL POSTGRADUATE SCHOOL   (United States)

Author keywords

Compressible flow; Element based Galerkin method; Euler; Navier Stokes; Parallelization

Indexed keywords

ATMOSPHERIC MOVEMENTS; DOMAIN DECOMPOSITION METHODS; GALERKIN METHODS; NAVIER STOKES EQUATIONS; THREE DIMENSIONAL COMPUTER GRAPHICS;

ATMOSPHERIC SIMULATIONS; CONTINUOUS DISCONTINUOUS; CONTINUOUS GALERKIN; DISCONTINUOUS GALERKIN; ELEMENT-BASED; ELEMENT-BASED GALERKIN METHOD; EULER; NAVIER STOKES; NONHYDROSTATIC MODEL; PARALLELIZATIONS;

SCALABILITY;

EID: 84866307953     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2012.04.042     Document Type: Article

References (42)

1. Ahmad N., Lindeman J. A Godunov-type finite volume scheme for meso- and micro-scale flows in three dimensions. Pure Appl. Geophys. 2008, 165(9):1929-1939.
2. Boyd J.P. Chebyshev and Fourier Spectral Methods 2001, Dover Publications Inc., Mineola, New York.
3. Texas Advanced Computing Center, Ranger user guide, 2012. http://www.tacc.utexas.edu/user-services/user-guides/ranger-user-guide.
4. Davies T., Cullen M.J.P., Malcolm A.J., Mawson M.H., Staniforth A., White A.A., Wood N. A new dynamical core for the Met Office's global and regional modelling of the atmosphere. Quart. J. Roy. Meteorol. Soc. 2005, 131:1759-1782.
5. Dea J.R., Giraldo F.X., Neta B. High-order non-reflecting boundary conditions for the linearized 2-D Euler equations: no mean flow case. Wave Motion 2009, 46:210-220.
6. T.J. DeLuca, Performance of hybrid Eulerian-Lagrangian semi-implicit time-integrators for nonhydrostatic mesoscale atmospheric modeling, Master's thesis, Naval Postgraduate School, 2008.
7. Dennis J.M., Edwards J., Evans K.J., Guba O.N., Lauritzen P.H., Mirin A., Cyr A.St., Taylor M., Worley P.H. CAM-SE: A scalable spectral element dynamical core for the community atmosphere model. Int. J. High Perform. Comput. Appl. 2012, 26(1):74-89.
8. J.M. Dennis, M. Levy, R.D. Nair, H.M. Tufo, T. Voran. Towards and efficient and scalable discontinuous Galerkin atmospheric model, in: Proceedings of the 19th IEEE International Parallel and Distributed Processing, Symposium, 2005, pp. 1-7.
9. Deville M.O., Fischer P.F., Mund E.H. High-Order Methods for Incompressible Fluid Flow 2002, Cambridge University Press.
10. Fey M. Multidimensional upwinding. Part I. The method of transport for solving the Euler equations. J. Comput. Phys. 1998, 143(1):159-180.
11. Fischer P.F., Patera A.T. Parallel spectral element solution of the Stokes problem. J. Comput. Phys. 1991, 92:380-421.
12. Fournier Aimé, Taylor Mark A., Tribbia Joseph J. The spectral element atmosphere model (SEAM): high-resolution parallel computation and localized resolution of regional dynamics. Mon. Weather Rev. 2004, 132(3):726-748.
13. S. Gabersek, F.X. Giraldo, J.D. Doyle, Dry and moist idealized experiments with a two-dimensional spectral element model, Mon. Weather Rev. , in press. doi:10.1175/MWR-D-11-00144.1.
14. Giraldo F.X. The Lagrange-Galerkin spectral element method on unstructured quadrilateral grids. J. Comput. Phys. 1998, 147(1):114-146.
15. Giraldo F.X., Restelli M. A study of spectral element and discontinuous Galerkin methods for the Navier-Stokes equations in nonhydrostatic mesoscale atmospheric modeling: equation sets and test cases. J. Comput. Phys. 2008, 227(8):3849-3877.
16. Giraldo F.X., Restelli M., L äuter M. Semi-implicit formulations of the Navier-Stokes equations: applications to non-hydrostatic atmospheric modeling. SIAM J. Sci. Comput. 2010, 32:3394-3425.
17. Giraldo F.X., Rosmond Thomas E. A scalable spectral element Eulerian atmospheric model (SEE-AM) for NWP: dynamical core tests. Mon. Weather Rev. 2004, 132(1):133-153.
18. Grinberg L., Karniadakis G.E. A new domain decomposition method with overlapping patches for ultrascale simulations: application to biological flows. J. Comput. Phys. 2010, 229:5541-5563.
19. Higdon R.L. Radiation boundary condtions for dispersive waves. SIAM J. Numer. Anal. 1994, 31(1):64-100.
20. Hodur R.M. The naval research laboratory's coupled ocean/atmosphere mesoscale prediction system (COAMPS). Mon. Weather Rev. 1997, 125(7):1414-1430.
21. Houzeaux G., Vázquez M., Aubry R., Cela J.M. A massively parallel fractional step solver for incompressible flows. J. Comput. Phys. 2009, 228:6316-6332.
22. Karypis G., Kuman V. A fast and highly quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 1998, 20(1):359-392.
23. Kessler E. On the Distribution and Continuity of Water Substance in Atmospheric Circulation 1969, AMS.
24. Klein R., Achatz U., Bresch D., Knio O.M., Smolarkiewicz P.K. Regime of validity of soundproof atmospheric flow models. J. Atmos. Sci. 2010, 67(10):3226-3237.
25. Klemp J.B., Skamarock W.C., Dudhia J. Conservative split-explicit time integration methods for the compressible nonhydrostatic equations. Mon. Weather Rev. 2007, 135(8):2897-2913.
26. Klockner A., Warburton T., Bridge J., J.S, Hesthaven Nodal discontinuous galerkin methods on graphics processors. J. Comput. Phys. 2009, 228(21):7863-7882.
27. 1 finite-element pair in shallow-water models. SIAM J. Sci. Comput. 2005, 27(2):394-414.
28. Lindquist Joseph M., Neta Beny, Giraldo Francis X. A spectral element solution of the Klein-Gordon equation with high-order treatment of time and non-reflecting boundary. Wave Motion 2010, 47(5):289-298.
29. Nair R.D., Choi H.W., Tufo H.M. Computational aspects of a scalable high-order discontinuous Galerkin atmospheric dynamical core. Comput. Fluids 2009, 30:309-319.
30. Norman M.R., Nair R.D., Semazzi F.H.M. A low communication and large time step explicit finite-volume solver for non-hydrostatic atmospheric dynamics. J. Comput. Phys. 2011, 230:1567-1584.
31. Prusa J.M., Smolarkiewicz P.K., Wyszogrodzki A.A. EULAG, a computational model for multiscale flows. Comput. Fluids 2008, 37:1193-1207.
32. Restelli M., Giraldo F.X. A conservative discontinuous galerkin semi-implicit formulation for the Navier-Stokes equations in nonhydrostatic mesoscale modeling. SIAM J. Sci. Comput. 2009, 31:2231-2257.
33. Schattler U., Doms G., Steppeler J. Requirements and problems in parallel model development at DWD. Sci. Program. 2000, 8(1):13-22.
34. W.C. Skamarock, J.D. Doyle, P. Clark, N. Wood, A standard test set for nonhydrostatic dynamical cores of NWP models, AMS NWP-WAF Conference Poster, p. P2.17, 2004.
35. Smith R.B. Linear theory of stratified hydrostatic flow past an isolated mountain. Tellus 1980, 32:348-364.
36. Smith R.B. Linear theory of stratified flow past an isolated mountain in isoteric coordinates. J. Atmos. Sci. 1988, 45(42):3889-3896.
37. Smolarkiewicz P.K., Pudykiewicz J.A. A class of semi-Lagrangian approximations for fluids. J. Atmos. Sci. 1992, 49(22):2082-2096.
38. Spiteri Raymond J., Ruuth Steven J. A new class of optimal high-order strong-stability-preserving time discretization methods. SIAM J. Numer. Anal. 2002, 40(2):469-491.
39. Thomas S.J., Hacker J.P., Smolarkiewicz P.K. Spectral preconditioners for nonhydrostatic atmospheric models. Mon. Weather Rev. 2003, 131:2464-2478.
40. Thuburn J., Ringler Todd D., Skamarock William C., Klemp Joseph B. Numerical representation of geostrophic modes on arbitrarily structured c-grids. J. Comput. Phys. 2009, 228:8321-8335.
41. Ullrich Paul A., Jablonowski C., van Leer B. High-order finite-volume methods for the shallow-water equations on the sphere. J. Comput. Phys. 2010, 229(17):6104-6134.
42. Wilcox L.C., Stadler G., Burstedde C., Ghattas O. A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media. J. Comput. Phys. 2010, 229(24):9373-9396.