A compressible nonhydrostatic cell-integrated semi-lagrangian semi-implicit solver (CSLAM-NH) with consistent and conservative transport

Monthly Weather Review

Volumn 142, Issue 4, 2014, Pages 1669-1687

  Wong, May ^a   Skamarock, William C ^b   Lauritzen, Peter H ^b   Klemp, Joseph B ^b   Stull, Roland B ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

Author keywords

Conservation equations; Nonhydrostatic models; Semi Lagrangian models

Indexed keywords

EQUATIONS OF MOTION; LAGRANGE MULTIPLIERS; STORMS;

CONSERVATION EQUATIONS; CONTINUITY EQUATIONS; NONHYDROSTATIC MODEL; SEMI-IMPLICIT SCHEME; SEMI-LAGRANGIAN MODELS; SHALLOW WATER EQUATIONS; SHAPE PRESERVATION; TIME INDEPENDENTS;

PASSIVE FILTERS;

EULERIAN ANALYSIS; HELMHOLTZ EQUATION; LAGRANGIAN ANALYSIS; NUMERICAL MODEL; SHALLOW-WATER EQUATION; WEATHER FORECASTING;

EID: 84897403265     PISSN: 00270644     EISSN: 15200493     Source Type: Journal    
DOI: 10.1175/MWR-D-13-00210.1     Document Type: Article

References (35)

1. Barth, T. J., and D.C. Jespersen, 1989: The design and application of upwind schemes on unstructured meshes. Proc. 27th Aerospace Sciences Meeting, Reno, NV, AIAA, AIAA-89-0366.
2. Erath, C., P. H. Lauritzen, J. H. Garcia, and H. M. Tufo, 2012: Integrating a scalable and efficient semi-Lagrangian multitracer transport scheme in HOMME. Proc. Comput. Sci., 9, 994-1003.
3. Erath, C., P. H. Lauritzen, and H. M. Tufo, 2013: On mass-conservation in highorder high-resolution rigorous remapping schemes on the sphere. Mon. Wea. Rev., 141, 2128-2133.
4. Harris, L. M., P. H. Lauritzen, and R. Mittal, 2011: A flux-form version of the conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed sphere grid. J. Comput. Phys., 230, 1215-1237.
5. Jablonowski, C., 2004: Adaptive grids in weather and climate modeling. Ph.D. thesis, University of Michigan, 292 pp.
6. Jöckel, P., R. vonKuhlmann, M. Lawrence, B. Steil, C. Brenninkmeijer, P. Crutzen, P. Rasch, and B. Eaton, 2001: On a fundamental problem in implementing flux-form advection schemes for tracer transport in 3-dimensional general circulation and chemistry transport models. Quart. J. Roy. Meteor. Soc., 127, 1035-1052.
7. Klemp, J. B., and R. B. Wilhelmson, 1978: The simulation of threedimensional convective storm dynamics. J. Atmos. Sci., 35, 1070-1096.
8. Klemp, J. B., W. C. Skamarock, and J. Dudhia, 2007: Conservative splitexplicit time integration methods for the compressible nonhydrostatic equations. Mon. Wea. Rev., 135, 2897-2913.
9. Laprise, J., and A. Plante, 1995: A class of semi-Lagrangian integrated-mass (SLIM) numerical transport algorithms. Mon. Wea. Rev., 123, 553-565.
10. Lauritzen, P. H., E. Kaas, and B. Machenhauer, 2006: A massconservative semi-implicit semi-Lagrangian limited-area shallow-water model on the sphere. Mon. Wea. Rev., 134, 1205-1221.
11. Lauritzen, P. H., E. Kaas, B. Machenhauer, and K. Lindberg, 2008: A mass-conservative version of the semi-implicit semi-Lagrangian HIRLAM. Quart. J. Roy. Meteor. Soc., 134, 1583-1595.
12. Lauritzen, P. H., R. D. Nair, and P. A. Ullrich, 2010: A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid. J. Comput. Phys., 229, 1401-1424.
13. Lauritzen, P. H., W. C. Skamarock, M. J. Prather, and M. A. Taylor, 2012: A standard test case suite for two-dimensional linear transport on the sphere. Geosci. Model Dev., 5, 887-901.
14. Lauritzen, P. H., and Coauthors, 2013: A standard test case suite for twodimensional linear transport on the sphere: Results from a collection of state-of-the-art schemes. Geosci. Model Dev. Discuss., 6(3), 4983-5076.
15. Machenhauer, B., and M. Olk, 1997: The implementation of the semi-implicit scheme in cell-integrated semi-Lagrangian models. Atmos.-Ocean, 35 (Special Issue), 103-126.
16. Machenhauer, B., E. Kaas, and P. H. Lauritzen, 2009: Finite volume meteorology. Computational Methods for the Atmosphere and the Oceans: Special Volume, R. Temam and J. Tribbia, Eds., Elsevier, 3-120.
17. McGregor, J. L., 1993: Economical determination of departure points for semi-Lagrangian models. Mon. Wea. Rev., 121, 221-230.
18. Melvin, T., M. Dubal, N. Wood, A. Staniforth, and M. Zerroukat, 2010: An inherently mass-conserving iterative semi-implicit semi-Lagrangian discretization of the non-hydrostatic verticalslice equations. Quart. J. Roy. Meteor. Soc., 136, 799-814.
19. Nair, R. D., and B. Machenhauer, 2002: The mass-conservative cell-integrated semi-Lagrangian advection scheme on the sphere. Mon. Wea. Rev., 130, 649-667.
20. 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.
21. Rancic, M., 1992: Semi-Lagrangian piecewise biparabolic scheme for two-dimensional horizontal advection of a passive scalar. Mon. Wea. Rev., 120, 1394-1406.
22. Rasch, P., and D. Williamson, 1990: Computational aspects of moisture transport in global-models of the atmosphere. Quart. J. Roy. Meteor. Soc., 116, 1071-1090.
23. Robert, A., 1981: A stable numerical integration scheme for the primitive meteorological equations. Atmos.-Ocean, 19, 35-46.
24. Robert, A., T. Yee, and H. Ritchie, 1985: A semi-Lagrangian and semiimplicit numerical-integration scheme for multilevel atmospheric models. Mon. Wea. Rev., 113, 388-394.
25. Rotunno, R., J. B. Klemp, and M. L. Weisman, 1988: A theory for strong, long-lived squall lines. J. Atmos. Sci., 45, 463-485.
26. Skamarock, W. C., and J. B. Klemp, 1994: Efficiency and accuracy of the Klemp-Wilhelmson time-splitting technique. Mon. Wea. Rev., 122, 2623-2630.
27. 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.
28. Straka, J., R. B. Wilhelmson, L. J. Wicker, J. R. Anderson, and K. K. Droegemeier, 1992: Numerical solutions of a non-linear density current: A benchmark solution and comparisons. Int. J. Numer. Methods Fluids, 17, 1-22.
29. Ullrich, P. A., P. H. Lauritzen, and C. Jablonowski, 2012: Some considerations for high-order 'incremental remap'-based transport schemes: Edges, reconstructions, and area integration. Int. J. Numer. Methods Fluids, 71, 1131-1151.
30. Weisman, M. L., and J. B. Klemp, 1982: The dependence of numerically simulated convective storms on vertical wind shear and buoyancy. Mon. Wea. Rev., 110, 504-520.
31. Weisman, M. L., J. B. Klemp, and R. Rotunno, 1988: Structure and evolution of numerically simulated squall lines. J. Atmos. Sci., 45, 1990-2013.
32. Wong, M., W. C. Skamarock, P. H. Lauritzen, and R. B. Stull, 2013: A cell-integrated semi-Lagrangian semi-implicit shallowwater model (CSLAM-SW) with conservative and consistent transport. Mon. Wea. Rev., 141, 2545-2560.
33. Xue, M., K. K. Droegemeier, and V. Wong, 2000: The Advanced Regional Prediction System (ARPS)-A multi-scale nonhydrostatic atmospheric simulation and prediction model. Part I: Model dynamics and verification. Meteor. Atmos. Phys., 75, 161-193.
34. Zerroukat, M., N. Wood, and A. Staniforth, 2002: SLICE: A semi-Lagrangian inherently conserving and efficient scheme for transport problems. Quart. J. Roy. Meteor. Soc., 128, 2801-2820.
35. Zhang, K., H. Wan, B. Wang, and M. Zhang, 2008: Consistency problem with tracer advection in the atmospheric model GAMIL. Adv. Atmos. Sci., 25, 306-318.