Numerical wave propagation for the triangular P1DG-P2 finite element pair

Journal of Computational Physics

Volumn 230, Issue 8, 2011, Pages 2806-2820

  Cotter, C J ^a   Ham, D A ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Geophysical fluid dynamics; Mixed finite elements; Numerical weather prediction; Rossby waves; Spurious modes

Indexed keywords

DISPERSION (WAVES); GEOMETRY; WAVE PROPAGATION;

DISCRETIZATIONS; GEOPHYSICAL FLUID DYNAMICS; HELMHOLTZ DECOMPOSITION; INERTIAL OSCILLATION; MIXED FINITE ELEMENTS; NUMERICAL WAVE PROPAGATION; NUMERICAL WEATHER PREDICTION; PLANAR GEOMETRIES; ROSSBY WAVE; SPURIOUS MODES;

EQUATIONS OF MOTION;

EID: 79951772112     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2010.12.024     Document Type: Article

References (22)

1. Arakawa A., Lamb V. Computational design of the basic dynamical processes of the UCLA general circulation model. Methods in Computational Physics 1977, vol. 17:173-265. Academic Press.
2. Brenner S., Scott R. The Mathematical Theory of Finite Element Methods 1994, Springer-Verlag.
3. Comblen R., Lambrechts J., Remacle J.-F., Legat V. Practical evaluation of five partly discontinuous finite element pairs for the non-conservative shallow water equations. Int. J. Numer. Meth. Fluid. 2010, 63(6):701-724.
4. Cotter C.J., Ham D.A., Pain C.C. A mixed discontinuous/continuous finite element pair for shallow-water ocean modelling. Ocean Model. 2009, 26:86-90.
5. Cotter C.J., Ham D.A., Pain C.C., Reich S. LBB stability of a mixed finite element pair for fluid flow simulations. J. Comput. Phys. 2009, 228(3):336-348.
6. Fox-Rabinovitz M. Computational dispersion properties of 3D staggered grids for a nonhydrostatic anelastic system. Mon. Weather Rev. 1996, 124:498-510.
7. Gresho P.M., Sani R.L. Incompressible Flow and the Finite Element Method. Isothermal Laminar Flow 2000, vol. 2. Wiley.
8. Kossevich A.M. Geometry of Crystal Lattices 2005, Wiley.
9. Le Roux D., Hanert E., Rostand V., Pouliot B. Impact of mass lumping on gravity and Rossby waves in 2D finite-element shallow-water models. Int. J. Numer. Meth. Fluid 2008, 59(7):767-790.
10. Le Roux D., Staniforth A., Lin C.A. Finite elements for shallow-water equation ocean models. Mon. Weather Rev. 1998, 126(7):1931-1951.
11. Majewski D., Liermann D., Prohl P., Ritter B., Buchhold M., Hanisch T., Paul G., Wergen W., Baumgardner J. The operational global icosahedral-hexagonal gridpoint model GME: description and high-resolution tests. Mon. Weather Rev. 2002, 130:319-338.
12. Randall D. Geostrophic adjustment and the finite-difference shallow-water equations. Mon. Weather Rev. 1994, 122:1371-1377.
13. Raviart Thomas A mixed finite element method for 2nd order elliptic problems. Mathematical Aspects of the Finite Element Method. Lecture Notes in Mathematics 1977, 292-315. Springer, Berlin.
14. Ringler T.D., Heikes R., Randall D. Modeling the atmospheric general circulation using a spherical geodesic grid: a new class of dynamical cores. Mon. Weather Rev. 2000, 128:2471-2490.
15. Roux D.Y.L., Pouliot B. Analysis of numerically induced oscillations in two-dimensional finite-element shallow-water models part II: free planetary waves. SIAM J. Sci. Comput. 2008, 30(4):1971-1991.
16. Roux D.Y.L., Rostand V., Pouliot B. Analysis of numerically induced oscillations in 2d finite-element shallow-water models part I: inertia-gravity waves. SIAM J. Sci. Comput. 2007, 29(1):331-360.
17. Satoh M., Matsuno T., Tomita H., Miura H., Nasuno T., Iga S. Nonhydrostatic icosahedral atmospheric model (NICAM) for global cloud resolving simulations. J. Comput. Phys. 2008, 227(7):3486-3514.
18. SymPy Development Team, SymPy: Python library for symbolic mathematics, 2009. http://www.sympy.org.
19. Thuburn J. Numerical wave propagation on the hexagonal C-grid. J. Comput. Phys. 2008, 227(11):5836-5858.
20. Thuburn J., Ringler T.D., Skamarock W.C., Klemp J.B. Numerical representation of geostrophic modes on arbitrarily structured C-grids. J. Comput. Phys. 2009, 228:8321-8335.
21. Umgiesser G., Canu D.M., Cucco A., Solidoro C. A finite element model for the Venice Lagoon. Development, set up, calibration and validation. J. Marine Syst. 2004, 51(1-4):123-145.
22. Walters R., Casulli V. A robust, finite element model for hydrostatic surface water flows. Commun. Numer. Methods Eng. 1998, 14:931-940.