next up previous
Next: About this document ... Up: ICOSAHEDRAL SHALLOW WATER MODEL Previous: ICOSWP SENSITIVITY TO SOME

Bibliography

1
A.S. Almgren, J.B. Bell, P. Colella, L. Howell, and M.L. Welcome.
A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations.
Journal of Computational Physics, 142:1-46, 1998.

2
A. Arakawa and V. Lamb.
A potential enstrophy and energy conserving scheme for the shallow water equations.
Monthly Weather Review, 109:18-136, 1981.

3
J. Baudisch, L. Bonaventura, A. Iske, and E. Miglio.
Matrix valued radial basis functions for local vector field reconstruction: applications to computational fluid dynamic models.
MOX Report, 75, 2006.

4
J.R. Baumgardner and P.O. Frederickson.
Icosahedral discretization of the two-sphere.
SIAM Journal of Scientific Computing, 22(6):1107-1115, December 1985.

5
M.J. Berger and P. Colella.
Local adaptive grid refinement for shock hydrodynamics.
Journal of Computational Physics, 82:64-84, 1989.

6
L. Bonaventura.
The ICON project: Development of a unified model using triangular geodesic grid.
In Proceedings of the ECMWF Annual Seminar on Development in Numerical Methods for Atmosphere and Ocean Modeling. ECMWF, 2004.

7
L. Bonaventura, L. Kornblueh, T. Heinze, and P. Rípodas.
A semi-implicit method conserving mass and potential vorticity for the shallow water equations on the sphere.
International Journal of Numerical Methods in Fluids, 47:863-869, 2005.

8
L. Bonaventura and T. Ringler.
Analysis of discrete shallow water models on geodesic Delaunay grids with C-type staggering.
Monthly Weather Review, 133:2351-2373, 2005.

9
L. Bonaventura and G. Rosatti.
A cascadic conjugate gradient algorithm for mass conservative, semi-implicit discretization of the shallow water equations on locally refined structured grids.
International Journal of Numerical Methods in Fluids, 40:217-230, 2002.

10
M.J.P. Cullen.
Integration of the primitive barotropic equations on a sphere using the finite element method.
Quarterly Journal of the Royal Meteorological Society, 100:555, 1974.

11
Francis X. Giraldo.
Lagrange-Galerkin methods on spherical geodesic grids: The shallow water equations.
Journal of Computational Physics, 160:336-368, 2000.

12
E.S. Gross, L. Bonaventura, and G. Rosatti.
Consistency with continuity in conservative advection schemes for free-surface models.
International Journal of Numerical Methods in Fluids, 38:307-327, 2002.

13
R. Heikes and D.A. Randall.
Numerical integration of the shallow-water equations on a twisted icosahedral grid. Part I: Basic design and results of tests.
Monthly Weather Review, 123:1862-1880, 1995.

14
R. Heikes and D.A. Randall.
Numerical integration of the shallow-water equations on a twisted icosahedral grid. Part II: A detailed description of the grid and an analysis of numerical accuracy.
Monthly Weather Review, 123:1881-1887, June 1995.

15
T. Heinze and A. Hense.
The shallow water equations on the sphere and their Lagrange-Galerkin solution.
Meteorology and Atmospheric Physics, 81:129-137, 2002.

16
R. Jakob-Chien, J.J. Hack, and D.L. Williamson.
Spectral transform solutions to the shallow water test set.
Journal of Computational Physics, 119:164-187, 1995.

17
P. Jöckel, R. von Kuhlmann, M.G. Lawrence, B. Steil, C.A.M. Brenninkmeijer, P.J. Crutzen, P.J. Rasch, and B. Eaton.
On a fundamental problem in implementing flux-form advection schemes for tracer transport in 3-dimensional general circulation and chemistry transport models.
Quarterly Journal of the Royal Meteorological Society, 127:1035-1052, 2001.

18
S.J. Lin and R.B. Rood.
Multidimensional flux-form semi-Lagrangian transport schemes.
Monthly Weather Review, 124:2046-2070, September 1996.

19
S.J. Lin and R.B. Rood.
An explicit flux-form semi-Lagrangian shallow water model on the sphere.
Quarterly Journal of the Royal Meteorological Society, 123:2477-2498, 1997.

20
D. Majewski, D. Liermann, P. Prohl, B. Ritter, M. Buchhold, T. Hanisch, G. Paul, W. Wergen, and J. Baumgardner.
The operational global icosahedral-hexagonal gridpoint model GME: description and high resolution tests.
Monthly Weather Review, 130:319-338, 2002.

21
K.W. Morton and P.L. Roe.
Vorticity preserving Lax-Wendroff type schemes for the system wave equation.
SIAM Journal of Scientific Computing, 23:170-192, 2001.

22
R.A. Nicolaides.
Direct discretization of planar div-curl problems.
SIAM Journal of Numerical Analysis, 29:32-56, 1992.

23
A. Quarteroni and A. Valli.
Numerical approximation of partial differential equations, chapter 9: The Stokes problem.
Springer Verlag, 1994.

24
D. Quiang, M. Gunzburger, and J. Lili.
Voronoi-based finite volume methods, optimal Voronoi meshes and PDEs on the sphere.
Computational Methods in Applied Mechanical Engineering, 192:3933-3957, 2003.

25
T.D. Ringler, R.P. Heikes, and D.A. Randall.
Modeling the atmospheric general circulation using a spherical geodesic grid: A new class of dynamical cores.
Monthly Weather Review, 128:2471-2490, July 2000.

26
T.D. Ringler and D.A. Randall.
A potential enstrophy and energy conserving numerical scheme for solution of the shallow-water equations a geodesic grid.
Monthly Weather Review, 130:1397-1410, July 2002.

27
R. Sadourny.
The dynamics of finite difference models of the shallow water equations.
Journal of the Atmospheric Sciences, 32:680-689, 1975.

28
C. Schär and P.K. Smolarkiewicz.
A synchronous and iterative flux-correction formalism for coupled transport.
Journal of Computational Physics, 128:101-120, 1996.

29
J. Thuburn.
A PV-based shallow-water model on a hexagonal-icosahedral grid.
Monthly Weather Review, 125:2328-2347, September 1997.

30
J. Thuburn and Y. Li.
Numerical simulation of Rossby-Haurwitz waves.
Tellus A, 52:181-189, 2000.

31
D.L. Williamson, J.B. Drake, J.J. Hack, R. Jakob, and R.N. Swarztrauber.
A standard test set for numerical approximations to the shallow water equations in spherical geometry.
Journal of Computational Physics, 102:221-224, 1992.



Maria Pilar Ripodas 2008-10-27