Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations

被引:198
作者
Giraldo, FX [1 ]
Hesthaven, JS
Warburton, T
机构
[1] USN, Res Lab, Monterey, CA 93943 USA
[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA
[3] Univ New Mexico, Dept Math & Stat, Albuquerque, NM 87131 USA
关键词
discontinuous Galerkin method; filters; high-order; icosahedral grid; shallow water equations; spectral element method; spherical geometry;
D O I
10.1006/jcph.2002.7139
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
We present a high-order discontinuous Galerkin method for the solution of the shallow water equations on the sphere. To overcome well-known problems with polar singularities, we consider the shallow water equations in Cartesian coordinates, augmented with a Lagrange multiplier to ensure that fluid particles are constrained to the spherical surface. The global solutions are represented by a collection of curvilinear quadrilaterals from an icosahedral grid. On each of these elements the local solutions are assumed to be well approximated by a high-order nodal Lagrange polynomial, constructed from a tensor-product of the Legendre-Gauss-Lobatto points, which also Supplies a high-order quadrature. The shallow water equations are satisfied in a local discontinuous element fashion with solution continuity being enforced weakly. The numerical experiments, involving a comparison of weak and strong conservation forms and the impact of over-integration and filtering, confirm the expected high-order accuracy and the potential for using such highly parallel formulations in numerical weather prediction. (C) 2002 Elsevier Science (USA).
引用
收藏
页码:499 / 525
页数:27
相关论文
共 38 条
[1]   High-order accurate discontinuous finite element solution of the 2D Euler equations [J].
Bassi, F ;
Rebay, S .
JOURNAL OF COMPUTATIONAL PHYSICS, 1997, 138 (02) :251-285
[2]   hp-Version discontinuous Galerkin methods for hyperbolic conservation laws [J].
Bey, KS ;
Oden, JT .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1996, 133 (3-4) :259-286
[3]  
BOYD J, 1996, HOUSTON J MATH
[4]  
Burk SD, 2000, MON WEATHER REV, V128, P1438, DOI 10.1175/1520-0493(2000)128<1438:TDOWCU>2.0.CO
[5]  
2
[6]   The Runge-Kutta discontinuous Galerkin method for conservation laws V - Multidimensional systems [J].
Cockburn, B ;
Shu, CW .
JOURNAL OF COMPUTATIONAL PHYSICS, 1998, 141 (02) :199-224
[7]  
COCKBURN B, 2001, J SCI COMPUT, V16, P145
[8]  
ENGQUIST B, 1981, MATH COMPUT, V36, P321, DOI 10.1090/S0025-5718-1981-0606500-X
[9]   Lagrange-Galerkin methods on spherical geodesic grids: The shallow water equations [J].
Giraldo, FX .
JOURNAL OF COMPUTATIONAL PHYSICS, 2000, 160 (01) :336-368
[10]  
Giraldo FX, 2001, INT J NUMER METH FL, V35, P869, DOI 10.1002/1097-0363(20010430)35:8<869::AID-FLD116>3.0.CO