On the accuracy of high-order finite elements in curvilinear coordinates

Authors:
Stephen J. Thomas;Amik St.-Cyr
Affiliations:
National Center for Atmospheric Research, Boulder, CO;National Center for Atmospheric Research, Boulder, CO
Venue:
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
Year:
2005

Citing 6
Cited 0

The spectral element method for the shallow water equations on the sphere

Journal of Computational Physics
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations

Journal of Computational Physics
An all-scale anelastic model for geophysical flows: dynamic grid deformation

Journal of Computational Physics
On Strong Stability Preserving Time Discretization Methods

Journal of Scientific Computing
A standard test set for numerical approximations to the shallow water equations in spherical geometry

Journal of Computational Physics
Discontinuous Galerkin Methods: Theory, Computation and Applications

Discontinuous Galerkin Methods: Theory, Computation and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

The governing equations for shallow water flow on the sphere are formulated in generalized curvilinear coordinates. The various analytic expressions for the differential operators are all mathematically equivalent. However, numerical approximations are not equally effective. The accuracy of high-order finite element discretizations are evaluated using the standard test problems proposed by Williamson et al (1992). The so-called strong conservation formulation is far more accurate and results in standard error metrics that are at least two orders of magnitude smaller than the weak conservation form, Jorgensen (2003), Prusa and Smolarkeiwicz (2003). Moreover, steady state solutions can be integrated much longer without filtering when time-stepping the physical velocities.