Quadratic spline methods for the shallow water equations on the sphere: Collocation

Anita T. Layton, Christina C. Christara and Kenneth R. Jackson

Mathematics and Computers in Simulation (MATCOM), 2006, vol. 71, issue 3, 187-205

Abstract: In this study, we present numerical methods, based on the optimal quadratic spline collocation (OQSC) methods, for solving the shallow water equations (SWEs) in spherical coordinates. The error associated with quadratic spline interpolation is fourth order locally at certain points and third order globally, but the standard quadratic spline collocation methods generate only second-order approximations. In contrast, the OQSC methods generate approximations of the same order as quadratic spline interpolation. In the one-step OQSC method, the discrete differential operators are perturbed to eliminate low-order error terms, and a high-order approximation is computed using the perturbed operators. In the two-step OQSC method, a second-order approximation is generated first, using the standard formulation, and then a high-order approximation is computed in a second phase by perturbing the right sides of the equations appropriately. In this implementation, the SWEs are discretized in time using the semi-Lagrangian semi-implicit method, and in space using the OQSC methods. The resulting methods are efficient and yield stable and accurate representation of the meteorologically important Rossby waves. Moreover, by adopting the Arakawa C-type grid, the methods also faithfully capture the group velocity of inertia-gravity waves.

Keywords: Numerical weather prediction; Finite element; Semi-Lagrangian semi-implicit; Rossby stability; Staggered grids (search for similar items in EconPapers)
Date: 2006
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:71:y:2006:i:3:p:187-205

DOI: 10.1016/j.matcom.2004.10.009

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