Math @ Duke

Publications [#243640] of Anita T. Layton
Papers Published
 Layton, AT; Christara, CC; Jackson, KR, Quadratic spline methods for the shallow water equations on the sphere: Collocation,
Mathematics and Computers in Simulation, vol. 71 no. 3
(2006),
pp. 187205, ISSN 03784754 [doi]
(last updated on 2018/03/23)
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 secondorder approximations. In contrast, the OQSC methods generate approximations of the same order as quadratic spline interpolation. In the onestep OQSC method, the discrete differential operators are perturbed to eliminate loworder error terms, and a highorder approximation is computed using the perturbed operators. In the twostep OQSC method, a secondorder approximation is generated first, using the standard formulation, and then a highorder 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 semiLagrangian semiimplicit 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 Ctype grid, the methods also faithfully capture the group velocity of inertiagravity waves. © 2006.


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