An adaptive solver for the spherical shallow water equations |
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| Authors: | L. Gavete, B. Alonso, M.L. Gavete, F. Ure a,J.J. Benito |
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| Affiliation: | aDepartment of Applied Mathematics in Natural Resources, Universidad Politécnica de Madrid, Spain;bI.E.S. Isabel La Católica, Madrid, Spain;cDepartment of Applied Mathematics, Castilla-La Mancha University, Ciudad Real, Spain;dDepartment of Construction and Production, UNED, Spain |
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| Abstract: | The shallow water equations (SWE), which describe the flow of a thin layer of fluid in two dimensions have been used by the atmospheric modelling community as a vehicle for testing promising numerical methods for solving atmospheric and oceanic problems. The SWE are important for the study of the dynamics of large-scale flows, as well for the development of new numerical schemes that are applied to more complex models. In this paper we present a finite difference p-adaptive method based on high order finite differences that is applied using an error indicator for solving the SWE on the sphere. A standard test set is used to evaluate the accuracy of the new method. The results obtained are compared with the pseudo-spectral method. |
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| Keywords: | Shallow water p-Adaptive Finite difference Partial differential equations |
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