Math @ Duke
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Publications [#243726] of Anita T. Layton
Papers Published
- Layton, AT, Cubic spline collocation method for the shallow water equations on the sphere,
Journal of Computational Physics, vol. 179 no. 2
(July, 2002),
pp. 578-592, Elsevier BV, ISSN 0021-9991 [doi]
(last updated on 2020/07/05)
Abstract: Spatial discretization schemes commonly used in global meteorological applications are currently limited to spectral methods or low-order finite-difference/finite-element methods. The spectral transform method, which yields high-order approximations, requires Legendre transforms, which have a computational complexity of O(N3), where N is the number of subintervals in one dimension. Thus, high-order finite-element methods may be a viable alternative to spectral methods. In this study, we present a new numerical method for solving the shallow water equations (SWE) in spherical coordinates. In this implementation, the SWE are discretized in time with the semi-implicit leapfrog method, and in space with the cubic spline collocation method on a skipped latitude-longitude grid. Numerical results for the Williamson et al. SWE test cases [D. L. Williamson, J. B. Blake, J. J. Hack, R. Jakob, and P. N. Swarztrauber, J. Comput. Phys. 102, 211 (1992)] are presented to demonstrate the stability and accuracy of the method. Results are also shown for an efficiency comparison between this method and a similar method in which spatial discretization is done on a uniform latitude-longitude grid. © 2002 Elsevier Science (USA).
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