Math @ Duke

Publications [#243721] of Anita T. Layton
Papers Published
 Layton, AT, A semiLagrangian collocation method for the shallow water equations on the sphere,
Siam Journal on Scientific Computing, vol. 24 no. 4
(2003),
pp. 14331449, ISSN 10648275 [doi]
(last updated on 2018/11/17)
Abstract: In this paper, we describe a numerical method for solving the shallow water equations (SWEs) in spherical coordinates. The most popular spatial discretization method used in global atmospheric models is currently the spectral transform method, which generates highorder numerical solutions and provides an elegant solution to the pole problems induced by a spherical coordinate system. However, the spectral transform method requires Legendre transforms, which have a computational complexity of script O sign(N 3), where N is the number of subintervals in one spatial dimension. Thus, highorder finite element methods may be a viable alternative. In this implementation, the SWEs are discretized in time using the threelevel semiLagrangian semiimplicit method and in space using the cubic spline collocation method. Numerical results for the standard SWEs test suite [D. L. Williamson et al., J. Comput. Phys., 102 (1992), pp. 211224] are presented to demonstrate the stability and accuracy of the method. When compared to a previously applied Eulerianbased method, our method generates solutions with comparable accuracy while allowing larger timesteps and thus lower computational cost.


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