Publications [#243726] of Anita T. Layton

Papers Published

  1. Layton, AT, Cubic spline collocation method for the shallow water equations on the sphere, Journal of Computational Physics, vol. 179 no. 2 (2002), pp. 578-592, ISSN 0021-9991
    (last updated on 2018/12/18)

    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).