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An improved method for integrating the Mixed Spectral Finite Difference (MSFD) model equations

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Abstract

In their Mixed Spectral Finite Difference (MSFD) model for flow over complex terrain, Beljaars et al. (1987) solve a set of coupled, second-order ordinary differential equations (ODEs) for the first-order perturbations to the logarithmic velocity profile caused by nonuniform surface roughness and topography. To solve this set of ODEs, they employ a Forward Euler Shooting Method. It is demonstrated here that the shooting method is computationally unstable for this problem. An absolutely stable finite-difference method based on a block tridiagonal LU factorization of the finite-difference matrix is presented. The advantages of the present algorithm over the method used by Beljaars et al. are demonstrated both by theoretical argument and numerical experiment.

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References

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Author notes

  1. S. R. Karpik

    Present address: Department of Physics, University of Toronto, M5S 1A7, Toronto, Ontario, Canada

Authors and Affiliations

  1. Boundary-Layer Research Division, Atmospheric Environment Service, 4905 Dufferin Street, M3H 5T4, Downview, Ontario, Canada

    S. R. Karpik

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  1. S. R. Karpik
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Karpik, S.R. An improved method for integrating the Mixed Spectral Finite Difference (MSFD) model equations. Boundary-Layer Meteorol 43, 273–286 (1988). https://doi.org/10.1007/BF00128407

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  • DOI: https://doi.org/10.1007/BF00128407

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