Boundary-Layer Meteorology

, Volume 43, Issue 3, pp 273–286

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

  • S. R. Karpik

DOI: 10.1007/BF00128407

Cite this article as:
Karpik, S.R. Boundary-Layer Meteorol (1988) 43: 273. doi:10.1007/BF00128407


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.

Copyright information

© Kluwer Academic Publishers 1988

Authors and Affiliations

  • S. R. Karpik
    • 1
  1. 1.Boundary-Layer Research DivisionAtmospheric Environment ServiceDownviewCanada
  2. 2.Department of PhysicsUniversity of TorontoTorontoCanada

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