Boundary-Layer Meteorology

, Volume 43, Issue 3, pp 273-286

First online:

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

  • S. R. KarpikAffiliated withBoundary-Layer Research Division, Atmospheric Environment Service

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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.