论文信息 - An improved method for integrating the Mixed Spectral Finite Difference (MSFD) model equations

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

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.

S. R. Karpik | S. Karpik

[1] F. Harlow,et al. Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[2] Francis H. Harlow,et al. Numerical Study of Large‐Amplitude Free‐Surface Motions , 1966 .

[3] C. W. Gear,et al. Numerical initial value problem~ in ordinary differential eqttations , 1971 .

[4] J. Varah,et al. On the Solution of Block-Tridiagonal Systems Arising from Certain Finite-Difference Equations* , 1972 .

[5] G. Marchuk. Methods of Numerical Mathematics , 1982 .

[6] Peter A. Taylor,et al. A mixed spectral finite-difference model for neutrally stratified boundary-layer flow over roughness changes and topography , 1987 .