Two Vectorized Algorithms for the Effective Calculation of Mass-Consistent Flow Fields

Abstract

The purpose of this paper is the calculation of mass-consistent wind velocity fields over complex orography on the basis of existing measurements. Measured data are used to generate an initial wind velocity field that in general does not satisfy continuity. For the adjustment of this velocity field a three-dimensional elliptic differential equation is solved. A transformation of this equation to a terrain-following coordinate system ensures the proper consideration of the orography. Two numerical algorithms for the solution of the transformed equation are presented. One algorithm makes use of a fast direct elliptic solver based on Fourier analysis, the other utilizes the red-black SOR method. Both algorithms achieve full vectorization on computers like the CYBER 205. A test problem is defined to compare the two algorithms with regard to the computing time: In the case of small terrain roughness, the algorithm using the fast direct elliptic solver is recommended, in the opposite case the red-black SOR method. Adjusted mass- consistent wind fields are presented for the Athens basin. The results are discussed in view of the elevated pollution levels in Athens; they are in good agreement with observations.