DEVELOPING AND OPTIMIZING A 3-D-SPECTRAL FINITE-DIFFERENCE HYDRODYNAMIC MODEL FOR THE CRAY X-MP

This paper deals with the development of a vectorizable and numerically efficient algorithm for solving the 3-D hydrodynamic equations describing the sea's motion in any area of arbitrary geographical extent. The method employs a finite difference grid in the horizontal with a spectral approach through the vertical. By this means a decomposition into equations describing changes in the sea surface elevation, (solved using a vectorizable explicit algorithm) and equations describing vertical current structure is possible. This latter set can be solved implicitly using vectorizable methods. The implicit solution of these equations enables them to be solved with a significantly longer time step than the free surface equations, thereby achieving a computationally efficient and fully vectorizable code for the total solution. The numerical accuracy and computational requirements of the method on the CRAY X-MP are discussed in detail, together with some brief indication of the algorithms implementation on CYBER-205, or massively parallel machines,based on transputer arrays. © 1990.