RAPPORT Vectorization Aspects of a Spherical Advection Scheme on a Reduced

This paper deals with the numerical solution of the two-dimensional transport equation on a sphere. Two diierent mass-conservative advection schemes are considered The rst is the standard rst-order scheme using forward Euler in time and rst-order upwind in space. The second scheme uses for time stepping a second-order explicit two-step method and for the space discretization a ux-limited, third-order upwind biased scheme. Both schemes are implemented on a uniform longitude-latitude grid and on a so-called reduced grid, where less cells are used near the poles than at the equator. Since we consider to use Fortran 90 for a software project where the transport equation is part of the problem, we implemented the schemes in Fortran 77 and in Fortran 90 to compare the performance both on scalar and on vector processors. To compare the numerical and the computational performance of all implementations we used a standard test problem describing a solid-body rotation on the sphere (cf. 9]). The results are obtained on a Cray C90.