APPLICATION OF A FRACTIONAL STEP ALGORITHM FOR THE THREE-DIMENSIONAL SHALLOW WATER EQUATIONS IN A ROTATING SPHERICAL SURFACE

Abstract

This paper is mainly concerned with the motion of an incompressible fluid in a slowly rotating spherical basin using the fractional step method. The algorithm is applied by splitting the three-dimensional shallow water equations into three problems each of one dimension in every direction using the Riemann invariant. The next step is the successive integration in all directions along the characteristics associated with cubic spline interpolation. It has the advantage of reducing the three-dimensional matrix problem into an equivalent one-dimensional problem, the simplicity of this algorithm makes it very suitable for parallel computers. Numerical results are represented in three-dimensional for the velocity components at different times with different Coriolis parameters. It is worthy to note that such a study has useful applications in the science of oceanography.