One Approach of Solving Tasks in the Presence of Free Surface Using a Multiprocessor Computing Systems

Abstract

The task about motion of a pair of vortices under a free surface for different Froude numbers and the problem of free oscillations of fluids in a rectangular container are considered. It is assumed that the liquid is weakly compressible and homogeneous. Comparative analysis with analytical and numerical solutions obtained using incompressible approach in the author’s previous works. To solve the system of equations obtained in curvilinear coordinates with appropriate boundary and initial conditions the explicit scheme of second order approximation by the method CABARET is used. Also includes parallel version of the algorithm of calculation using Descartes cell decomposition. Evaluation of parallelization on supercomputing facility with distributed memory was performed. The results give way to further generalize this approach for solving problems with a free surface in a three-dimensional setting. The author’s plan to construct an effective method for investigation of a non homogeneous fluid flows through the further development of this approach. Such explicit techniques offer the possibility of efficient use of multiprocessor systems (clusters) for solving problems, which previously dominated by models of incompressible medium.