Explicit-Implicit Schemes for Parallel Solving of the Suspension Transport Problems in Coastal Systems

Abstract

This paper is devoted to the parallel algorithms development for numerical simulation of 3D weighted suspension particles transport in coastal systems, using explicit-implicit difference schemes on multiprocessor systems. For the numerical solution of the initial-boundary value problem of suspension transport, explicit-implicit difference schemes are used. Decomposition of 3D grid region by vertical planes has been used for parallel algorithm constructing. Also second order time derivative with relatively small time-multiplier has been added for the permissible time step increasing in accordance of B. Chetverushkin method of regularization. Using these schemes allows to organize fully parallel computations. A set of independent one-dimensional three-point problems obtained as a result of implicit approximation (with optimal weight parameter) of the one-dimensional advection-diffusion and gravity sedimentation operator in the vertical direction may be solved in each processor independently without data exchanges between processors. Data exchanges requires only for the neighboring nodes in subdomains and they may be executed independently for each processor in horizontal spatial directions. The permissible value of time step is defined of stability requirements for the explicit difference scheme for grid equation of hyperbolic type and it is better in comparison of explicit schemes without regularization. Optimal value of weight parameter for this scheme has been defined. As the result the total time of parallel solution is also less in comparison of totally implicit schemes.