Parallel Numerical Solution of the Suspension Transport Problem on the Basis of Explicit-Implicit Schemes

Abstract

We discuss the construction and study of parallel algorithms for the numerical implementation of a 3D model of suspension transport in coastal marine systems. The corresponding parallel numerical modeling can be helpful in predicting spread of pollutants, as well as changes in the bottom topography which significantly affect the quality of the aquatic environment and the safety of navigation. The numerical method for solving the initial-boundary value problem for the transport of suspensions is based on the idea of constructing explicit-implicit difference schemes involving the approximation of the transfer operator (diffusion-convection) in horizontal directions based on explicit approximation on the previous time layer, and the implicit approximation of the diffusion-convection-gravity operator sedimentation in the vertical direction. Compared with traditional explicit schemes, the constructed scheme requires less time for exchange between processors when implemented on a multiprocessor system. To increase the stability margin and the allowable time step, we add a second-order difference in time to the explicit-implicit approximation. Using this scheme allows you to organize fully parallel computations, when a set of independent one-dimensional three-point problems obtained as a result of approximation with weights at the current and previous time layer of the one-dimensional diffusion-convection-gravity sedimentation operator in the vertical direction is solved in each processor independently of the others. The constructed scheme minimizes the amount of data exchange between adjacent processors when passing from a layer to another in parallel mode at the border nodes of subdomains in the case of a three-dimensional grid domain geometrically decomposed into vertical planes.