Parallel Algorithms for Numerical Solution of Spatially Three-Dimensional Diffusion-Convection Equations in Coastal Systems Based on Splitting Schemes

Abstract

Introduction. To prevent the occurrence and mitigate the consequences of hazardous and catastrophic phenomena associated with sediment transport in natural systems, it is necessary to develop operational and scientifically justified forecasts, identify critical states at which the emergence of emergency situations is possible. For these purposes, it is necessary to create an accurate and efficient toolkit, including algorithms for numerical solution of a model problem that takes into account the specifics of natural systems. In this work, parallel algorithms for numerical solution of a spatially three-dimensional diffusion-convection problem of sediment are presented, which allow a significant reduction in computation time (by more than 4 times) compared to calculations conducted using a sequential algorithm.Materials and Methods. For the parallel solution of the spatially three-dimensional diffusion-convection problem, an implicit splitting scheme is constructed, in which the original continuous problem is replaced by a chain of two-dimensional and one-dimensional problems. The splitting schemes proposed in the work are physically justified and take into account the specifics of coastal marine systems, for which the influence of micro-turbulent diffusion and advective transport of substances are comparable, and the Peclet number does not exceed unity when approximating real problems. For the parallel numerical implementation, a method of decomposing the grid domain into two families of vertical planes parallel to the coordinate planes Oxz and Oyz, combined with the Seidel method for solving two-dimensional grid problems in horizontal planes and the tridiagonal matrix algorithm when solving one-dimensional three-point problems in the vertical direction, is used. Within the framework of the parallel computing software implementation, a parallel algorithm is presented that implements the diffusion-convection problem on a computing system using MPI technology.Results. A comparative analysis of parallel and sequential algorithms is obtained using a model problem.Discussion and Conclusions. The developed software allows its practical use for solving specific hydrophysical problems, including as part of a software complex.