Additive two-dimensional splitting schemes for solving 3D suspension transport problems on optimal boundary-adaptive grids with uniform spacing’s in the vertical direction

Abstract

The article considers3D matter transport model in dissolved and suspended forms (impurities) in coastal marine systems. The initial boundary value problem numerical solution is carried out on the basis of local2D splitting schemes. In this case, special attention is paid to the hig-hquality computational grid construction. As a rule, in the proposed methods, Cartesian grids are used, a variety of which are grids with boundary adaptation. The technology of constructing 3D vertically uniform boundary-adaptive grids on the basis of surface 2D grids, which is created using the procedure of minimizing the generalized Dirichlet functional, is presented. Previously, this approach has shown its effectiveness in constructing 2D non-degenerate regular grids containing the minimum number of cells (convex quadrangles) for test Z-shape regions, such as the “Maltese cross” and others, as well as in the 2Dhydrophysicsproblems numerical solution of coastal systems.

Two-Dimensional-One-Dimensional Alternating Direction Schemes for Coastal Systems Convection-Diffusion Problems

“…Let us consider the formulation of the initial-boundary value problem for the spatial three-dimensional convection-diffusion equation in a parallelepiped G [12,13]:…”