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This work is devoted to the development and numerical study of coupled models of sediment transport and suspended matter, taking into account coastal currents and stress near the bottom caused by wind waves, turbulent spatially 3D movement of the aquatic environment, the complex shape of the coastline, bottom topography, and other factors. Conservative stable difference schemes are constructed and investigated. A comparative analysis of the efficiencies of using explicit difference schemes with implicit schemes, as well as with schemes of a special form, explicitly implicit schemes, is given. The main idea is to use an additive difference scheme, consisting of a chain of spatially one-dimensional implicit and spatially two-dimensional explicit difference problems, approximating the original problem in the total sense. The explicit two-dimensional diffusion-convection-reaction problems, as well as the spatially two-dimensional sediment transport problems are approximated by regularized explicit schemes that involve the introduction of second-order difference derivatives with respect to the time variable with a relatively small time step the regularizer as an additional term in the left-hand sides of the equations. This allows us to repeatedly increase the admissible time step in comparison with the unregularized explicit difference equations of the parabolic type. It is this method that has shown its advantage over explicit and implicit schemes. Keywords—coastal zone; sediment transport; suspended matter transport; mathematical model; linearization of the initial-boundary value problem; difference scheme.

Efficient Algorithms for the Numerical Solution of the Coupled Sediment and Suspended Matter Transport Problems in Coastal Systems