Two-dimensional-one-dimensional splitting scheme for numerical solution of problems of suspended matter transport in coastal systems

Abstract

This article discusses the problems of numerical solution of non-stationary convection-diffusion-reaction problems using the model problem of suspended matter transport as an example. In the difference scheme proposed by the authors, at each time layer, the original spatial-three-dimensional problem is split along horizontal directions into a chain of two-dimensional and one-dimensional problems. In order to ensure the unconditional skew-symmetry of the convective transfer operator and its energy neutrality, the convective terms are written in symmetric form (half the sum of the non-divergent and divergent forms). The approximation of the initial boundary value problem, to which the suspended matter transport model is reduced, is considered in the Hilbert space of grid functions, which in subsequent discussions will allow us to focus on the use of general results of the theory of stability (correctness) of operator-difference schemes.