Abstract
The initial boundary value problem for the 3D convection-diffusion equation corresponding to the mathematical model of suspended matter transport in coastal marine systems and extended shallow water bodies is considered. Convective and diffusive transport operators in horizontal and vertical directions for this type of problem have significantly different physical and spectral properties. In connection with the above, a two-dimensional–one-dimensional splitting scheme has been built—a three-dimensional analog of the Peaceman–Rachford alternating direction scheme, which is suitable for the operational suspension spread prediction in coastal systems. The paper has proved the theorem of stability solution with respect to the initial data and functions of the right side, in the case of time-independent operators in special energy norms determined by one of the splitting scheme operators. The accuracy has been investigated, which, as in the case of the Peaceman–Rachford scheme, with the special definition of boundary conditions on a fractional time step, is the value of the second order in dependency of time and spatial steps. The use of this approach makes it possible to obtain parallel algorithms for solving grid convection-diffusion equations which are economical in the sense of total time of problem solution on multiprocessor systems, which includes time for arithmetic operations realization and the one required to carry of information exchange between processors.
Highlights
In this article the splitting scheme for the 3D convection-diffusion equation has been considered as an analog of the Peaceman–Rachford alternating direction scheme [1,2,3]
The choice made by the authors in favor of these splitting schemes is based on the following physical motivation for convection-diffusion problems in coastal marine systems and shallow water bodies [4,5,6]
The user is interested in minimizing the total time expenditure of solving the problem, the main part of which is the cost of performing arithmetic, logical operations and information exchange operations between the processor units
Summary
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