Abstract
We consider two difference schemes that describe the convective-diffusion transfer and settling of multifractional suspensions in coastal systems. The first is based on an explicit-implicit scheme with reduced cost of arithmetic operations. This difference scheme uses an explicit approximation of the diffusion-convection operator (on the lower time layer) along the horizontal directions and an implicit approximation along the vertical direction. We determine the admissible values of the time step for this scheme from the conditions of monotonicity, solvability, and stability. We deem appropriate the use of this scheme, which naturally leads to a parallel algorithm, on grids having a relatively moderate number of nodes along each of the indicated horizontal directions, up to several hundred. The admissible value of the time step in this case is in the interval from \(10^{-2}\) s to 1 s. The second is an additive scheme obtained by splitting the original spatial three-dimensional problem into a chain of two-dimensional ones in the horizontal directions and a one-dimensional problem in the vertical direction of the task. In this case, the allowable time step can be increased to several hundred seconds. We consider in detail the parallel implementation, based on the decomposition of the grid domain, of the set of two-dimensional diffusion-convection problems included in the chain. The speedup of the algorithm was estimated on the K60 computer cluster, installed at the Keldysh Institute of Applied Mathematics (Russian Academy of Sciences).
The study was financially supported by the Russian Science Foundation (project № 22-11-00295, https://rscf.ru/project/22-11-00295/).
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Sukhinov, A.I., Chistyakov, A.E., Sidoryakina, V.V., Kuznetsova, I.Y., Atayan, A.M., Porksheyan, M.V. (2023). Parallel Algorithms for Simulation of the Suspension Transport in Coastal Systems Based on the Explicit-Implicit and Splitting Schemes. In: Sokolinsky, L., Zymbler, M. (eds) Parallel Computational Technologies. PCT 2023. Communications in Computer and Information Science, vol 1868. Springer, Cham. https://doi.org/10.1007/978-3-031-38864-4_17
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