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- Title
Studying the Accuracy and Applicability of the Finite Difference Scheme for Solving the Diffusion–Convection Problem at Large Grid Péclet Numbers.
- Authors
Sukhinov, A. I.; Kuznetsova, I. Yu.; Chistyakov, A. E.; Protsenko, E. A.; Belova, Yu. V.
- Abstract
The work is devoted to studying a finite difference scheme for solving the diffusion–convection problem at large grid Péclet numbers. The suspension transport problem is proposed to be numerically solved using the improved upwind leapfrog finite difference scheme. Its difference operator is a linear combination of the operators of upwind and standard leapfrog finite difference schemes while the modified scheme is obtained from the schemes with optimal weighting coefficients. At certain values of the weighting coefficients, this combination leads to mutual compensation of approximation errors, and the resulting scheme acquires better properties than the original schemes. In addition, it includes the cell filling function that allows naturally simulating problems in areas with complex geometry. Computational experiments are carried out to solve the suspension transport problem which arises, for instance, in propagation of suspended matter plumes in an aquatic environment and in changing bottom topography due to deposition of suspended soil particles in the course of soil unloading into a reservoir (dumping). The results of modeling the suspension transport problem are presented for various values of the grid Péclet number. The algorithm is implemented using the software and hardware architecture of parallel computing on a central processing unit (CPU) and on a graphics processing unit (GPU). The solution to an applied problem shows its efficiency on CPU for small computational grids, but, when the spatial steps should be decreased, the GPU solution becomes preferable. It is revealed that, in using the modified upwind leapfrog scheme, acceleration of the water flow does not lead to a loss in the solution accuracy due to dissipation sources and is accompanied by an insignificant increase in computational labor costs.
- Subjects
FINITE differences; PROBLEM solving; CENTRAL processing units; LINEAR operators; DIFFERENCE operators; GRAPHICS processing units; GRID computing
- Publication
Journal of Applied Mechanics & Technical Physics, 2021, Vol 62, Issue 7, p1255
- ISSN
0021-8944
- Publication type
Article
- DOI
10.1134/S002189442107018X