Study of the accuracy and applicability of the difference scheme for solving the diffusion-convection problem at large grid Péclet numbers

Abstract

The work is devoted to the study of a difference scheme for solving the diffusion-convection problem at large grid Peclet numbers. The suspension transport problem numerical solving is carried out using the improved Upwind Leapfrog difference scheme. Its difference operator is a linear combination of the operators of Upwind and Standard Leapfrog difference schemes, while the modified scheme is obtained from 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 gets better properties than the original schemes. In addition, it includes a cell filling function that allows simulating problems in areas with complex geometry. Computational experiments were carried out to solve the suspension transport problem, which arises, for example, during the propagation of suspended matter plumes in an aquatic environment and changes in the bottom topography due to the deposition of suspended soil particles into the sediment during soil unloading into a reservoir (dumping). The results of modeling the suspension transport problem at various values of the grid Peclet number are presented. The algorithm implementation was carried out using the software and hardware architecture of parallel computing: on a central processing unit (Central Processing Unit - CPU) and on a graphics accelerator (Graphics Processing Unit - GPU). The solution to the applied problem has shown its efficiency on the CPU with small computational grids and, if it is necessary to decrease the space steps, then the GPU solution is preferable. It was found that, when using the modified Upwind Leapfrog scheme, an increase in the speed of the water flow does not lead to a loss of solution accuracy due to dissipative sources and is accompanied by an insignificant increase in computational labor costs.