Mathematical model of process of sedimentation of multicomponent suspension on the bottom and changes in the composition of bottom materials

A. I. Sukhinov ; A. E. Chistyakov ; A. M. Atayan ; I. Yu. Kuznetsova ; V. N. Litvinov ; A. V. Nikitina

Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 60 (2022), pp. 73-89.

Résumé

The paper considers 2D and 3D models of transport of suspended particles, taking into account the following factors: movement of aqueous medium; variable density depending on the suspension concentration; multicomponent character of suspension; changes in bottom geometry as a result of suspension sedimentation. The approximation of the three-dimensional diffusion-convection equation is based on splitting schemes into two-dimensional and one-dimensional problems. In this work, we use discrete analogues of convective and diffusion transfer operators in the case of partial cell occupancy. The geometry of the computational domain is described based on the occupancy function. The difference scheme used is a linear combination of the Upwind and Standard Leapfrog difference schemes with weight coefficients obtained by minimizing the approximation error. This scheme is designed to solve the problem of impurity transfer at large grid Peclet numbers. Based on the results of numerical experiments, conclusions are drawn about the advantage of the 3D model of multicomponent suspension transport in comparison with the 2D model. Computational experiments have been performed to simulate the process of sedimentation of a multicomponent suspension, as well as its effect on the bottom topography and changes in its composition.

Détail

Keywords: suspension transport model, variable density, Upwind Leapfrog difference scheme, Standard Leapfrog difference scheme, bottom topography change, parallel algorithms.

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