Year: 2012
Author: R. Bürger, R. Ruiz-Baier, K. Schneider, H. Torres
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 3 : pp. 479–504
Abstract
An adaptive multiresolution scheme is proposed for the numerical solution of a spatially two-dimensional model of sedimentation of suspensions of small solid particles dispersed in a viscous fluid. This model consists in a version of the Stokes equations for incompressible fluid flow coupled with a hyperbolic conservation law for the local solids concentration. We study the process in an inclined, rectangular closed vessel, a configuration that gives rise a well-known increase of settling rates (compared with a vertical vessel) known as the "Boycott effect". Sharp fronts and discontinuities in the concentration field are typical features of sedimentation phenomena. This solution behavior calls for locally refined meshes to concentrate computational effort on zones of strong variation. The spatial discretization presented herein is naturally based on a finite volume (FV) formulation for the Stokes problem including a pressure stabilization technique, while a Godunov-type scheme endowed with a fully adaptive multiresolution (MR) technique is applied to capture the evolution of the concentration field, which in addition induces an important speed-up of CPU time and savings in memory requirements. Numerical simulations illustrate that the proposed scheme is robust and allows for substantial reductions in computational effort while the computations remain accurate and stable.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2012-IJNAM-643
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 3 : pp. 479–504
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Two-dimensional sedimentation transport-flow coupling Boycott effect space adaptivity multiresolution analysis finite volume approximation.