A multiresolution method for the simulation of sedimentation in inclined Channels

Raimund Bürger, Ricardo Ruiz-Baier, Kai Schneider, Héctor Torres

Research output: Contribution to journalArticleResearchpeer-review

9 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)479-504
Number of pages26
JournalInternational Journal of Numerical Analysis and Modeling
Volume9
Issue number3
Publication statusPublished - 29 Jun 2012
Externally publishedYes

Keywords

  • Boycott effect
  • Finite volume approximation
  • Multiresolution analysis
  • Spaceadaptivity
  • Transport-flow coupling
  • Two-dimensional sedimentation

Cite this