Convergence of H(div)-conforming schemes for a new model of sedimentation in circular clarifiers with a rotating rake

Raimund Bürger, Paul E. Méndez, Ricardo Ruiz-Baier

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Abstract

A macroscopic model is introduced for simulating the sedimentation–consolidation of solid particles in an incompressible fluid under the effect of gravity and in the presence of a slowly rotating arm assisting the removal of sediment on the bottom of clarifier–thickener units. The governing model is an initial–boundary value problem for the Navier–Stokes equations describing the flow of the mixture coupled with a nonlinear parabolic equation describing the volume fraction of solids. The rotating structure is accounted for by suitable drag laws on the momentum balance of the mixture and on the mass balance of the solid phase. An H(div)-conforming method for the coupled problem is proposed, a rigorous proof of convergence is provided, and the validity of the new model and the performance of the scheme are demonstrated numerically by several computational tests.

Original languageEnglish
Article number113130
Number of pages24
JournalComputer Methods in Applied Mechanics and Engineering
Volume367
DOIs
Publication statusPublished - 1 Aug 2020

Keywords

  • Error estimates
  • H(div)-conforming schemes
  • Immersed structures
  • Navier–Stokes equations
  • Numerical simulation
  • Sedimentation–consolidation

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