Simulating the Hele-Shaw flow in the presence of various obstacles and moving particles

D. Peck, Sergei Rogosin, Michal Wrobel, Gennady Mishuris

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Abstract

A generalization of the approach developed in the recent papers by the authors is presented. It aims to provide a description of the Hele-Shaw cell in the presence of multiple small obstacles/moving particles. We perform an asymptotic analysis of the dynamics of the moving boundary and the moving particles. For this, a modification of Maz'ya-Movchan-Nieves uniform asymptotic formula for the Green's function of the mixed boundary value problem for the Laplace equation in a multiply connected domain is utilized. The paper contains extensive numerical analysis, accounting for various physical mechanisms of particle movement in the Hele-Shaw flow.

Original languageEnglish
Pages (from-to)1041-1055
Number of pages15
JournalMeccanica
Volume51
Issue number5
Early online date08 Sept 2015
DOIs
Publication statusPublished - 01 May 2016

Keywords

  • Hele-Shaw flow
  • Point source/sink
  • Moving obstacles
  • Green's function
  • Neumann function
  • Mixed boundary value problem
  • Asymptotic analysis
  • Numerical simulation
  • UNIFORM ASYMPTOTICS
  • HYDRAULIC FRACTURE
  • GREENS KERNELS
  • TOOLBOX
  • DOMAINS
  • MATLAB

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