2015
DOI: 10.1007/s11012-015-0271-4
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Simulating the Hele-Shaw flow in the presence of various obstacles and moving particles

Abstract: This is the author accepted manuscript. The final version is available from Springer via http://dx.doi.org/10.1007/s11012-015-0271-4A 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 formu… Show more

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Cited by 7 publications
(4 citation statements)
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“…Uniform asymptotics in multiply perforated bodies for problems of vector elasticity were constructed in [18,19]. Uniform asymptotic approximations of Green's kernels have been used to study a Hele-Shaw flow containing several obstacles in [37].…”
Section: Background and Previous Resultsmentioning
confidence: 99%
“…Uniform asymptotics in multiply perforated bodies for problems of vector elasticity were constructed in [18,19]. Uniform asymptotic approximations of Green's kernels have been used to study a Hele-Shaw flow containing several obstacles in [37].…”
Section: Background and Previous Resultsmentioning
confidence: 99%
“…Meso-scale approximations have also been shown to be effective in modelling the response of elastic solids with rigid and free clouds of impurities [48,49], low frequency acoustic problems involving rigid defect clusters [50] and steady-state heat conduction in densely packed composites [51]. The approximations have also proven to be useful in modelling flows involving fluids interacting with many small obstacles within narrow spaces [52], important for understanding CO2-sequestration processes.…”
Section: Introductionmentioning
confidence: 99%
“…Free and moving boundary problems [1,2], where the problem domain is a priori unknown are encountered in different areas of science and engineering [3], including laser drilling of metals [4,5], crack propagation and delamination in composite materials [6,7], in Hele-Shaw flow [8,9], and elastic and plastic torsion [10,11].…”
Section: Introductionmentioning
confidence: 99%