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

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

doi:10.1007/s11012-015-0271-4

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

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

Department of Mathematics

Belarusian State University

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

343 Downloads (Pure)

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 language	English
Pages (from-to)	1041-1055
Number of pages	15
Journal	Meccanica
Volume	51
Issue number	5
Early online date	08 Sept 2015
DOIs	https://doi.org/10.1007/s11012-015-0271-4
Publication status	Published - 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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10.1007/s11012-015-0271-4

Simulating the Hele-Shaw flow in the presence of various obstacles and moving particlesAccepted author manuscript, 1.08 MB

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title = "Simulating the Hele-Shaw flow in the presence of various obstacles and moving particles",

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.",

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author = "D. Peck and Sergei Rogosin and Michal Wrobel and Gennady Mishuris",

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T1 - Simulating the Hele-Shaw flow in the presence of various obstacles and moving particles

AU - Peck, D.

AU - Rogosin, Sergei

AU - Wrobel, Michal

AU - Mishuris, Gennady

N1 - This is the author accepted manuscript. The final version is available from Springer via http://dx.doi.org/10.1007/s11012-015-0271-4

PY - 2016/5/1

Y1 - 2016/5/1

N2 - 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.

AB - 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.

KW - Hele-Shaw flow

KW - Point source/sink

KW - Moving obstacles

KW - Green's function

KW - Neumann function

KW - Mixed boundary value problem

KW - Asymptotic analysis

KW - Numerical simulation

KW - UNIFORM ASYMPTOTICS

KW - HYDRAULIC FRACTURE

KW - GREENS KERNELS

KW - TOOLBOX

KW - DOMAINS

KW - MATLAB

UR - http://hdl.handle.net/2160/43020

U2 - 10.1007/s11012-015-0271-4

DO - 10.1007/s11012-015-0271-4

M3 - Article

SN - 0025-6455

VL - 51

SP - 1041

EP - 1055

JO - Meccanica

JF - Meccanica

IS - 5

ER -

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

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Keywords

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