An integral equation method for a mixed initial boundary value problem for unsteady Stokes system in a doubly-connected domain

R.S. Chapko, B.T. Johansson, I.S. Kantor

Research output: Contribution to journalArticle

Abstract

We present a novel numerical method for a mixed initial boundary value problem for the unsteady Stokes system in a planar doubly-connected domain. Using a Laguerre transformation the unsteady problem is reduced to a system of boundary value problems for the Stokes resolvent equations. Employing a modied potential approach we obtain a system of boundary integral equations with various singularities and we use a trigonometric quadrature method for their numerical solution. Numerical examples are presented showing that accurate approximations can be obtained with low computational cost.
Original languageEnglish
Pages (from-to)29-39
Number of pages11
JournalJournal of Numerical and Applied Mathematics
Volume100
Issue number1
Publication statusPublished - 2010

Fingerprint

Mixed Initial-boundary Value Problem
Stokes System
Integral Equation Method
Resolvent Equations
Quadrature Method
Stokes Equations
Boundary Integral Equations
Computational Cost
Boundary Value Problem
Numerical Methods
Numerical Solution
Singularity
Numerical Examples
Approximation

Keywords

  • unsteady Stokes system
  • mixed initial boundary value problem
  • Laguerre transformation
  • boundary integral equations
  • trigonometrical quadratures
  • Nyström method

Cite this

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abstract = "We present a novel numerical method for a mixed initial boundary value problem for the unsteady Stokes system in a planar doubly-connected domain. Using a Laguerre transformation the unsteady problem is reduced to a system of boundary value problems for the Stokes resolvent equations. Employing a modied potential approach we obtain a system of boundary integral equations with various singularities and we use a trigonometric quadrature method for their numerical solution. Numerical examples are presented showing that accurate approximations can be obtained with low computational cost.",
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An integral equation method for a mixed initial boundary value problem for unsteady Stokes system in a doubly-connected domain. / Chapko, R.S.; Johansson, B.T.; Kantor, I.S.

In: Journal of Numerical and Applied Mathematics, Vol. 100, No. 1, 2010, p. 29-39.

Research output: Contribution to journalArticle

TY - JOUR

T1 - An integral equation method for a mixed initial boundary value problem for unsteady Stokes system in a doubly-connected domain

AU - Chapko, R.S.

AU - Johansson, B.T.

AU - Kantor, I.S.

PY - 2010

Y1 - 2010

N2 - We present a novel numerical method for a mixed initial boundary value problem for the unsteady Stokes system in a planar doubly-connected domain. Using a Laguerre transformation the unsteady problem is reduced to a system of boundary value problems for the Stokes resolvent equations. Employing a modied potential approach we obtain a system of boundary integral equations with various singularities and we use a trigonometric quadrature method for their numerical solution. Numerical examples are presented showing that accurate approximations can be obtained with low computational cost.

AB - We present a novel numerical method for a mixed initial boundary value problem for the unsteady Stokes system in a planar doubly-connected domain. Using a Laguerre transformation the unsteady problem is reduced to a system of boundary value problems for the Stokes resolvent equations. Employing a modied potential approach we obtain a system of boundary integral equations with various singularities and we use a trigonometric quadrature method for their numerical solution. Numerical examples are presented showing that accurate approximations can be obtained with low computational cost.

KW - unsteady Stokes system

KW - mixed initial boundary value problem

KW - Laguerre transformation

KW - boundary integral equations

KW - trigonometrical quadratures

KW - Nyström method

M3 - Article

VL - 100

SP - 29

EP - 39

JO - Journal of Numerical and Applied Mathematics

JF - Journal of Numerical and Applied Mathematics

SN - 0868-6912

IS - 1

ER -