Integral equation methods for unsteady Stokes flow in two dimensions

Document Type

Article

Publication Date

1-1-2012

Abstract

We present an integral equation formulation fo r the unsteady Stokes equations in two dimensions. This problem is of interest in its own right as a model for slow viscous flow, but perhaps more importantly as an ingredient in the solution of the full, incompressible Navier-Stokes equations. Using the unsteady Green's function, the velocity evolves analytically as a divergence-free vector field. This avoids the need for either the solution of coupled field equations (as in fully implicit PDE-based marching schemes) or the projection of the velocity field onto a divergence-free field at each time step (as in operator splitting methods). In addition to discussing the analytic properties of the operators that arise in the integral formulation, we describe a family of high order accurate numerical schemes and illustrate their performance with several examples. © 2012 Society for Industrial and Applied Mathematics.

Identifier

84866396703 (Scopus)

Publication Title

SIAM Journal on Scientific Computing

External Full Text Location

https://doi.org/10.1137/110860537

e-ISSN

10957200

ISSN

10648275

First Page

A2197

Last Page

A2219

Issue

4

Volume

34

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