Integral equation methods for unsteady Stokes flow in two dimensions

Shidong Jiang, Shravan Veerapanen, Leslie Greengard

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)A2197-A2219
JournalSIAM Journal on Scientific Computing
Volume34
Issue number4
DOIs
StatePublished - 2012

Keywords

  • Boundary integral equations
  • Fast algorithms
  • Linearized Navier-Stokes equations
  • Unsteady Stokes

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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