## 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 language | English (US) |
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Pages (from-to) | A2197-A2219 |

Journal | SIAM Journal on Scientific Computing |

Volume | 34 |

Issue number | 4 |

DOIs | |

State | Published - 2012 |

## Keywords

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

## ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics