A new mixed potential representation for unsteady, incompressible flow

Document Type

Article

Publication Date

1-1-2019

Abstract

We present a new integral representation for the unsteady, incompressible Stokes or Navier-Stokes equations, based on a linear combination of heat and harmonic potentials. For velocity boundary conditions, this leads to a coupled system of integral equations: one for the normal component of velocity and one for the tangential components. Each individual equation is well-conditioned, and we show that using them in predictor-corrector fashion, combined with spectral deferred correction, leads to high-order accuracy solvers. The fundamental unknowns in the mixed potential representation are densities supported on the boundary of the domain. We refer to one as the vortex source, the other as the pressure source, and to the coupled system as the combined source integral equation.

Identifier

85077993907 (Scopus)

Publication Title

SIAM Review

External Full Text Location

https://doi.org/10.1137/18M1216158

ISSN

00361445

First Page

733

Last Page

755

Issue

4

Volume

61

Grant

DMS-1720405

Fund Ref

National Science Foundation

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