Vol. 7, No. 1, 2012

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An embedded boundary method for the Navier–Stokes equations on a time-dependent domain

Gregory H. Miller and David Trebotich

Vol. 7 (2012), No. 1, 1–31

We present a new conservative Cartesian grid embedded boundary method for the solution of the incompressible Navier–Stokes equations in a time-dependent domain. It is a Godunov-projection fractional step scheme in which hyperbolic advection and a variety of implicit and explicit Helmholtz operations are performed on time-stationary domains. The transfer of data from one fixed domain to another uses third-order interpolation. The method is second order accurate in L1 and first order in L. The algorithm is verified on flow geometries with prescribed boundary motion.

Navier–Stokes, embedded boundary, finite volume, moving domain
Mathematical Subject Classification 2010
Primary: 35Q30, 35R37, 65M08
Received: 12 January 2011
Revised: 1 July 2011
Accepted: 19 September 2011
Published: 22 December 2011
Gregory H. Miller
Department of Chemical Engineering and Materials Science
University of California
1 Shields Ave
Davis, CA 95616
United States
David Trebotich
Applied Numerical Algorithms Group
Lawrence Berkeley National Laboratory
1 Cyclotron Road
Berkeley, CA 94720
United States