An embedded boundary method for the navier-stokes equations on a time-dependent domain

Abstract

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 L1. The algorithm is verified on flow geometries with prescribed boundary motion. © 2012 by Mathematical Sciences Publishers.