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 $L_1$ and first order in $L_{\infty }$. The algorithm is verified on flow geometries with prescribed boundary motion.