Open boundary conditions in numerical simulations of unsteady incompressible flow

Abstract

In numerical simulations of unsteady incompressible flow, mass conservation can be enforced using a fractional step method in which the momentum equations are solved in combination with a pressure or pressure correction equation. While there is an obvious way to implement most spatial boundary conditions commonly applied to these equations, the situation for so-called open boundaries is less clear. Open boundaries must allow fluid to leave the domain with minimal effect on the upstream flow and, at the same time, ensure global conservation of mass. Previous work found that the open boundary condition implementations commonly used with lower order fractional step methods, such as the projection-1 and projection-2 methods, can cause the higher order projection-3 method to become unstable. We discuss the implementation of open boundary conditions in combination with fractional step methods, and investigate three possible approaches. © Austral. Mathematical Soc. 2009.