Inflow and outflow boundary conditions for direct numerical simulations

Abstract

New inflow and outflow boundary conditions are proposed. These conditions are applied to two test problems. One is a problem in which a vortex convected by a uniform mean flow passes through an outflow boundary. The other is a two-dimensional spatially developing mixing layer. The new boundary conditions which give highly accurate results for both test problems consist of convective-viscous conditions and an approximate transport equation for pressure. The applicability of the convective-viscous conditions is verified by numerical tests which show that conventional boundary conditions do not approximate the velocity or the pressure fields on the boundary. The pressure transport equation proposed in this work is used to obtain the pressure on the inflow and outflow boundaries from a previous time step pressure field. As a result, we can conclude that the new boundary conditions are appropriate for direct numerical simulations of spatially developing flows.