Improved boundary conditions for the direct numerical simulation of turbulent subsonic flows. I. Inviscid flows

In the context of compressible flows, the standard non-reflecting boundary conditions of Hedstrom [J. Comput. Phys. 30 (1979) 222–237] produce spurious pressure oscillations when applied to turbulent flows. In this paper, we present an analysis of the characteristics used to define non-reflecting boundary conditions. The analysis is conducted in terms of a low Mach number asymptotic series. It is shown that the Hedstrom condition is not necessary for non-reflecting boundary conditions. Based on this analysis, new boundary conditions are presented. Crucially, the revised boundary conditions allow the specification of non-reflecting outflows and inflows. The new conditions are tested for three 2-dimensional inviscid flows: an inviscid vortex crossing an outflow boundary, an evolving vortex pair crossing an outflow, and a two dimensional turbulent flow with a prescribed energy spectrum. The new boundary conditions are found to perform considerably better than standard treatments in flows where vorticity crosses the boundary.