Three-dimensional boundary conditions for direct and large-eddy simulation of compressible viscous flows

Navier–Stokes characteristic boundary conditions (NSCBC) usually assume the flow to be normal to the boundary plane. In this paper, NSCBC is extended to account for convection and pressure gradients in boundary planes, resulting in a 3D-NSCBC approach. The introduction of these additional transverse terms requires a specific treatment for the computational domain’s edges and corners, as well as a suited set of compatibility conditions for boundaries joining regions associated to different flow properties, as inlet, outlet or wall. A systematic strategy for dealing with edges and corners is derived and compatibility conditions for inlet/outlet and wall/outlet boundaries are proposed. Direct numerical simulation (DNS) tests are carried out on simplified flow configurations at first. 3D-NSCBC brings a drastic reduction of flow distortion and numerical reflection, even in regions of strong transverse convection; the accuracy and convergence rate toward target values of flow quantities is also improved. Then, 3D-NSCBC is used for large-eddy simulation (LES) of a free jet and an impinging round-jet. Edge and corner boundary treatment, combining multidirectional characteristics and compatibility conditions, yields stable and accurate solutions even with mixed boundaries characterized by bad posedness issues (e.g. inlet/outlet). LES confirms the effectiveness of the proposed boundary treatment in reproducing mean flow velocity and turbulent fluctuations up to the computational domain limits.