Acoustically Nonreflecting and Reflecting Boundary Conditions for Vortcity Injection in Compressible Solvers

Injecting turbulence into computational domains is needed in many direct numerical simulations or large eddy simulations. This task may become difficult in compressible formulations in which acoustic waves must also be controlled on boundaries. In this paper, three characteristic boundary conditions are compared with inject isolated vortices or turbulence into the flow and control the acoustic behavior of the boundary at the same time. The first two methods are the usual characteristic boundary conditions (reflecting and nonreflecting Navier―Stokes characteristic boundary-condition techniques) used to introduce acoustic waves. The third one is a new boundary condition (vortical-flow characteristic boundary condition) constructed to introduce turbulence or vortices while being nonreflecting for acoustic waves. The three methods are tested in two academic cases: 1) injection of an isolated vortex and 2) injection of isotropic turbulence. These two tests are first performed in a quiet flow and then in a domain in which acoustic waves propagate toward the inlet and interact with vorticity injection. Results show that the reflecting Navier―Stokes characteristic boundary condition performs correctly to introduce vorticity waves (vortices or turbulence) and totally reflect acoustic waves. To introduce vorticity waves and let acoustic waves propagate without reflection, the vortical-flow characteristic boundary condition is required and the usual Navier―Stokes characteristic boundary-condition method cannot be used.