Towards a Transparent Boundary Condition for Compressible Navier–stokes Equations

A new artificial boundary condition for 2D subsonic flows governed by the compressible Navier–Stokes equations is derived. It is based on the hyperbolic part of the equations, according to the way of propagation of the characteristic waves. A reference flow as well as a convection velocity are used to properly discretize the terms corresponding to the entering waves. Numerical tests on various classical model problems whose solution is known and comparisons with other boundary conditions show the efficiency of the boundary condition. Direct numerical simulations of more complex flows over a dihedral plate are simulated, without creation of acoustic waves going back in the flow.