Boundary conditions for direct simulations of compressible viscous flows

The present consideration of procedures for the definition of boundary conditions for the Navier-Stokes equations emphasizes the derivation of boundary conditions that are compatible with nondissipative algorithms applicable to direct simulations of turbulent flows. A novel formulation for the Euler equations is derived on the basis of characteristic wave relations through boundaries; this formulation is generalized to the Navier-Stokes equations. The method, which applies to both sub- and supersonic flows, is used in reflecting and nonreflecting boundary-condition treatments. Attention is given to practical implementations involving inlet and outlet boundaries and slip and nonslip walls, as well as the test cases of a ducted shear layer, vortices propagating through boundaries, and Poiseuille flow.