Numerical model

1.3 CFD tool

Simulations were performed using the computational model referenced as PROUST [12] and developed to simulate steady and unsteady, viscous and inviscid fbws. The fully three-dimensional unsteady, compressible, RANS equations are solved. The space discretization is based on a MUSCL finite vol­ume formulation. The convective flixes are evaluated using an upwind scheme based on Roe’s approximate Riemann solver, and the viscous terms are com­puted by a second order centered scheme. The turbulence closure problem is solved using Wilcox k-w two equations model and fully accounts for the ef­fect of the boundary layer (BL) separation which originates at the shock foot location. Compatibility relations are used to account for physical boundary conditions. One-dimensional numerical boundary conditions are implemented by retaining the equations associated to the incoming characteristics and fixing the wave velocity to zero to prohibit propagation directed into the computa-

tional domain. The resulting semi discrete scheme is integrated in time using an explicit five steps Runge-Kutta time marching algorithm.