RNS/Euler pressure relaxation and flux vector splitting (Q1118479)

The present author and co-workers have previously presented composite primitive variable and velocity/potential formulations for the computation of viscous/inviscid interacting flows. These procedures have been designed to emulate large Reynolds number (Re) asymptotic behavior, but, at the same time, to allow for the efficient solution of a single composite system of equations. This methodology is intermediate to that of full time-dependent Navier-Stokes solvers and to that of interacting or inverse matched boundary layer-inviscid solvers. The resulting system of reduced Navier-Stokes or RNS equations is a composite of the full Euler and second-order boundary layer systems. The neglected Navier- Stokes or diffusive terms are higher-order in Re for appropriate ``streamline'' coordinates. Although, these terms can be retained through an explicit deferred-corrector, it must be emphasized that the boundary conditions and the discrete approximation to the differential equations are dictated solely by the form of the lowest-order implicit RNS operator.