A residual-based compact scheme for the compressible Navier-Stokes equations

A simple and efficient time-dependent method is presented for solving the steady compressible Euler and Navier-Stokes equations with third-order accuracy. Owing to its residual-based structure, the numerical scheme is compact without requiring any linear algebra, and it uses a simple numerical dissipation built on the residual. The method contains no tuning parameter. Accuracy and efficiency are demonstrated for 2-D inviscid and viscous model problems. Navier-Stokes calculations are presented for a shock/boundary layer interaction, a separated laminar flow. and a transonic turbulent flow over an airfoil. (C) 2001 Academic Press.