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

A dissipative compact scheme is developed within a dual time stepping framework for the computation of unsteady compressible flows. The design of the scheme relies on the vanishing, at steady state with respect to the dual time, of a residual that includes the physical time-derivative. High-order accuracy and numerical dissipation are obtained in a simple way through the systematic use of derivatives of this residual. The accuracy and robustness of the approach are assessed on the simple advection of an inviscid vortex and compressible mixing layer problems involving shock waves.