Time-consistent pressure relaxation procedure for compressible reduced Navier-Stokes equations

Abstract

A time-consistent global pressure relaxation procedure for the unsteady, compressible, reduced Navier-Stokes equations is presented. The shock-capturing capability of the procedure is investigated with different forms of pressure gradient splitting. An efficient conservative method for capturing shocks is detailed. The transient behaviour of laminar, high Reynolds number, low subsonic flow past a sine-wave airfoil geometry is analysed using the new reduced Navier-Stokes based algorithm. These solutions are compared with steady and unsteady results previously obtained with a modified interacting boundary-layer procedure. The strong influence of grid refinement and the type of differencing of the streamwise convection term on the existence or stability of separated laminar solutions is reaffirmed. More stable turbulent flow results are also presented. Finally, an unsteady solution for the flow past a finite flat plate at incidence is described in order to demonstrate the time accuracy of the algorithm.