New scheme for the computation of compressible flows

A new approach for the computation of unsteady compressible flows has been developed. The new scheme employs upwinding of the convective flux based on particle velocity and has been termed the particle velocity upwinding (PVU) scheme. The PVU scheme is an explicit two-step predictor-corrector scheme, in which the convective fluxes are evaluated on cell faces using a first-order upwinding method. The scheme is accurate and stable, giving solutions free from oscillations near the discontinuities without any explicit addition of artificial viscosity. The PVU scheme has an edge over state-of-the-art high-resolution schemes in terms of simplicity of implementation in multidimensional flows and problems involving complex domains. The numerical scheme, is validated for both Euler and Navier-Stokes equations. Furthermore, the PVU scheme is used to investigate laminar supersonic viscous flow over a forward-facing step. The results are obtained for M_∞ = 1.5-3.5 in steps of 0.5 and for Re_∞ = 10⁴. Step heights H_s of 10 and 20% of the characteristic length of the problem are considered. The effect of step height and the incoming freestream Mach number on the spatial flow structure and on the important design parameters such as wall pressure, skin friction, heat transfer, and length of separated region are investigated.