A Multi-Dimensional Virtual Characteristic Scheme for Laminar and Turbulent Incompressible Flows

Abstract

A multi-dimensional virtual characteristic-based scheme (MVCB) by the aid of artificial compressibility is developed for convective fluxes in laminar and turbulent incompressible flows. The proper combinations of compatibility equations are determined to obtain primitive variables on cell interfaces. The Reynolds averaged Navier-Stokes equations joined with Spalart-Allmaras turbulent model are solved by finite volumes. This scheme is applied to the flows between parallel plates, over backward-facing step, and in square lid-driven cavity at a wide range of Reynolds numbers. A FORTRAN 90 code has been written and all the results have come out from this code. Several comparisons confirm the scheme ability in accurate simulation of flows without need to any artificial viscosity in laminar and turbulent regimes.

Keywords

• Navier-Stokes equations; Reynolds averaging; Spalart-Allmaras model; multi-dimensional characteristics; artificial compressibility; Finite volume method.