Investigations of a compressible second order finite volume code towards the incompressible limit

Abstract

The accuracy of many existing codes, originally implemented for transonic or supersonic problems, often degrades as the inflow Mach number tends to zero. At low Mach number, the Roe scheme or a similar formulated artificial viscosity scheme which is close to a Roe scheme presents an excess of artificial viscosity. As a result, several years ago a correction of these kinds of schemes was introduced by Turkel. Such correction yields a significant improvement of the accuracy of the solution for the low Mach regime. In particular, for inviscid low Mach number flows it was shown in the literature that the accuracy of the results obtained with the modification of Turkel is comparable with results obtained with CFD codes designed for incompressible flows. Unfortunately, a loss of robustness for the correction of Turkel is often observed when considering compressible high Reynolds number viscous flows. Typical examples investigated in aerodynamics are configurations at high angle of attack, for example an aircraft in landing configuration. Besides other complex flow phenomena, for these kinds of flows both strong locally compressible flows and large incompressible regions are observed. In particular for these kinds of flows the modification of the code needs to work reliably. Based on the work of Rossow and Swanson we are going to present a further modification for the extension of a compressible code towards the incompressible limit. Numerical examples demonstrate the superiority of the method when compared with the modification suggested by Turkel. Moreover, 2D and 3D examples are given demonstrating the applicability of the method to flows of locally compressible and large incompressible effects. Furthermore, the suggested method does not show severe robustness problems for these kinds of flows when compared with the non-modified scheme.