High Order Finite Volume Schemes for Numerical Solution of Unsteady Flows

Abstract

The aim of this contribution is to present two modern high-order finite volume (FVM) schemes for numerical solution of unsteady transonic flows. The first one is derived from the total variation diminishing (TVD) version of the classical MacCormack scheme proposed by Causon. In our case it is used with slight modifications and hence refered to as Modified Causon’s scheme. It is no more TVD, but with no loss of accuracy to the TVD version and with a significantly lower demands on computational power and memory (cca 30% less). The second one, based on a similar approach as the WENO family schemes, is the implicit Weighted Least-Square Reconstruction scheme (WLSQR) used in combination with the AUSMPW+ numerical flux. For the turbulence modelling the Kok’s TNT turbulence model is employed. Unsteady effects (forced oscillatory motion) are simulated by Arbitrary Lagrangian–Eulerian method (ALE). As the transonic test cases the inviscid and turbulent flow around the NACA 0012 profile and inviscid flow over the ONERA M6 wing were chosen. Comparison of numerical and experimental results for inviscid flow is very good, which is unfortunately not the case of turbulent flow.