Kybernetika 45 no. 4, 567-579, 2009

High Order Finite Volume Schemes for Numerical Solution of 2D and 3D Transonic Flows

Jiří Fürst, Karel Kozel and Petr Furmánek


The aim of this article is a qualitative analysis of two modern finite volume (FVM) schemes. First one is the so called Modified Causon's scheme, which is based on the classical MacCormack FVM scheme in total variation diminishing (TVD) form, but is simplified in such a way that the demands on computational power are much smaller without loss of accuracy. Second one is implicit WLSQR (Weighted Least Square Reconstruction) scheme combined with various types of numerical fluxes (AUSMPW+ and HLLC). Two different test cases were chosen for the comparison $-1$) two-dimensional transonic inviscid nonstationary flow over an oscillating NACA 0012 profile and 2) three-dimensional transonic inviscid stationary flow around the Onera M6 wing. Nonstationary effects were simulated with the use of Arbitrary Lagrangian-Eulerian Method (ALE). Experimental results for these regimes of flow are easily available and so the numerical results are compared both in-between and with experimental data. The obtained numerical results in all considered cases (2D and 3D) are in a good agreement with experimental data.


finite volume method, ALE method, AUSMPW+, HLLC, nonstationary flow, transonic flow, TVD


76M12, 76H05, 76N99