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.
This contribution deals with the modern finite volume schemes solving the Euler and Navier-Stokes equations for transonic flow problems. We will mention the TVD theory for first order schemes and some numerical examples obtained by 2D central and upwind schemes for 2D transonic flows in the GAMM channel or through the SE 1050 turbine of Škoda Plzeň. The TVD MacCormack method is extended to a 3D method for solving flows through turbine cascades. Numerical examples of unsteady transonic viscous (laminar) flows through the DCA 8% cascade are also presented for Re = 4600. Next, a new finite volume implicit scheme is presented for the case of unstructured meshes (with both triangular and quadrilateral cells) and inviscid compressible flows through the GAMM channel as well as the SE 1050 turbine cascade.