QUASI-1D EDGE-BASED SCHEMES ON UNSTRUCTURED MESHES FOR SOLVING AERODYNAMICS AND AEROACOUSTICS PROBLEMS

The talk presents an overview of quasi-1D edge-based schemes for solving hyperbolic problems on unstructured meshes. "Linear" scheme of T.Barth can be considered as an ancestor of second-order edge based schemes. The ideas of quasi-1D reconstruction of variables and flux correction are then implemented to improve accuracy. We develop higher-accuracy edge-based schemes which are theoretically still of second order on arbitrary unstructured meshes however demonstrate a faster convergence (between second and third order) on real meshes used in applications. The accuracy improvement is achieved thanks to the special (TI-) property i.e. the ability of the schemes to coincide with the high-order finite difference schemes of translationally-invariant (TI) meshes. As a result the schemes provide significantly higher accuracy than most second-order Godunov-type schemes and appear much cheaper computationally than very high-order methods. We use these schemes for solving various applied problems in aerodynamics and aeroacoustics. In the talk we present the numerical results of solving model acoustics and nonlinear gas dynamics problems, the simulations of canonical and complex turbulent flows with the evaluations of acoustic fields. Among the industry-oriented problem we show the results on subsonic jets, helicopter rotors, transonic cavity flows.