INVESTIGATION OF WENO AND SEVERAL FLUXES SCHEMES FOR HIGH-SPEED FLOWS ON OVERALL UNSTRUCTURED MESHES

WENO (“Weighted Essentially Non-Oscillatory”) is the evolutionary product of a sequence of additive studies, which started with the seminal work of Godunov in the last years of the 50s of the last century. From the pure Riemann reconstruction of Godunov the high-resolution schemes passed by the MUSCL (“Monotonic Upstream-centered Scheme for Conservation Laws”), the ENO (“Essentially Non Oscillatory), finally reaching the WENO stage. WENO schemes are high order accurate schemes designed for problems with piecewise smooth solutions containing discontinuities. The key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil, hence avoiding crossing discontinuities in the interpolation procedure as much as possible. Following closely this evolutionary path, another very important feature is connected to approximating as accurately as possible the Riemann fluxes at the boundary of the tesselation cell. Many ideas for this approximation appeared along the way. The schemes of Lax-Friedrichs, Roe, Steger-Warming, AUSM, AUSMPW, HLL, HLLE, are all in use today. A high-resolution, high-order computer code based on the WENO algorithm, called Fweno, for the simulation of flows at high speeds and with eventually piece-wise smooth solutions, was developed by the present authors. Many of the most efficient flux calculation schemes were implemented, and, in this paper, a thourough comparison between Lax-Friedrichs, Roe, AUSM and AUSMPW is explored on strictly unstructured grids. The validation problems are all benchmarking test cases usually found in the literature: the internal supersonic ramp, the internal supersonic forward-facing step, and the supersonic flow about a circular cylinder. After validation the code was applied to the hypersonic flow about a pressure probe. In the near future cases of hypersonic flow of real gases about blunt bodies will be simulated and analysed.