| Abstract: | We compare in this paper the properties of Osher flux with O-variant and
P-variant (Osher-O flux and Osher-P flux) in finite volume methods for the two-dimensional
Euler equations and propose an entropy fix technique to improve their
robustness. We consider both first-order and second-order reconstructions. For inviscid
hypersonic flow past a circular cylinder, we observe different problems for different
schemes: a first-order Osher-O scheme on quadrangular grids yields a carbuncle
shock, while a first-order Osher-P scheme results in a dislocation shock for high Mach
number cases. In addition, a second-order Osher scheme can also yield a carbuncle
shock or be unstable. To improve the robustness of these schemes we propose an entropy
fix technique, and then present numerical results to show the effectiveness of
the proposed method. In addition, the influence of grid aspects ratio, relative shock
position to the grid and Mach number on shock stability are tested. Viscous heating
problem and double Mach reflection problem are simulated to test the influence of the
entropy fix on contact resolution and boundary layer resolution. |
