Osher Flux with Entropy Fix for Two-Dimensional Euler Equations (Advances in Applied Mathematics and Mechanics, 2018)
We compare in this paper the properties of Osher flux with O-variant andP-variant (Osher-O flux and Osher-P flux) in finite volume methods for the two-dimensionalEuler equations and propose an entropy fix technique to improve theirrobustness. We consider both first-order and second-order reconstructions. For inviscidhypersonic flow past a circular cylinder, we observe different problems for differentschemes: a first-order Osher-O scheme on quadrangular grids yields a carbuncleshock, while a first-order Osher-P scheme results in a dislocation shock for high Machnumber cases. In addition, a second-order Osher scheme can also yield a carbuncleshock or be unstable. To improve the robustness of these schemes we propose an entropyfix technique, and then present numerical results to show the effectiveness ofthe proposed method. In addition, the influence of grid aspects ratio, relative shockposition to the grid and Mach number on shock stability are tested. Viscous heatingproblem and double Mach reflection problem are simulated to test the influence of theentropy fix on contact resolution and boundary layer resolution.