Analytical And Numerical Study On Carbuncle Phenomenon - Wahi, Nadihah (2016)
Most newly developed schemes in the literatures to solve the shock instability in hyperbolic conservation laws mainly focused on adding ad hoc diffusion factor without properly indulging into the sources of the problem. An example of shock instabilities is the carbuncle phenomenon which occurs when simulating a blunt body subjected to a high speed flow. The shock formed ahead of the body is unphysical. Therefore, the goals of this study are to find at least one possible cause of the problem and to fix the instability from that cause. Extruding a possible source of the problem, herein the elimination process was applied to reduce the number of conservative variables involve, starting from the Burgers’ equation followed by isothermal equations to the full Euler equations. Then, a small perturbation definition to the hyperbolic conservation equations was used as a mean to ease the nonlinearity from the equations. After that, the method of normal mode was used to analytically analyze the instability mechanism. The cause was found to be the perturbation from density which seeding into the instability. Numerical tests were then used to check the validity of the analytical result and they gave a good agreement with the analysis. Finally, a tunable dissipative coefficient was inserted only to the density equation and a range value of 0:02