Toward a reliable prediction of shocks in hypersonic flow: Resolving carbuncles with entropy and vorticity control

Numerical shock prediction is a critical aspect of computing aerodynamic flows especially under hypersonic conditions. Presently, shock capturing methods are commonly used to predict shocks in various settings from simple to complex configurations and for low subsonic to moderate supersonic flows with considerable success. However, most shock capturing methods fall short in predicting strong, steady shocks. This is a crucial element in designing hypersonic vehicles. Except for perhaps a few notoriously diffusive schemes, all schemes in Computational Fluid Dynamics (CFD) exhibit some form of anomalies when predicting strong shocks. The most infamous of these anomalies is the "carbuncle" phenomenon.; The carbuncle phenomenon can be observed when computing supersonic or hypersonic flow past a blunt body, for example, a circular cylinder. Instead of having a smooth bow shock upstream of the cylinder, there exists a pair of oblique shocks ahead of the stagnation point. The carbuncle evolves in three distinct stages: "pimple", "bleeding" and "carbuncle". The "pimple" represents initial shock instability whereas the "bleeding" depicts these instabilities being propagated downstream of the shock. The "carbuncle" stage 'weakly' satisfies the Euler equations but cannot be observed experimentally except by some artificial setup.; The oblique shocks contain a pair of spurious counter rotating vortices hence the carbuncle is maybe due to inadequate vorticity control. In this thesis, a new vorticity capturing method is introduced. The method is originally developed to prevent the carbuncle, however, it could also be used to predict more general vortical flows. This includes Blade-Vortex-Interaction (BVI) in helicopter analysis, prediction of high-lift systems and unsteady flights where vorticity capturing is extremely important.; Another possible source of the carbuncle is due to imprecise enforcement of entropy in shock capturing methods. To overcome this, the concept of directly including entropy conservation law in a numerical flux function will be introduced. It will be shown that although vorticity control does eliminate the carbuncle, it must be done very strongly, and sometimes the results are not satisfactory. Control of entropy, on the other hand, eliminates the carbuncle directly with no side-effects.