Advanced Shock-Fitted/Shock-Attached Methods for Unsteady Detonations

Accurately resolving the shock front in unsteady, unstable detonations is critical to accurately represent the flow field. For flows near failure and stability limits in particular, the reaction zone becomes highly sensitive to the shock state. Shock-capturing has limitations in this regard as such techniques must inevitably balance numerical diffusion with dispersion depending on the employed method. In contrast, a shock-fitted/shock-attached (ShockFit) technique utilizes a geometric transformation to impose the shock front as a boundary condition of the flow. The shock state is directly calculated from the normal component of the wave speed and ambient state, and the reacting flow behind the shock is simulated using modified, conservative fluxes.

This ShockFit technique was originally developed for simulating steady detonations, with minimal transient behavior and no expectation for cellular detonation structures. Recent advances in this technique now allow us to apply the ShockFit method to unsteady, highly irregular detonations at high resolutions. Due to the sensitive nature of these unstable detonations, this techniques proves reliable for accurately simulating unsteady detonations compared to traditional shock-capturing techniques.

In this study, we will present our general approach for developing the ShockFit method, including recent advances for simulating flows beyond simple inviscid systems, including weakly confined detonations, nonuniform ambient states, etc. As part of this work, we will discuss the advantages of the ShockFit method, including its accuracy compared to other numerical approaches, as well as its limitations for specific flow configurations.