Shape Matching for Reduced Order Models of High-Speed Fluid Flows

While computational fluid dynamics (CFD) simulations are an indispensable tool in modern aerospace engineering design, they bear a severe computational burden in applications where simulation results must be found quickly or repeatedly. Therefore, creating computationally inexpensive models that can capture complex fluid behaviors is a long-sought-after goal. As a result, methods to construct these reduced order models (ROMs) have seen increasing research interest. Still, parameter dependent high-speed flows that contain shock waves are a particularly challenging class of problems that introduces many complications in ROM frameworks. To make approximations in a linear space, ROM techniques for these problems require that basis functions are transformed such that discontinuities are aligned into a consistent reference frame. Techniques to construct these transformations, however, fail when the topology of shocks is not consistent between data snapshots. In this work, we first identify key features of these topology changes, and how that constrains transformations of this kind. We then construct a new modeling framework that can effectively deal with shockwave interactions that are known to cause failures. The capabilities of the resulting model were evaluated by analyzing supersonic flows over a wedge and a forward-facing step. In the case of the forward-facing step, when shock topology changes with Mach number, our method exhibits significant accuracy improvements. Suggestions for further developments and improvements to our methodology are also identified and discussed