Reduced Basis Model for Compressible Flow

Abstract

Numerical simulations are a valuable research and layout tool for fluid flow problems, yet repeated evaluations of parametrized problems, necessary to solve optimization problems, can be very costly. One option to speed up this process is to replace the costly CFD model with a cheaper one. These surrogate models can be either data-driven or they can also rely on reduced basis (RB) methods to speed up the calculations. In contrast to data-driven surrogate models, the latter are not based on regression techniques but are still aimed at explicitly solving the conservation equations. Their speed-up comes from a strong reduction of the solution space, which results in much smaller algebraic systems that need to be solved. Within this work, an RB model, suited for slightly compressible flow, is presented and tested on different flow configurations. The model is stabilized using a Petrov-Galerkin method with trial and test function spaces of different dimensionality to generate stable results for a wide range of Reynolds numbers. The presented model applies to geometrically and physically parametrized flow problems. Finally, a data-driven approach was used to extend it to turbulent flows.