Reduced Basis Model for Compressible Flow

TL;DR

This paper introduces a reduced basis model for slightly compressible flow that accelerates simulations by reducing the solution space, stabilized with Petrov-Galerkin methods, and extended to turbulent flows using a data-driven approach.

Contribution

It presents a novel RB model for compressible flow, stabilized with Petrov-Galerkin methods, and extends it to turbulence with a data-driven technique.

Findings

Model achieves stable results across various Reynolds numbers.

Significant reduction in computational cost compared to full CFD models.

Extension to turbulent flows demonstrates versatility of the approach.

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.