Application of the iteratively regularized Gauss–Newton method to parameter identification problems in Computational Fluid Dynamics

Field Inversion and Machine Learning is an active field of research in Computational Fluid Dynamics (CFD). This approach can be leveraged to obtain a closed-form correction for a given turbulence model to improve the predictions. The fundamental approach is to insert a parameter into the system of RANS equations and determine it in a way such that, for example, a given pressure distribution is better approximated compared to the one obtained with the original set of equations. The goal of this article is twofold. Numerical arguments are presented that these kinds of problems can be severely ill-posed. In the second part, an approach is presented to directly reconstruct the turbulent viscosity field along with an example. The Iteratively Regularized Gauss-Newton Method (IRGNM) is used for a realization. The construction of a problem-adapted norm for a finite volume method is presented. Finally, an outlook is presented on how this approach can be used to possibly modify or improve turbulence models such that not only one, but a larger number of test cases are considered.