An Analytical View on Data-Driven Turbulence Modeling and a Realization via a regularized Newton Method

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 dissipation 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. Second, instead of introducing a field parameter into a given turbulence model, an approach is presented to directly reconstruct the eddy viscosity field along with an example of an RAE2822 airfoil in transonic conditions. A regularized Gauss-Newton method is used for a realization. Finally, an outlook is presented in which way 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.