Iterative Bayesian optimization of an implicit les method for under-resolved simulations of incompressible flows

In the numerical simulation of turbulent flows, resolution is often low. The solution in those under-resolved regions is strongly affected by the truncation error of the underlying numerical schemes. Although, the truncation error can be used to model the evolution of otherwise resolved scales - it acts as a physically consistent subgrid-scale (SGS) model. In particular, the truncation error of high-order WENO-based schemes can function as an implicit SGS model. The sixth-order adaptive central-upwind weighted essentially non-oscillatory scheme with implicit scale-separation, denoted as WENO-CU6-M1, allows for physically consistent implicit SGS modeling when its parameters are chosen properly. Schranner et al. (2016) determined an optimal combination of the WENO-CU6-M1 modeling parameters by means of design optimization (DO). Optimizing the WENO-CU6-M1 parameters is computationally expensive. This work proposes a general iterative optimization algorithm which is based on hierarchical Bayesian modeling. It allows to reduce the computational costs for optimizing WENO-CU6-M1 parameters. Optimization implies the procedure of identifying input-output relations of a system. Thereby, the minimum or the maximum output of a system, as well as the input for which it occurs, may be sought. The proposed optimization algorithm relies on Gaussian Processes (GP). Methods to fit a GP are proposed. Based thereupon, an optimization algorithm which iteratively improves the quality of the GP is introduced. To complete this work, the algorithm is used to identify an optimal parameter set for the WENO-CU6-M1 scheme.