Optimization of an Implicit LES Method for Underresolved Simulations of Incompressible Flows

In engineering applications resolution is often low. In these underresolved regions, the truncation error of the underlying numerical schemes strongly affects the solution. If the truncation error functions as a physically consistent subgrid-scale (SGS) model, i.e. it models the evolution of otherwise resolved scales, resolution may remain low. Thereby, computational efficiency is improved. The sixth-order adaptive central-upwind weighted essentially non-oscillatory scheme with implicit scale-separation, denoted as WENO-CU6M1, potentially allows for physically consistent implicit SGS modelling, when shaped accordingly. In this work, finding an optimal formulation of WENO-CU6-M1 is considered within a deterministic design optimization framework. Possible surrogate modelling and sampling strategies are considered. Design optimization is based on evaluating the potential of a WENO-CU6-M1 scheme formulation to reproduce Kolmogorov scaling for a Taylor-Green vortex in its quasi-isotropic state. As in the absence of physical viscosity, kinetic-energy dissipates exclusively due to SGS, the Reynolds number is infinite and the evolution of the flow is determined by proper SGS modelling. To complete the work, we quantify the effective numerical dissipation rate of the WENOCU6-M1 model optimized for artificially compressible fluid flows and compare it to the original one.