Optimization of an implicit LES method for underresolved simulations of incompressible flows

In engineering applications resolution, even within complex flow regions, 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 be kept low. Thereby, computational efficiency is improved. The truncation error of high-order WENO-based schemes can function as an implicit subgrid-scale (SGS) model. The sixth-order adaptive central-upwind weighted essentially non-oscillatory scheme with implicit scale-separation, denoted as WENO-CU6-M1, potentially allows for physically consistent implicit SGS modeling, when shaped accordingly. In this work, finding an optimal formulation of WENO-CU6-M1 is considered within a deterministic design optimization framework. Possible surrogate modeling and sampling strategies are evaluated for their applicability. Design optimization bases on evaluation of a WENO-CU6-M1 formulation’s potential to reproduce Kolmogorov scaling for a TaylorGreen vortex flow 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 modeling. To complete the work, we quantify the effective numerical dissipation rate of the WENO-CU6-M1 model optimized for artificially compressible fluid flows and compare it to the original one.