Optimization of an Implicit Large-Eddy Simulation Method for Underresolved Incompressible Flow Simulations

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 model (that is, 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 nonoscillatory scheme with implicit scale separation, denoted as WENO-CU6-M1, potentially allows for physically consistent implicit subgrid-scale 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 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 the subgrid-scales, the Reynolds number is infinite, and the evolution of the flow is determined by proper subgrid-scale modeling. To complete the work, the effective numerical dissipation rate of the WENO-CU6-M1 model optimized for artificially compressible fluid flows is quantified, and it is compared to the original one. Not only is the zero viscosity limit considered, but the model behavior is benchmarked offdesign, for low to high Reynolds numbers. A comparison to an alternative explicit and implicit subgrid-scale model demonstrates its superior behavior for the chosen test flow.