Speaker
Description
Flows with high Mach and Reynolds numbers exhibit pronounced multi-scale features due to turbulence and compressibility effects. Implicit large-eddy simulation (ILES) models for such flows require numerical discretizations with tailored truncation error properties, enabling coarse-resolution simulations to closely approximate low-pass filtered direct numerical simulation (DNS) data. These ILES discretizations must adapt to local flow characteristics to best approximate subgrid-scale structures while maintaining stability and robustness in the presence of shocks. In this SPP-2410 project, we explore the potential of machine-learned implicit large-eddy simulations (ML-ILES) for modeling compressible turbulence. As an initial step, we replace the classical ENO-type cell-face reconstruction operator within a Godunov-type finite-volume framework with a machine learning surrogate. Specifically, shallow artificial neural networks (ANNs) substitute classical smoothness indicators and are hybridized with standard Harten-type interpolation polynomials. Separate reconstruction ANNs are used for each physical flow quantity, facilitating dedicated cell-face reconstruction. The hybrid approach ensures Galilean invariance of the model and convergence upon mesh refinement. The ANNs are trained end-to-end within the automatically differentiable JAX-Fluids computational fluid dynamics solver, using a training data set composed of coarse-grained spatio-temporal DNS trajectories of compressible homogeneous isotropic turbulence (HIT). A posteriori tests on unseen HIT data demonstrate a promising performance of the trained ML-ILES model compared to established ILES discretizations. Notably, ML-ILES shows improved dissipation characteristics at high wave numbers and generalizes well to unseen computational grids. Finally, application of ML-ILES to more complex test cases, along with potential extensions on the modeling side, are discussed.
