Implicit Large Eddy Simulation of Nearly Incompressible Flows with a Discontinuous Galerkin-Boltzmann Formulation

Abstract: We present a high-order implicit large eddy simulation (ILES) approach for simulating flows at the nearly incompressible regime. Our methodology based on utilization of a nodal discontinuous Galerkin (DG) discretization of the Boltzmann equations. The compactness and low-dissipative nature of the discontinuous Galerkin method are leveraged to mimic traditional large eddy simulations with subgrid-scale models. One of the key requirements of ILES is to provide dissipation only within a narrow band of high wavenumbers. This is validated through numerical experiments on the Taylor-Green Vortex problem in detail at a Reynolds number where varying scales of coherent turbulent structures are present. Furthermore, the approach is validated for external aerodynamic configurations by simulating the flow over a sphere at a Reynolds number of $Re=3700$, capturing the laminar-turbulent transition and the complex multiscale vortex dynamics characteristic of this regime. The results demonstrate the capability of the high-order DG-Boltzmann formulation to accurately capture transitional and turbulent flow features without the use of explicit sub-grid scale modeling, highlighting its potential as a robust and physically consistent framework for ILES of nearly incompressible turbulent flows.