Large-eddy simulation of decaying isotropic turbulence across a grid refinement interface using explicit filtering and reconstruction

Abstract

This paper explores numerical errors that arise when large-eddy simulation (LES) is used with adaptive mesh refinement (AMR). LES and AMR combined can reduce the computational cost of turbulence simulations compared to direct numerical simulations, but are rarely used together due to complications that arise with the application of the turbulence closure model at different grid resolutions. Errors appear at grid refinement interfaces due to dependence of computed quantities on the LES filter width and insufficient smoothness of the solution at the grid scale. Here, explicit filtering and approximate reconstruction of the unfiltered velocity field are used to mitigate the effects of these errors in a simulation of decaying isotropic turbulence advected past a grid refinement interface. In particular, different explicit filter types and levels of reconstruction are tested. Explicit filtering with zero-level reconstruction is found to produce the best long-term convergence to a uniform grid solution with minimum perturbation at the interface. Higher levels of reconstruction yield better near-interface convergence. When explicit filtering is used, the explicit filter width transition is more important than the grid spacing transition in terms of solution convergence and interface perturbation. These results inform the use of LES on more complicated AMR grids.

Keywords:

• large-eddy simulation
• adaptive grids
• explicit filtering
• approximate reconstruction

Acknowledgements

This work was funded by the National Science Foundation through Fluid Dynamics program grant CBET-0933642/0932613 and the Department of Defense through the National Defense Science and Engineering Graduate Fellowship Program (for the first author). The authors also thank Bowen Zhou for his helpful comments on the manuscript.