A physics-inspired alternative to spatial filtering for large-eddy simulations of turbulent flows

Abstract

Large-eddy simulations (LES) are widely-used for computing high Reynolds number turbulent flows. Spatial filtering theory for LES is not without its shortcomings, including how to define filtering for wall-bounded flows, commutation errors for non-uniform filters, and extensibility to flows with additional complexity, such as multiphase flows. In this paper, the theory for LES is reimagined using a coarsening procedure that imitates nature. This physics-inspired approach is equivalent to Gaussian filtering for single-phase wall-free flows but opens up new insights for modeling even in that simple case. Boundaries and nonuniform resolution can be treated seemlessly in this framework without commutation errors, and the divergence-free condition is retained for incompressible flows. An alternative to the Germano identity is introduced and used to define a dynamic procedure without the need for a test filter. Potential extensions to more complex physics are briefly discussed.