Fluid Dynamics Beyond the Continuum -- A Physical Perspective on Large Eddy Simulation

TL;DR

This paper develops a physically consistent theory for Large Eddy Simulation (LES) based on first principles, explaining its foundations and implications beyond traditional turbulence modeling.

Contribution

It introduces a first-principles derivation of LES equations, clarifies the physical basis of Favre filtering, and discusses LES as more than just a numerical model.

Findings

Favre filtering is a physical consistency condition.

Boussinesq's hypothesis is justified within this framework.

LES may serve as a fundamental physical theory, not just a computational tool.

Abstract

In this work, we will present a physically consistent theory to derive the governing equations of the Large Eddy Simulation (LES) framework based on first principles rather than the motivation to conduct computationally affordable simulations of turbulent flows. Therefore, we assume that a coarse-grained fluid element, subsequently called super fluid element, can be locally defined comprising a large number of smaller elementary fluid elements. Then, similar to non-equilibrium molecular dynamics (NEMD), in which the transport equations of an elementary fluid element can be consistently reconstructed from the local, collective dynamics of molecules, the transport equations of a super fluid element can be derived from the local, collective dynamics of elementary fluid elements. Interestingly, we find: (a) Favre filtering is a physical consistency condition, (b) why Boussinesq's hypothesis in conjunction with eddy viscosity models is commonly employed in LES and (c) that the LES framework might be more than a numerical turbulence model for computational fluid dynamics (CFD).