Fluid dynamics beyond the continuum: A physical perspective on large-eddy simulation

In this Letter, 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 superfluid element, can be locally defined comprising a large number of smaller elementary fluid elements. Then, similar to nonequilibrium molecular dynamics 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 superfluid 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.

Figure 1

Schematic of fluid dynamics beyond the continuum. By consecutive application of Hardy theory to a sufficiently large number of molecules and, further, elementary fluid elements, one first obtains the local dynamics of elementary fluid elements (blue) and finally the dynamics of coarse-grained superfluid elements (orange).