Vorticity-dependent and symmetry-preserving LES models

TL;DR

The paper develops a Lie-group–based framework to construct symmetry-preserving SGS models for the incompressible NS equations, with closures that depend on the filtered strain-rate $S$ and vorticity $Omega$. It-derived invariant tensor forms under $G_t$, $Gal$, $SO(3)$, $G_p$, and $G_s$, and shows how $ au^d$ can be expressed as a potential-driven closure using a scalar function $g$ of invariants, guaranteeing positive total dissipation under convexity conditions. A central result links the SGS tensor to a potential $ ewphi$, yielding explicit forms in terms of a generating function $g(v_1,v_3,v_4)$ and establishing a convexity-based criterion for stability. The work positions these symmetry-preserving models alongside established SGS approaches, outlining pathways for numerical validation and extensions to multiphase and wall-boundary contexts.

Abstract

Within the Large Eddy Simulation framework, we propose a methodology based on the Lie theory to derive symmetry-preserving turbulence models. We apply this methodology to the incompressible Navier-Stokes equations.} These models explicitly depend on both the filtered strain-rate tensor and the filtered vorticity tensor. Particular emphasis is placed on models that additionally ensure stability.

Theorems & Definitions (11)

• Theorem 1
• proof
• Remark 1
• Theorem 2
• proof
• Remark 2
• Theorem 3
• proof
• Remark 3
• Theorem 4