IJPAM: Volume 38, No. 4 (2007)

A NEW RULE OF TURBULENT CLOSURE RELATIONS
IN LARGE EDDY SIMULATION

Francesco Gallerano$^1$, Giovanni Cannata$^2$
$^{1,2}$Department of Hydraulics
University of Rome ``La Sapienza"
Via Eudossiana 18, Rome, 00184, ITALY
$^1$e-mail: francesco.gallerano@uniroma1.it
$^2$e-mail: giovanni.cannata@libero.it


Abstract.In this paper the relation between the Noll formulation of the principle of material frame indifference and the principle of turbulent frame indifference in large eddy simulation is revised; the definition of a new rule of turbulent closure relations is proposed. In this paper we demonstrate that the transport equation of the generalised sub-grid scale (SGS) turbulent stress tensor is form-invariant but not frame-indifferent under Euclidean transformations of the frame. A new closure relation for the generalized SGS turbulent stress tensor is proposed: this closure relation complies with the rule of turbulent closure relations. In the proposed model the generalized SGS turbulent stress tensor is related exclusively to the generalized SGS turbulent kinetic energy (which is calculated by means of its balance equation) and the modified Leonard tensor. The viscous dissipation $\varepsilon $ of the generalized SGS turbulent kinetic energy is calculated by solving the balance equation of $\varepsilon $. It is demonstrated that the balance equation of the viscous dissipation is form-invariant but frame-dependent under Euclidean transformations of the frame; the closure relations proposed in this paper allow the modelled balance equation of $\varepsilon $ to respect the properties of Euclidean form-invariance and frame-dependence of the exact equation.

Received: May 16, 2007

AMS Subject Classification: 26A33

Key Words and Phrases: LES, form-invariance, frame indifference, closure relations

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 38
Issue: 4