On the convergence of an approximate deconvolution model to the 3D mean Boussinesq equations

TL;DR

This paper investigates a Large Eddy Simulation model for 3D Boussinesq equations, demonstrating that solutions of the approximate deconvolution model converge to the filtered Boussinesq equations as the deconvolution parameter approaches zero.

Contribution

It proves the convergence of an approximate deconvolution LES model for 3D Boussinesq equations, establishing existence, uniqueness, and the limit behavior of solutions.

Findings

Existence and uniqueness of regular weak solutions.

Convergence of the model solutions to the filtered Boussinesq equations.

Validation of the approximate deconvolution approach for LES.

Abstract

In this paper we study a Large Eddy Simulation (LES) model for the approximation of large scales of the 3D Boussinesq equations. This model is obtained using the approach first described by Stolz and Adams, based on the Van Cittern approximate deconvolution operators, and applied to the filtered Boussinesq equations. Existence and uniqueness of a regular weak solution are provided. Our main objective is to prove that this solution converges towards a solution of the filtered Boussinesq equations, as the deconvolution parameter goes to zero.