Numerical Analysis of a Corrected Smagorinsky Model

TL;DR

This paper develops and analyzes a modified Smagorinsky model that better captures energy transfer in turbulent flows, providing theoretical properties and effective numerical algorithms for its approximation.

Contribution

It introduces a well-posed modification to the classical Smagorinsky model and provides a comprehensive numerical analysis of two effective algorithms for its approximation.

Findings

The modified model accurately represents energy transfer from unresolved to resolved scales.

The proposed algorithms are proven to be effective through numerical tests.

Basic properties of the modified model are established.

Abstract

The classical Smagorinsky model's solution is an approximation to a (resolved) mean velocity. Since it is an eddy viscosity model, it cannot represent a flow of energy from unresolved fluctuations to the (resolved) mean velocity. This model has recently been modified to incorporate this flow and still be well-posed. Herein we first develop some basic properties of the modified model. Next, we perform a complete numerical analysis of two algorithms for its approximation. They are tested and proven to be effective.