A high accuracy Leray-deconvolution model of turbulence and its limiting behavior

TL;DR

This paper introduces a family of high-accuracy Leray-type turbulence models that improve simulation precision without requiring finer meshes, analyzing their limiting behaviors as model order increases or averaging radius decreases.

Contribution

It develops a theoretical framework for high-order Leray models, demonstrating their potential for more accurate turbulence simulation at lower computational costs.

Findings

Established the basic theory of high-order Leray models.

Analyzed the limiting behavior as averaging radius approaches zero.

Showed that increasing model order can be more cost-effective than refining the mesh.

Abstract

In 1934 J. Leray proposed a regularization of the Navier-Stokes equations whose limits were weak solutions of the NSE. Recently, a modification of the Leray model, called the Leray-alpha model, has atracted study for turbulent flow simulation. One common drawback of Leray type regularizations is their low accuracy. Increasing the accuracy of a simulation based on a Leray regularization requires cutting the averaging radius, i.e., remeshing and resolving on finer meshes. This report analyzes a family of Leray type models of arbitrarily high orders of accuracy for fixed averaging radius. We establish the basic theory of the entire family including limiting behavior as the averaging radius decreases to zero, (a simple extension of results known for the Leray model). We also give a more technically interesting result on the limit as the order of the models increases with fixed averaging radius. Because of this property, increasing accuracy of the model is potentially cheaper than decreasing the averaging radius (or meshwidth) and high order models are doubly interesting.