TKE Model Involving the Distance to the Wall—Part 1: The Relaxed Case

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2024-09-02 DOI:10.1007/s00021-024-00895-y

Cherif Amrouche, Guillaume Leloup, Roger Lewandowski

引用次数: 0

Abstract

We are considering a steady-state turbulent Reynolds-Averaged Navier–Stokes (RANS) one-equation model, that couples the equation for the velocity-pressure mean field with the equation for the turbulent kinetic energy. Eddy viscosities vanish at the boundary, characterized by terms like \(d(x, \Gamma )^\eta \) and \(d(x, \Gamma )^\beta \), where \(0< \eta , \beta < 1\). We determine critical values \(\eta _c\) and \(\beta _c\) for which the system has a weak solution. This solution is obtained as the limit of viscous regularizations for \(0< \eta < \eta _c\) and \(0< \beta < \beta _c\).

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与墙壁距离有关的 TKE 模型--第 1 部分：松弛情况

我们考虑的是稳态湍流雷诺平均纳维-斯托克斯（RANS）一元模型，它将速度-压力平均场方程与湍流动能方程耦合在一起。涡流粘度在边界处消失，其特征为 \(d(x, \Gamma )^\eta \) 和 \(d(x, \Gamma )^\beta \)，其中 \(0< \eta , \beta < 1\).我们确定临界值\(\eta _c\)和\(\beta _c\)，对于这两个值，系统有一个弱解。这个解是作为 \(0< \eta < \eta _c\) 和 \(0< \beta < \beta _c\) 的粘性正则化的极限而得到的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical Fluid Mechanics 物理-力学

CiteScore

2.00

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.