On the determination of the grad-div criterion

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:467

Article

DeCaria, V.¹  Layton, W.¹  Pakzad, A.¹  Rong, Y.²  Sahin, N.³  Zhao, H.¹ 

[1] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

[2] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China

[3] Ankara Yildirim Beyazit Univ, Dept Math & CS, Ankara, Turkey

关键词: grad-div stabilization;    Energy dissipation;    Turbulence;   

DOI  :  10.1016/j.jmaa.2018.07.040

来源: Elsevier

【 摘 要 】

Grad-div stabilization, adding a term -gamma grad div u to penalize violation of incompressibility, has proven to be a useful tool in the simulation of incompressible flows. Such a term requires a choice of the coefficient gamma and studies have begun appearing with various suggestions for its value. We give an analysis herein that provides a restricted range of possible values for the coefficient in 3d turbulent flows away from walls. If U, L denote the large scale velocity and length respectively and kappa is the signal to noise ratio of the body force, estimates suggest that gamma should be restricted to the range k(2)/24 LU <= gamma <= kappa(2)/4 ReLU, mesh independent case, k(2)/24 LU <= gamma <= kappa(2)/4(h/L)(-4/3) LU, mesh independent case. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free