On the determination of the grad-div criterion

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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.467, no.2, pp.1032-1037, 2018 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 467 Issue: 2
• Publication Date: 2018
• Doi Number: 10.1016/j.jmaa.2018.07.040
• Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.1032-1037
• Open Archive Collection: AVESIS Open Access Collection
• Ankara Yıldırım Beyazıt University Affiliated: Yes

Abstract

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