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Numerical analysis of two ensemble eddy viscosity numerical regularizations of fluid motion
Author(s) -
Jiang Nan,
Layton William
Publication year - 2015
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21908
Subject(s) - regularization (linguistics) , mathematics , realization (probability) , turbulence modeling , turbulence , reynolds number , mixing (physics) , large eddy simulation , stability (learning theory) , flow (mathematics) , convection , viscosity , statistical physics , mechanics , mathematical analysis , physics , geometry , thermodynamics , computer science , statistics , quantum mechanics , artificial intelligence , machine learning
This report analyzes an efficient ensemble regularization algorithm for under‐resolved and convection dominated flows (including ones at higher Reynolds numbers). Computing an ensemble simultaneously allows each realization to access ensemble data. This allows use of means and fluctuations in regularizations used for each realization. The combined approach of ensemble time stepping and ensemble regularizations allows direct calculation of the turbulent viscosity coefficient and gives an unconditionally stable algorithm. It also suggests reconsidering an old but not as well‐developed definition of the mixing length. This mixing length vanishes at solid walls without van Driest damping, increases stability, and improves flow predictions in our preliminary tests. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 630–651, 2015