Numerical Analysis of Two Ensemble Eddy Viscosity Numerical Regularizations of Fluid Motion
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.
N. Jiang and W. Layton, "Numerical Analysis of Two Ensemble Eddy Viscosity Numerical Regularizations of Fluid Motion," Numerical Methods for Partial Differential Equations, vol. 31, no. 3, pp. 630-651, John Wiley & Sons, May 2015.
The definitive version is available at https://doi.org/10.1002/num.21908
Mathematics and Statistics
Keywords and Phrases
Algorithms; Mixing; Reynolds number; Viscosity; Convection-dominated flow; Direct calculation; Eddy viscosity; regularization; Regularization algorithms; Turbulent viscosity; Uncertainty quantifications (UQ); Unconditionally stable algorithms; Navier Stokes equations; Ensemble calculation; Navier-Stokes equations; Regularization
International Standard Serial Number (ISSN)
Article - Journal
© 2015 John Wiley & Sons, All rights reserved.
01 May 2015