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