Numerical Analysis of Two Ensemble Eddy Viscosity Models of Fluid Motion

This report extends a recent method that calculates an ensemble of solutions of the Navier-Stokes equations efficiently to higher Reynolds number flows. To do so herein we develop and analyze two ensemble eddy viscosity models that do not obviate the good algorithmic properties of the ensemble method. The combined approach of ensemble time stepping and ensemble eddy viscosity modelling has other significant advantages. The form of the ensemble algorithm allows a new (and more accurate) parameterization of the turbulent viscosity coefficient that is more direct and gives an unconditionally stable algorithm. It also suggests a new definition of the mixing length. This new mixing length gives superior predictions of flows in our preliminary tests.