A Higher Order Ensemble Simulation Algorithm for Fluid Flows

This report presents an efficient, higher order method for fast calculation of an ensemble of solutions of the Navier-Stokes equations. We give a complete stability and convergence analysis of the method for laminar flows and an extension to turbulent flows. For high Reynolds number flows, we propose and analyze an eddy viscosity model with a recent reparameterization of the mixing length. This turbulence model depends on an ensemble mean compatible with the higher order method. We show the turbulence model has superior stability, also demonstrated in numerical tests. We also give tests showing the potential of the new method for exploring flow problems to compute turbulence intensities, effective Lyapunov exponents, windows of predictability and to verify the selective decay principle