An algorithm for fast calculation of flow ensembles

Abstract

This report presents an algorithm for computing an ensemble of p solutions of the Navier-Stokes equations. The solutions are found, at each timestep, by solving a linear system with one shared coefficient matrix and p right hand sides, reducing both storage required and computational cost of the solution process. The price that must be paid is a timestep condition involving the timestep and the size of the fluctuations about the ensemble mean. Since the method is a one step method and the timestep condition involves only known quantities, it can be imposed to adapt the next timestep. The report gives a comprehensive stability analysis, an error estimate, and some first tests.