Robust SAV-Ensemble algorithms for parametrized flow problems with energy stable open boundary conditions

Abstract

In this report we propose fast and robust ensemble simulation algorithms for parametrized nonlinear flow problems with open boundaries. We synthesize the recent SAV idea, the ensemble timestepping and the energy stable open boundary conditions, and develop efficient ensemble algorithms that only require a single matrix assembly for all realizations and all time steps. Moreover, the proposed algorithms are unconditionally stable without any restricting assumptions on the variance of the viscosities or the time steps, and they always produce positive values for the auxiliary variables. The second order algorithm is numerically tested on three benchmark flow problems with open boundaries, and is shown to be both accurate and effective in preventing the backflow instabilities.