A minimum action method for small random perturbations of two-dimensional parallel shear flows

Abstract

In this work, we develop a parallel minimum action method for small random perturbations of Navier–Stokes equations to solve the optimization problem given by the large deviation theory. The Freidlin–Wentzell action functional is discretized by hp finite elements in time direction and spectral methods in physical space. A simple diagonal preconditioner is constructed for the nonlinear conjugate gradient solver of the optimization problem. A hybrid parallel strategy based on MPI and OpenMP is developed to improve numerical efficiency. Both h- and p-convergence are obtained when the discretization error from physical space can be neglected. We also present preliminary results for the transition in two-dimensional Poiseuille flow from the base flow to a non-attenuated traveling wave.