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

Document Type

Article

Publication Date

2-15-2013

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. © 2012 Elsevier Inc.

Publication Source (Journal or Book title)

Journal of Computational Physics

First Page

497

Last Page

514

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