An Adaptive Time and Space Discretization Approach for Simulating Unsteady Navier-Stokes Flows

An Adaptive Time and Space Discretization Approach for Simulating Unsteady Navier-Stokes Flows

Year:    2019

Author:    Biao Peng, Chunhua Zhou, Junqiang Ai

Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 2 : pp. 406–427

Abstract

In this paper, we develop a technique of adaptive time stepping and combine it with dynamic mesh adaptation to simulate unsteady Navier-Stokes flows over stationary or moving bodies. The second order Backward Differentiation Formula (BDF2) is employed for time discretization and the adaptation of time step is based on the estimation of temporal error. Via a PID (Proportional Integral Derivative) controller or a classical heuristic controller, the size of time step is determined adaptively by the estimate of temporal error and the specified tolerance. In order to eliminate the lag of the adapted mesh behind the unsteady solution, which is associated with the size of time step, a predictor-corrector scheme is adopted in the dynamic mesh adaptation. The efficiency and reliability of the present adaptive time and space discretization approach are validated by the numerical experiments for two- and three-dimensional flows. In the numerical experiments, the behaviors of different error estimators and step-size controllers have also been compared and discussed.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2018-0004

Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 2 : pp. 406–427

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Adaptive time stepping unsteady flow dynamic mesh adaptation temporal error estimation immersed boundary.

Author Details

Biao Peng

Chunhua Zhou

Junqiang Ai