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Volume 11, Issue 2
An Adaptive Time and Space Discretization Approach for Simulating Unsteady Navier-Stokes Flows

Biao Peng, Chunhua Zhou & Junqiang Ai

Adv. Appl. Math. Mech., 11 (2019), pp. 406-427.

Published online: 2019-01

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  • 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.

  • Keywords

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

  • AMS Subject Headings

93C40, 65M50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-11-406, author = {Peng , BiaoZhou , Chunhua and Ai , Junqiang}, title = {An Adaptive Time and Space Discretization Approach for Simulating Unsteady Navier-Stokes Flows}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {2}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0004}, url = {http://global-sci.org/intro/article_detail/aamm/12969.html} }
TY - JOUR T1 - An Adaptive Time and Space Discretization Approach for Simulating Unsteady Navier-Stokes Flows AU - Peng , Biao AU - Zhou , Chunhua AU - Ai , Junqiang JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 406 EP - 427 PY - 2019 DA - 2019/01 SN - 11 DO - http://doi.org/10.4208/aamm.OA-2018-0004 UR - https://global-sci.org/intro/article_detail/aamm/12969.html KW - Adaptive time stepping, unsteady flow, dynamic mesh adaptation, temporal error estimation, immersed boundary. AB -

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.

Biao Peng, Chunhua Zhou & Junqiang Ai. (2020). An Adaptive Time and Space Discretization Approach for Simulating Unsteady Navier-Stokes Flows. Advances in Applied Mathematics and Mechanics. 11 (2). 406-427. doi:10.4208/aamm.OA-2018-0004
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