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Volume 17, Issue 2
A Time-Accurate, Adaptive Discretization for Fluid Flow Problems

Victor Decaria, William Layton & Haiyun Zhao

Int. J. Numer. Anal. Mod., 17 (2020), pp. 254-280.

Published online: 2020-02

[An open-access article; the PDF is free to any online user.]

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  • Abstract

This report presents a low computational and cognitive complexity, stable, time accurate and adaptive method for the Navier-Stokes equations. The improved method requires a minimally intrusive modification to an existing program based on the fully implicit / backward Euler time discretization, does not add to the computational complexity, and is conceptually simple. The backward Euler approximation is simply post-processed with a two-step, linear time filter. The time filter additionally removes the overdamping of Backward Euler while remaining unconditionally energy stable, proven herein. Even for constant stepsizes, the method does not reduce to a standard / named time stepping method but is related to a known 2-parameter family of A-stable, two step, second order methods. Numerical tests confirm the predicted convergence rates and the improved predictions of flow quantities such as drag and lift.

  • Keywords

Navier-Stokes, backward Euler, time filter, time discretization, finite element method.

  • AMS Subject Headings

65M99, 76M10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

decariavp@ornl.gov (Victor Decaria)

wjl@pitt.edu (William Layton)

haz50@pitt.edu (Haiyun Zhao)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-17-254, author = {Victor and Decaria and decariavp@ornl.gov and 6554 and Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA. and Victor Decaria and William and Layton and wjl@pitt.edu and 6553 and Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA. and William Layton and Haiyun and Zhao and haz50@pitt.edu and 6552 and Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA. and Haiyun Zhao}, title = {A Time-Accurate, Adaptive Discretization for Fluid Flow Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {2}, pages = {254--280}, abstract = {

This report presents a low computational and cognitive complexity, stable, time accurate and adaptive method for the Navier-Stokes equations. The improved method requires a minimally intrusive modification to an existing program based on the fully implicit / backward Euler time discretization, does not add to the computational complexity, and is conceptually simple. The backward Euler approximation is simply post-processed with a two-step, linear time filter. The time filter additionally removes the overdamping of Backward Euler while remaining unconditionally energy stable, proven herein. Even for constant stepsizes, the method does not reduce to a standard / named time stepping method but is related to a known 2-parameter family of A-stable, two step, second order methods. Numerical tests confirm the predicted convergence rates and the improved predictions of flow quantities such as drag and lift.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13650.html} }
TY - JOUR T1 - A Time-Accurate, Adaptive Discretization for Fluid Flow Problems AU - Decaria , Victor AU - Layton , William AU - Zhao , Haiyun JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 254 EP - 280 PY - 2020 DA - 2020/02 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/13650.html KW - Navier-Stokes, backward Euler, time filter, time discretization, finite element method. AB -

This report presents a low computational and cognitive complexity, stable, time accurate and adaptive method for the Navier-Stokes equations. The improved method requires a minimally intrusive modification to an existing program based on the fully implicit / backward Euler time discretization, does not add to the computational complexity, and is conceptually simple. The backward Euler approximation is simply post-processed with a two-step, linear time filter. The time filter additionally removes the overdamping of Backward Euler while remaining unconditionally energy stable, proven herein. Even for constant stepsizes, the method does not reduce to a standard / named time stepping method but is related to a known 2-parameter family of A-stable, two step, second order methods. Numerical tests confirm the predicted convergence rates and the improved predictions of flow quantities such as drag and lift.

Victor Decaria, William Layton & Haiyun Zhao. (2020). A Time-Accurate, Adaptive Discretization for Fluid Flow Problems. International Journal of Numerical Analysis and Modeling. 17 (2). 254-280. doi:
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