@Article{IJNAM-17-2,
author = {Victor, Decaria and William, Layton and Zhao, Haiyun},
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 = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/2020-IJNAM-13650},
url = {https://global-sci.com/article/83019/a-time-accurate-adaptive-discretization-for-fluid-flow-problems}
}