@Article{IJNAM-17-254, author = {Decaria , VictorLayton , William 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 = {

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} }