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.