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 - <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>