Year: 2020
Author: Victor Decaria, William Layton, Haiyun Zhao
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 2 : pp. 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.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2020-IJNAM-13650
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 2 : pp. 254–280
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Navier-Stokes backward Euler time filter time discretization finite element method.