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Title: A time accurate, adaptive discretization for fluid flow problems
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.
Authors:
; ;
Award ID(s):
1817542
Publication Date:
NSF-PAR ID:
10147662
Journal Name:
International journal of numerical analysis and modeling
Volume:
17
Issue:
2
Page Range or eLocation-ID:
254-280
ISSN:
2617-8710
Sponsoring Org:
National Science Foundation
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