A time-accurate, adaptive discretization for fluid flow problems
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.
Cite
@article{arxiv.1810.06705,
title = {A time-accurate, adaptive discretization for fluid flow problems},
author = {Victor DeCaria and William Layton and Haiyun Zhao},
journal= {arXiv preprint arXiv:1810.06705},
year = {2019}
}
Comments
Substantial revisions. A variable order, variable stepsize algorithm is added along with two new figures. Velocity error analysis is moved to the appendix. Some new references