A Time-Accurate, Adaptive Discretization for Fluid Flow Problems

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.

Author Details

Victor Decaria

William Layton

Haiyun Zhao