Analysis of a low complexity, time-accurate discretization of the Navier-Stokes equations

Victor DeCaria, William Layton, Haiyun Zhao

Published 2018-10-15Version 1

This report presents a low complexity, stable and time accurate 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. Numerical tests confirm the predicted convergence rates and the improved predictions of flow quantities such as drag and lift.