A time-accurate, adaptive discretization for fluid flow problems
For computational fluid dynamics practitioners, this offers a simple, minimally intrusive upgrade to existing backward Euler solvers that improves accuracy without added computational cost.
The paper presents a low-complexity, stable, time-accurate adaptive method for Navier-Stokes equations by post-processing backward Euler with a two-step linear time filter, achieving second-order accuracy and unconditional energy stability with minimal code modification. Numerical tests confirm predicted convergence rates and improved drag/lift predictions.
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.