  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.
