  We present a second-order ensemble method based on a blended three-step
backward differentiation formula (BDF) timestepping scheme to compute an
ensemble of Navier-Stokes equations. Compared with the only existing
second-order ensemble method that combines the two-step BDF timestepping scheme
and a special explicit second-order Adams-Bashforth treatment of the advection
term, this method is more accurate with nominal increase in computational cost.
We give comprehensive stability and error analysis for the method. Numerical
examples are also provided to verify theoretical results and demonstrate the
improved accuracy of the method.
