  We present a second order ensemble method based on a blended three-step 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.
