A second order ensemble method based on a blended BDF timestepping scheme for time dependent Navier-Stokes equations

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.