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.

翻译：我们根据混合的三步后向差异公式(BDF)时间步制,提出了一个第二阶共和方法,用以计算纳维埃-斯托克斯方程式的共和式。与现有的将双步BDF时间步制办法和特别明确的二阶二阶共和法相结合的唯一第二阶共和法方法相比,这一方法更精确,计算成本名义上增加了。我们为该方法提供了全面的稳定性和误差分析。还提供了数字示例,以核实理论结果,并表明该方法的准确性提高。