  We consider settings for which one needs to perform multiple flow simulations
based on the Navier-Stokes equations, each having different values for the
physical parameters and/or different initial condition data, boundary
conditions data, and/or forcing functions. For such settings, we propose a
second-order time accurate ensemble-based method that to simulate the whole set
of solutions, requires, at each time step, the solution of only a single linear
system with multiple right-hand-side vectors. Rigorous analyses are given
proving the conditional stability and error estimates for the proposed
algorithm. Numerical experiments are provided that illustrate the analyses.
