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Many applications of computational fluid dynamics require multiplesimulations of a flow under different input conditions. In this paper, anumerical algorithm is developed to efficiently determine a set of suchsimulations in which the individually independent members of the set aresubject to different viscosity coefficients, initial conditions, and/or bodyforces. The proposed scheme applied to the flow ensemble leads to need to solvea single linear system with multiple right-hand sides, and thus iscomputationally more efficient than solving for all the simulations separately.We show that the scheme is nonlinearly and long-term stable under certainconditions on the time-step size and a parameter deviation ratio. Rigorousnumerical error estimate shows the scheme is of first-order accuracy in timeand optimally accurate in space. Several numerical experiments are presented toillustrate the theoretical results.

An efficient algorithm for simulating ensembles of parameterized flow problems