An efficient algorithm for simulating ensembles of parameterized flow problems
For computational fluid dynamics practitioners, this provides a more efficient method for multiple simulations under varying conditions, but the improvement is incremental.
The paper develops a numerical algorithm that reduces the cost of simulating ensembles of parameterized flow problems by solving a single linear system with multiple right-hand sides, achieving first-order accuracy in time and optimal spatial accuracy. Numerical experiments confirm stability and error estimates.
Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to efficiently determine a set of such simulations in which the individually independent members of the set are subject to different viscosity coefficients, initial conditions, and/or body forces. The proposed scheme applied to the flow ensemble leads to need to solve a single linear system with multiple right-hand sides, and thus is computationally more efficient than solving for all the simulations separately. We show that the scheme is nonlinearly and long-term stable under certain conditions on the time-step size and a parameter deviation ratio. Rigorous numerical error estimate shows the scheme is of first-order accuracy in time and optimally accurate in space. Several numerical experiments are presented to illustrate the theoretical results.