A second-order time-stepping scheme for simulating ensembles of parameterized flow problems
For computational scientists needing to run many flow simulations, this method reduces computational cost while maintaining accuracy.
The paper proposes a second-order time-accurate ensemble method for simulating multiple Navier-Stokes flow problems with different parameters, requiring only one linear system solve per time step. Numerical experiments confirm the theoretical stability and error estimates.
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.