Time relaxation algorithm for flow ensembles

Modeling for fast calculation of fluid flow ensembles based on time relaxation regularization is studied herein. At each time step, the proposed model requires the storage of a single coefficient matrix with multiple right‐hands sides, corresponding to each ensemble member. The time relaxation regularization penalizes the deviation of the fluctuations from the ensemble average. The algorithm is shown to be stable under a time step restriction, which holds provided fluctuations are small enough. Also, the numerical tests show that a grad‐div stabilization weakened the condition considerably. Finite element convergence results for the time relaxation ensemble algorithm are studied too. Then, 2D and 3D numerical experiments that support the theoretical results are presented. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 757–777, 2016