An Efficient Second-Order-in-Time Penalty-Projection Ensemble Eddy Viscosity Method for Parameterized Navier-Stokes Flows
Year: 2026
Type: preprint
Abstract: We propose a novel, robust, and second-order-accurate parameterized penalty-projection ensemble algorithm for incompressible Navier--Stokes flow problems. The resulting linearized algorithm, based on the second-order Backward Differentiation Formula (BDF-2), is computationally efficient because it shares the same coefficient matrix across all realizations for each subproblem at every time step. To enhance robustness in convection-dominated flows, the scheme incorporates Ensemble Eddy Viscosity (EEV) regularization. In addition, it is equipped with grad-div stabilization parameter $γ$, which controls the splitting error; under the assumptions of the analysis, the splitting error decreases and vanishes asymptotically as $γ\to\infty$. We establish the stability of the proposed scheme and rigorously prove its optimal convergence by demonstrating that, as $γ\to\infty$, the scheme converges to an equivalent coupled formulation. We further validate the method through a series of numerical experiments designed to verify the theoretically predicted convergence rates and evaluate its performance on benchmark convection-dominated problems. The numerical results are in excellent agreement with the theoretical analysis and confirm the effectiveness of the proposed scheme.
Source: arXiv (Cornell University)
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7203923188
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