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Efficient, accurate, and robust penalty-projection algorithm for parameterized stochastic Navier-Stokes flow problems
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DOI：10.1016/j.apnum.2026.01.010.png)
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Abstract
En 中文
This paper presents and analyzes a fast, robust, efficient, and optimally accurate fully discrete splitting algorithm for the Uncertainty Quantification (UQ) of convection-dominated flow problems modeled by parameterized Stochastic Navier-Stokes Equations (SNSEs). The time-stepping algorithm is an implicit backward-Euler linearized method, grad-div and Ensemble Eddy Viscosity (EEV) regularized, and split using discrete Hodge decomposition. Moreover, the scheme's subproblems are all designed to have different Right-Hand-Side (RHS) vectors but the same system matrix for all realizations at each time-step. The stability of the algorithm is rigorously proven, and it has been shown that appropriately large grad-div stabilization parameters cause the splitting error to vanish. The proposed UQ algorithm is then combined with the Stochastic Collocation Methods (SCMs). Several numerical experiments are presented to verify the predicted convergence rates and performance of this superior scheme on benchmark problems with high expected Reynolds numbers (Re).
Keywords:
Finite element method
Uncertainty quantification
Penalty-projection method
Fast ensemble calculation
Journal
IF:
2.4
Papers:
85
Citations:
6.7K
