Two Robust, Efficient, and optimally Accurate Algorithms for parameterized stochastic navier-stokes Flow Problems
Year: 2024
Type: preprint
Abstract: This paper presents and analyzes two robust, efficient, and optimally accurate fully discrete finite element algorithms for computing the parameterized Navier-Stokes Equations (NSEs) flow ensemble. The timestepping algorithms are linearized, use the backward-Euler method for approximating the temporal derivative, and Ensemble Eddy Viscosity (EEV) regularized. The first algorithm is a coupled ensemble scheme, and the second algorithm is decoupled using projection splitting with grad-div stabilization. We proved the stability and convergence theorems for both algorithms. We have shown that for sufficiently large grad-div stabilization parameters, the outcomes of the projection scheme converge to the outcomes of the coupled scheme. We then combine the Stochastic Collocation Methods (SCMs) with the proposed two Uncertainty Quantification (UQ) algorithms. A series of numerical experiments are given to verify the predicted convergence rates and performance of the schemes on benchmark problems, which shows the superiority of the splitting algorithm.
Source: arXiv (Cornell University)
Authors: Raveendran, Neethu Suma, Aziz, Md Abdul, Mohebujjaman, Muhammad
Institution: University of Alabama at Birmingham
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4404088730