Efficient, accurate, and robust penalty-projection algorithm for parameterized stochastic Navier-Stokes flow problems

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2026-05-01 Epub Date: 2026-01-21 DOI:10.1016/j.apnum.2026.01.010

Neethu Suma Raveendran , Md. Abdul Aziz , Sivaguru S. Ravindran , Muhammad Mohebujjaman

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Abstract

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 sub-problems 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).

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参数化随机Navier-Stokes流问题的有效、准确、鲁棒的惩罚-投影算法

本文提出并分析了一种快速、鲁棒、高效、最优精确的全离散分裂算法，用于参数化随机Navier-Stokes方程（SNSEs）模拟的对流主导流问题的不确定性量化（UQ）。时间步进算法采用隐式后向欧拉线性化方法，梯度梯度和集合涡动黏度（EEV）正则化，并采用离散Hodge分解进行分割。此外，该方案的子问题都被设计成具有不同的右手边（RHS）向量，但每个时间步的所有实现都具有相同的系统矩阵。严格证明了算法的稳定性，并表明适当大的梯度稳定参数可以使分裂误差消失。然后将提出的UQ算法与随机配置方法（SCMs）相结合。通过数值实验验证了该算法在高期望雷诺数（Re）基准问题上的收敛速度和性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.