Mixed FEM for Coupled Unsteady Fluid Flow Problems with [math]-Type Brinkman–Forchheimer Framework and its Application for Reverse-Osmosis Desalination

IF 3.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2026-08-12 DOI:10.1137/25m1767650

Zeinab Gharibi, Mostafa Abbaszadeh, Mehdi Dehghan

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引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 64, Issue 4, Page 1645-1681, August 2026.
Abstract. This work analyzes a fully discrete mixed finite element method in a Banach space framework for solving nonstationary coupled fluid flow problems modeled by the Brinkman–Forchheimer equations, with applications to reverse osmosis. The model couples unsteady [math]-type convective Brinkman–Forchheimer and transport equations with nonlinear boundary conditions across a semipermeable membrane. A mixed formulation is used for both the fluid equation (pseudostress-velocity) and the transport equation (concentration, its gradient, and a Lagrange multiplier from the membrane condition). The continuous problem is reformulated in Banach spaces as a fixed-point problem, enabling a well-posedness analysis via differential-algebraic system theory. Spatial discretization employs lowest-order Raviart–Thomas elements for fluxes and piecewise constants for primal variables, while linear elements are used for the Lagrange multiplier. A fully discrete Galerkin scheme with backward Euler time-stepping is proposed. Its well-posedness and stability are proven using a fixed-point argument, and optimal convergence rates are established. Numerical results confirm the theoretical error estimates and demonstrate the method’s effectiveness.

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[数学]型Brinkman-Forchheimer框架耦合非定常流体流动问题的混合有限元法及其在反渗透海水淡化中的应用

SIAM数值分析学报，64卷，第4期，1645-1681页，2026年8月。摘要。本文分析了Banach空间框架下的完全离散混合有限元方法，用于求解由Brinkman-Forchheimer方程模拟的非稳态耦合流体流动问题，并应用于反渗透。该模型耦合非定常[数学]型对流Brinkman-Forchheimer方程和具有非线性边界条件的跨半透膜输运方程。流体方程（伪应力-速度）和输运方程（浓度、梯度和来自膜条件的拉格朗日乘子）均采用混合公式。将连续问题在巴拿赫空间中重新表述为不动点问题，利用微分代数系统理论进行适定性分析。空间离散化采用最低阶Raviart-Thomas元表示通量，分段常数表示原始变量，而线性元用于拉格朗日乘子。提出了一种具有向后欧拉时间步进的全离散伽辽金格式。利用不动点论证证明了该方法的适定性和稳定性，并建立了最优收敛速率。数值结果证实了理论估计的误差，证明了方法的有效性。

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.