Coupling Arbogast–Correa and Bernardi–Raugel elements to resolve coupled Stokes–Darcy flow problems
Coupling Arbogast–Correa and Bernardi–Raugel elements to resolve coupled Stokes–Darcy flow problems
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DOI：
10.1016/j.cma.2020.113469
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发表时间：
2021
影响因子：
7.2
通讯作者：
Graham Harper;Jiangguo Liu;S. Tavener;T. Wildey
中科院分区：
文献类型：
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作者：
Graham Harper;Jiangguo Liu;S. Tavener;T. Wildey
本文将经典的Bernardi-Raugel有限元与新近发展的Arbogast-Correa（AC）空间相结合，提出了一种求解Stokes-Darcy耦合流动问题的四边形网格有限元方法。新的弱伽辽金方法离散的达西方程。具体地说，分段常数逼近分别定义在单元内部和边缘上的达西压力。这些形状函数的离散弱梯度和数值达西速度建立在最低阶AC空间。采用Bernardi-Raugel元（B R1，Q 0）离散Stokes方程。这两种类型的离散相结合的接口，运动学，正应力，和海狸约瑟夫萨夫曼（BJS）条件。严格的误差分析沿着数值实验表明，该方法是稳定的，并具有最优阶精度。
This paper presents a finite element method for solving coupled Stokes–Darcy flow problems by combining the classical Bernardi–Raugel finite elements and the recently developed Arbogast–Correa (AC) spaces on quadrilateral meshes. The novel weak Galerkin methodology is employed for discretization of the Darcy equation. Specifically, piecewise constant approximants separately defined in element interiors and on edges are utilized to approximate the Darcy pressure. The discrete weak gradients of these shape functions and the numerical Darcy velocity are established in the lowest order AC space. The Bernardi–Raugel elements (B R 1, Q 0) are used to discretize the Stokes equations. These two types of discretizations are combined at an interface, where kinematic, normal stress, and the Beavers–Joseph–Saffman (BJS) conditions are applied. Rigorous error analysis along with numerical experiments demonstrate that the method is stable and has optimal-order accuracy.