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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Two finite element approaches for Darcy and Darcy-Brinkman flow through deformable porous media-Mixed method vs. NURBS based (isogeometric) continuity
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Two finite element approaches for Darcy and Darcy-Brinkman flow through deformable porous media-Mixed method vs. NURBS based (isogeometric) continuity

机译:通过可变形多孔介质的Darcy和Darcy-Brinkman流动的两种有限元方法-混合方法与基于NURBS的(等几何)连续性

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摘要

Porous media problems with coupled finite deformations and flow are still quite challenging. If large deformations occur, a non homogeneous porosity field is almost inevitable, as the porosity can vary due to deformation or due to flow and pore pressure. From a numerical point of view this significantly changes the mathematical description of the problem. In this contribution, we will analyze the consequences of the occurrence of porosity gradients on the finite element formulations of saturated, two phase porous media for Darcy and Darcy-Brinkman flow. We will present two approaches which are capable of fulfilling the numerical requirements for convergence. The first will be an approach based on NURBS shape functions. The second is a mixed formulation including the porosity as primary solution field. In addition, we will propose a method to include no-penetration or no-slip constraints into the monolithic system using a dual Lagrange multiplier method. The potential of the proposed methods for solving porous flow structure interaction undergoing large deformations will be illustrated by numerical examples. (C) 2016 Elsevier B.V. All rights reserved.
机译:带有有限变形和流动耦合的多孔介质问题仍然非常具有挑战性。如果发生大的变形,则几乎不可避免的是不均匀的孔隙率场,因为孔隙率可能由于变形或由于流动和孔隙压力而变化。从数字角度来看,这极大地改变了问题的数学描述。在这一贡献中,我们将分析孔隙度梯度对达西和达西-布林克曼流的饱和两相多孔介质有限元公式的影响。我们将介绍两种能够满足数值收敛要求的方法。第一种是基于NURBS形状函数的方法。第二种是将孔隙度作为主要溶液场的混合配方。另外,我们将提出一种使用双重拉格朗日乘数法将无渗透或无滑移约束纳入单片系统的方法。数值实例说明了所提出的解决大变形的多孔结构相互作用的方法的潜力。 (C)2016 Elsevier B.V.保留所有权利。

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