Primal interface formulation for coupling multiple PDEs: A consistent derivation via the Variational Multiscale method
Primal interface formulation for coupling multiple PDEs: A consistent derivation via the Variational Multiscale method
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DOI：
10.1016/j.cma.2013.08.005
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发表时间：
2014-01-01
影响因子：
7.2
通讯作者：
Masud, Arif
中科院分区：
文献类型：
--
作者：
Truster, Timothy J.;Masud, Arif
本文提出了一种原始接口制定，是在一个系统的方式从拉格朗日乘子方法提供一个一致的框架，耦合不同的偏微分方程（PDE），以及捆绑在一起的网格。推导依赖于至关重要的概念，从变分多尺度（VMS）的方法，其中添加剂的多尺度分解应用于主要的解决方案领域。利用气泡函数对界面上的细尺度进行局部建模，得到了边界上一致的基于残差的项，这些项随后被嵌入到粗尺度问题中。由此产生的稳定的拉格朗日乘子配方转化为一个强大的不连续Galerkin（DG）方法，采用不连续插值的乘子沿着段的接口。作为一个副产品，解析表达式推导出的稳定项和加权的数值通量，反映了跳跃的材料性能，控制方程，或元素的几何形状在整个接口。此外，提出了一个程序自动生成的细尺度气泡功能，这是由一个性能研究的残余自由气泡的接口问题的启发。一系列的数值试验证实了该方法的鲁棒性，用于解决界面问题的非均匀元素，材料，和/或控制方程，也突出的好处和重要性，推导出的通量和稳定项。(C)2013爱思唯尔有限公司版权所有。
This paper presents a primal interface formulation that is derived in a systematic manner from a Lagrange multiplier method to provide a consistent framework to couple different partial differential equations (PDE) as well as to tie together nonconforming meshes. The derivation relies crucially on concepts from the Variational Multiscale (VMS) approach wherein an additive multiscale decomposition is applied to the primary solution field. Modeling the fine scales locally at the interface using bubble functions, consistent residual-based terms on the boundary are obtained that are subsequently embedded into the coarse-scale problem. The resulting stabilized Lagrange multiplier formulation is converted into a robust Discontinuous Galerkin (DG) method by employing a discontinuous interpolation of the multipliers along the segments of the interface. As a byproduct, analytical expressions are derived for the stabilizing terms and weighted numerical flux that reflect the jump in material properties, governing equation, or element geometry across the interface. Also, a procedure is proposed for automatically generating the fine-scale bubble functions that is inspired by a performance study of residual-free bubbles for the interface problem. A series of numerical tests confirms the robustness of the method for solving interface problems with heterogeneous elements, materials, and/or governing equations and also highlights the benefit and importance of deriving the flux and stabilization terms. (C) 2013 Elsevier B.V. All rights reserved.