Variational coupling of non-matching discretizations across finitely deforming fluid-structure interfaces.
Variational coupling of non-matching discretizations across finitely deforming fluid-structure interfaces.
复制标题
有限变形流体-结构界面上不匹配离散的变分耦合。
DOI：
10.1002/fld.5071
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发表时间：
2022
影响因子：
1.8
通讯作者：
Masud,Arif
中科院分区：
文献类型：
--
作者：
Kang,Soonpil;Kwack,JaeHyuk;Masud,Arif
本文提出了一种稳定的整体方法，用于耦合不可压缩粘性流体与非匹配界面网格上的可压缩变形弹性固体。固体的控制方程被写在有限变形拉格朗日框架中，使用速度场作为主要未知量，而流体的控制方程被写在任意拉格朗日-欧拉（ALE）框架中，以适应流体-固体界面的大运动。通过在变分多尺度（VMS）框架中嵌入不连续Galerkin（DG）思想并从流体和固体子域沿公共界面沿着局部求解细尺度变分方程来导出界面耦合项。变分多尺度间断伽辽金（VMDG）方法的独特之处在于它能系统地推导出流固界面上的牵引力拉格朗日乘子的解析表达式。界面稳定张量的结构自然出现，并示出为与域内部运营商从流体和固体子域的边界运营商的函数。所导出的稳定化张量具有面积平均和应力平均的特征，并随界面处非线性场的演化而时空演化。的界面稳定张量的数学性质的分析，随后进行了数值验证。该方法是使用四节点四面体元素的流体以及固体子域，同时采用等阶插值的各种相互作用的领域。为了验证该方法的有效性，提出了一种基于基准问题的流固耦合变形分析方法。
This paper presents a stabilized monolithic method for coupling incompressible viscous fluids with finitely deforming elastic solids across non‐matching interfacial meshes. Governing equations for the solid are written in the finite deformation Lagrangian frame using velocity field as the primary unknown, while the governing equations for the fluid are written in an Arbitrary Lagrangian–Eulerian (ALE) frame to accommodate large motions of the fluid–solid interfaces. Interface coupling terms are derived by embedding Discontinuous Galerkin (DG) ideas in the Variational Multiscale (VMS) framework and locally resolving the fine‐scale variational equations from the fluid and the solid subdomains along the common interface. The unique attribute of the proposed Variational Multiscale Discontinuous Galerkin (VMDG) method is a systematic procedure for deriving analytical expression for the traction Lagrange multiplier at the fluid–solid interface. The structure of the interface stabilization tensor emerges naturally and is shown to be a function of the boundary operators that are associated with the domain interior operators from the fluid and the solid subdomains. The derived stabilization tensor possesses the features of area‐averaging and stress‐averaging and evolves spatially and temporally with the evolving nonlinear fields at the interface. An analysis of the mathematical properties of the interface stabilization tensor is presented and subsequently verified numerically. The method is implemented using four‐node tetrahedral elements for the fluid as well as the solid subdomains while employing equal‐order interpolations for the various interacting fields. Benchmark problems are presented for the verification of the method for finitely deforming fluid–structure interfaces.