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Unified Lagrangian formulation for solid and fluid mechanics and FSI problems

机译：统一的拉格朗日公式，用于解决固体和流体力学以及FSI问题

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摘要

We present a Lagrangian monolithic strategy for solving fluid-structure interaction (FSI) problems. The formulation is called Unified because fluids and solids are solved using the same solution scheme and unknown variables. The method is based on a mixed velocity-pressure formulation. Each time step increment is solved via an iterative partitioned two-step procedure. The Particle Finite Element Method (PFEM) is used for solving the fluid parts of the domain, while for the solid ones the Finite Element Method (FEM) is employed. Both velocity and pressure fields are interpolated using linear shape functions. For quasi-incompressible materials, the solution scheme is stabilized via the Finite Calculus (FIC) method. The stabilized elements for quasi-incompressible hypoelastic solids and Newtonian fluids are called VPS/S-element and VPS/F-element, respectively. Other two non-stabilized elements are derived for hypoelastic solids. One is based on a Velocity formulation (V-element) and the other on a mixed Velocity-Pressure scheme (VP-element). The algorithms for coupling the solid elements with the VPS/F fluid element are explained in detail. The Unified formulation is validated by solving benchmark FSI problems and by comparing the numerical solution to the ones published in the literature. (C) 2015 Elsevier B.V. All rights reserved.
机译：我们提出了一种拉格朗日整体策略来解决流固耦合（FSI）问题。该公式之所以称为统一的，是因为使用相同的求解方案和未知变量来求解流体和固体。该方法基于混合的速度-压力公式。每个时间步长增量都通过迭代的分区两步过程进行求解。粒子有限元方法（PFEM）用于求解区域的流体部分，而对于固体部分，则采用有限元方法（FEM）。速度和压力场都使用线性形状函数进行插值。对于准不可压缩材料，解决方案通过有限演算（FIC）方法得以稳定。准不可压缩的次弹性固体和牛顿流体的稳定元素分别称为VPS / S元素和VPS / F元素。对于次弹性固体，导出了其他两个非稳定元素。一种基于速度公式（V元素），另一种基于混合速度-压力方案（VP元素）。详细说明了将固体元素与VPS / F流体元素耦合的算法。通过解决基准FSI问题并将数值解与文献中发布的数值解进行比较，可以验证统一公式。 （C）2015 Elsevier B.V.保留所有权利。

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