An immersed interface method for discrete surfaces
An immersed interface method for discrete surfaces
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DOI：
10.1016/j.jcp.2019.07.052
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发表时间：
2020-01-01
影响因子：
4.1
通讯作者：
Griffith, Boyce E.
中科院分区：
文献类型：
--
作者：
Kolahdouz, Ebrahim M.;Bhalla, Amneet Pal Singh;Griffith, Boyce E.
流体结构系统出现在一系列科学和工程应用中。浸没边界（IB）方法是一种被广泛认可的模拟此类系统中的流固耦合（FSI）的有效建模范例，但IB公式化的困难在于流固界面处的压力和粘性应力通常是不连续的。传统的IB方法正则化这些不连续性，这通常会产生低阶精度在这些接口。浸没界面法（IIM）是一种类似于IB的方法，它强烈地施加应力跳跃条件，从而实现更高的精度，但IIM的先前应用在很大程度上限于依赖于界面几何形状的光滑表示的数值方法。本文介绍了一种浸入式界面配方，只使用C-0表示的浸入式界面，如标准节点拉格朗日有限元方法提供的。具有规定的接口运动的模型的验证实例表明，该方法急剧解决应力不连续性沿着浸没边界，同时避免了需要的接口几何形状的分析信息。我们的结果还表明，只有最低阶的压力和速度梯度的跳跃条件需要实现全球二阶精度。具体来说，我们证明了二阶全局收敛率沿着与近二阶局部收敛的欧拉速度场，和一阶和二阶全局收敛率沿着与约一阶局部收敛的欧拉压力场。我们还证明了近似二阶局部收敛的界面位移和速度沿着与一阶局部收敛的流体牵引沿着界面。作为该方法处理更复杂几何形状的能力的证明，本方法还用于模拟下腔静脉的患者平均解剖模型中的流动，下腔静脉是将脱氧血液从下半身和中半身运送回心脏的大静脉。一般的血液动力学和壁面切应力的比较，通过本IIM和一个身体拟合的离散化方法得到的结果表明，本方法产生的结果是在良好的协议与身体拟合的方法得到的。(C)2019爱思唯尔公司All rights reserved.
Fluid-structure systems occur in a range of scientific and engineering applications. The immersed boundary (IB) method is a widely recognized and effective modeling paradigm for simulating fluid-structure interaction (FSI) in such systems, but a difficulty of the IB formulation of these problems is that the pressure and viscous stress are generally discontinuous at fluid-structure interfaces. The conventional IB method regularizes these discontinuities, which typically yields low-order accuracy at these interfaces. The immersed interface method (IIM) is an IB-like approach to FSI that sharply imposes stress jump conditions, enabling higher-order accuracy, but prior applications of the IIM have been largely restricted to numerical methods that rely on smooth representations of the interface geometry. This paper introduces an immersed interface formulation that uses only a C-0 representation of the immersed interface, such as those provided by standard nodal Lagrangian finite element methods. Verification examples for models with prescribed interface motion demonstrate that the method sharply resolves stress discontinuities along immersed boundaries while avoiding the need for analytic information about the interface geometry. Our results also demonstrate that only the lowest-order jump conditions for the pressure and velocity gradient are required to realize global second-order accuracy. Specifically, we demonstrate second-order global convergence rates along with nearly second-order local convergence in the Eulerian velocity field, and between first- and second-order global convergence rates along with approximately first-order local convergence for the Eulerian pressure field. We also demonstrate approximately second-order local convergence in the interfacial displacement and velocity along with first-order local convergence in the fluid traction along the interface. As a demonstration of the method's ability to tackle more complex geometries, the present approach is also used to simulate flow in a patient-averaged anatomical model of the inferior vena cava, which is the large vein that carries deoxygenated blood from the lower and middle body back to the heart. Comparisons of the general hemodynamics and wall shear stress obtained by the present IIM and a body-fitted discretization approach show that the present method yields results that are in good agreement with those obtained by the body-fitted approach. (C) 2019 Elsevier Inc. All rights reserved.