An Effective Fluid-Structure Interaction Formulation for Vascular Dynamics by Generalized Robin Conditions
An Effective Fluid-Structure Interaction Formulation for Vascular Dynamics by Generalized Robin Conditions
复制标题
广义 Robin 条件下血管动力学的有效流固耦合公式
DOI：
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发表时间：
2008
影响因子：
3.1
通讯作者：
C. Vergara
中科院分区：
文献类型：
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作者：
F. Nobile;C. Vergara
本文主要研究血管动力学中流固耦合机理的建模与数值模拟。我们首先提出了一个简单的膜模型来描述动脉壁的变形，这是来自Koiter壳方程，适用于任意的几何形状。其次，我们考虑重新制定的流体结构问题，其中新衍生的膜模型，由于其简单性，被嵌入到流体方程，并将出现作为一个广义罗宾边界条件。原始问题，然后减少到随后的流体方程的解决方案上定义的移动域，可以实现与流体求解器。我们还得到了一个稳定性估计所产生的数值方案。最后，我们提出了新的外流吸收边界条件，这是很容易实现，并允许我们显着减少虚假的压力波反射，通常出现在人为截断的计算域。我们提出了几个数值结果表明所提出的方法的有效性。
In this work we focus on the modeling and numerical simulation of the fluid-structure interaction mechanism in vascular dynamics. We first propose a simple membrane model to describe the deformation of the arterial wall, which is derived from the Koiter shell equations and is applicable to an arbitrary geometry. Secondly, we consider a reformulation of the fluid-structure problem, in which the newly derived membrane model, thanks to its simplicity, is embedded into the fluid equations and will appear as a generalized Robin boundary condition. The original problem is then reduced to the solution of subsequent fluid equations defined on a moving domain and may be achieved with a fluid solver only. We also derive a stability estimate for the resulting numerical scheme. Finally, we propose new outflow absorbing boundary conditions, which are easy to implement and allow us to reduce significantly the spurious pressure wave reflections that typically appear in artificially truncated computational domains. We present several numerical results showing the effectiveness of the proposed approaches.