Penalty immersed boundary method for an elastic boundary with mass
Penalty immersed boundary method for an elastic boundary with mass
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DOI：
10.1063/1.2734674
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发表时间：
2007-05-01
影响因子：
4.6
通讯作者：
Peskin, Charles S.
中科院分区：
文献类型：
--
作者：
Kim, Yongsam;Peskin, Charles S.
浸没边界（IB）方法已广泛应用于涉及浸没在流体中并与其相互作用的移动弹性边界的问题。 IB 方法以前的大多数应用都涉及无质量弹性边界，并使用有效的傅里叶变换方法来求解数值解。扩展该方法以覆盖大质量边界的情况需要将边界质量分散到流体网格上，然后求解具有可变质量密度的纳维-斯托克斯方程。先前方法的可变质量密度使得傅立叶变换方法不适用，并且需要多重网格求解器。在这里，我们提出了一种新的、简单的方法来为弹性边界赋予质量，并表明该方法可以应用于边界质量很重要的许多问题。该方法不会将质量传播到流体网格，保留了傅立叶变换方法的使用，并且易于在无质量情况下的现有 IB 方法代码的背景下实现。给出了该方法的两个验证。其中之一是数值收敛研究，表明我们的数值方案对于特定的测试问题是二阶精确的。另一种是与大圆柱体涡激振动实验数据的直接比较，表明该方法得到的结果与实验数据具有相当的可比性。 (c) 2007 年美国物理研究所。
The immersed boundary (IB) method has been widely applied to problems involving a moving elastic boundary that is immersed in fluid and interacting with it. Most of the previous applications of the IB method have involved a massless elastic boundary and used efficient Fourier transform methods for the numerical solutions. Extending the method to cover the case of a massive boundary has required spreading the boundary mass out onto the fluid grid and then solving the Navier-Stokes equations with a variable mass density. The variable mass density of this previous approach makes Fourier transform methods inapplicable, and requires a multigrid solver. Here we propose a new and simple way to give mass to the elastic boundary and show that the method can be applied to many problems for which the boundary mass is important. The method does not spread mass to the fluid grid, retains the use of Fourier transform methodology, and is easy to implement in the context of an existing IB method code for the massless case. Two verifications of the method are given. One is a numerical convergence study that shows that our numerical scheme is second-order accurate for a particular test problem. The other is direct comparison with experimental data of vortex-induced vibrations of a massive cylinder, which shows that the results obtained by the present method are quite comparable to the experimental data. (c) 2007 American Institute of Physics.