On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems
On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems
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DOI：
10.1016/j.jcp.2005.02.011
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发表时间：
2005-09-01
影响因子：
4.1
通讯作者：
Peskin, CS
中科院分区：
文献类型：
--
作者：
Griffith, BE;Peskin, CS
浸没边界方法是一种求解粘性不可压缩流体与(粘弹性)结构相互作用问题的数学公式和数值格式。在[M.-C.Lai，作为浸没边界方法测试的一组圆柱体绕流的模拟，纽约大学Courant数学科学研究所博士论文，1998；M.-C.Lai，C.S.Peskin，一种具有形式二阶精度和降低数值粘性的浸没边界方法，J.Comput.太棒了。160(2000)705-719]一文中，Lai和Peskin提出了一种形式上的二阶精确浸没边界方法，但他们的算法的收敛性质只对具有非光滑解的问题进行了计算检验。因此，在实践中只观察到了一阶收敛速度。在本文中，我们描述了一种新的形式上的二阶精确浸没边界方法，并证明了它在一个典型的流固耦合问题中的性能，该问题涉及一个有限厚度的浸没粘弹性壳，研究了较宽的雷诺数范围。我们考虑了粘弹性结构的两组材料特性，其中包括耦合系统的材料特性在流固界面处不连续的情况。对于这两组材料特性，真正的解似乎具有足够的光滑性，使得该方法能够以二阶速率收敛，以进行完全解析的计算。(C)2005 Elsevier Inc.保留所有权利。
The immersed boundary method is both a mathematical formulation and a numerical scheme for problems involving the interaction of a viscous incompressible fluid and a (visco-)elastic structure. In [M.-C. Lai, Simulations of the flow past an array of circular cylinders as a test of the immersed boundary method, Ph.D. thesis, Courant Institute of Mathematical Sciences, New York University, 1998; M.-C. Lai, C.S. Peskin, An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. Comput. Phys. 160 (2000) 705-719], Lai and Peskin introduced a formally second order accurate immersed boundary method, but the convergence properties of their algorithm have only been examined computationally for problems with nonsmooth solutions. Consequently, in practice only first order convergence rates have been observed. In the present work, we describe a new formally second order accurate immersed boundary method and demonstrate its performance for a prototypical fluid-structure interaction problem, involving an immersed viscoelastic shell of finite thickness, studied over a broad range of Reynolds numbers. We consider two sets of material properties for the viscoelastic structure, including a case where the material properties of the coupled system are discontinuous at the fluid-structure interface. For both sets of material properties, the true solutions appear to possess sufficient smoothness for the method to converge at a second order rate for fully resolved computations. (c) 2005 Elsevier Inc. All rights reserved.