A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations
A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations
复制标题
离散δ函数的平滑技术及其在移动边界模拟中的浸入边界法的应用
DOI：
10.1016/j.jcp.2009.07.023
复制
发表时间：
2009-11-01
影响因子：
4.1
通讯作者：
He, Guo-Wei
中科院分区：
文献类型：
--
作者：
Yang, Xiaolei;Zhang, Xing;He, Guo-Wei
在浸入边界法中，复杂边界条件对流动的影响用体积力来表示。这种表示的问题是体积力在移动边界模拟中表现出非物理振荡。本文提出了一种离散δ函数的光滑化方法，以抑制体积力的非物理振荡。我们发现非物理振荡主要是由于正则离散δ函数的导数不满足一定的矩条件。证明了本文构造的光滑离散δ函数比常规δ函数具有高一阶导数。此外，光滑离散δ函数不仅满足前两个离散矩条件，而且其导数满足比规则函数高一阶的矩条件。平滑离散δ函数进行了测试的三个测试用例：一维热方程与移动奇异力，二维流动通过一个振荡的气缸，和涡激振动的气缸。数值算例表明，光滑离散δ函数能有效抑制体积力的非物理振荡，提高直接强迫浸入边界法在动边界模拟中的精度。(C)2009 Elsevier Inc. All rights reserved.
The effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods. The problem with this representation is that the volume force exhibits non-physical oscillations in moving boundary simulations. A smoothing technique for discrete delta functions has been developed in this paper to suppress the non-physical oscillations in the volume forces. We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions. It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones. Moreover, not only the smoothed discrete delta functions satisfy the first two discrete moment conditions, but also their derivatives satisfy one-order higher moment condition than the regular ones. The smoothed discrete delta functions are tested by three test cases: a one-dimensional heat equation with a moving singular force, a two-dimensional flow past an oscillating cylinder, and the vortex-induced vibration of a cylinder. The numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations. (C) 2009 Elsevier Inc. All rights reserved.