A one-sided direct forcing immersed boundary method using moving least squares
A one-sided direct forcing immersed boundary method using moving least squares
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DOI：
10.1016/j.jcp.2021.110359
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发表时间：
2021-04
期刊：
影响因子：
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通讯作者：
Rahul Bale;A. Bhalla;Boyce E. Griffith;M. Tsubokura
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文献类型：
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作者：
Rahul Bale;A. Bhalla;Boyce E. Griffith;M. Tsubokura
提出了一种利用移动最小二乘法构造核函数的单边浸入边界法。所得到的核只在流固界面的一侧有效地将结构自由度与流体变量耦合。这减少了在使用各向同性核函数将结构与界面两侧的流体自由度耦合的IB模型中通常观察到的虚假反馈强迫和内部流动。本文开发的方法扩展了Vanella和Balaras(2009)[27]引入的原始MLS方法。先前的IB/MLS方法使用各向同性核函数，将边界两侧的流体变量耦合到界面自由度。原始的IB/MLS方法将MLS重建中通常使用的三次样条权值转换为满足特定离散矩条件的IB核函数。本文表明，同样的方法可以用于构造单侧核函数（核函数在MLS文献中被称为生成函数）。我们还研究了Peskin引入的核函数族的新方法的性能。结果表明，单侧MLS构造容易产生具有较大上突和下突的非单调插值核。我们提出了两种简单的权重转移策略来构造正单调的生成函数，这增强了所得IB方法的稳定性。使用基准案例测试了精度顺序，并在二维和三维空间上验证了单边IB/MLS模拟。这种新的IB/MLS方法也用于模拟Ahmed汽车模型上的流动，这突出了该方法对复杂工程流程建模的适用性。
This paper presents a one-sided immersed boundary (IB) method using kernel functions constructed via a moving least squares (MLS) method. The resulting kernels effectively couple structural degrees of freedom to fluid variables on only one side of the fluid-structure interface. This reduces spurious feedback forcing and internal flows that are typically observed in IB models that use isotropic kernel functions to couple the structure to fluid degrees of freedom on both sides of the interface. The method developed here extends the original MLS methodology introduced by Vanella and Balaras (2009) [27]. Prior IB/MLS methods have used isotropic kernel functions that coupled fluid variables on both sides of the boundary to the interfacial degrees of freedom. The original IB/MLS approach converts the cubic spline weights typically employed in MLS reconstruction into an IB kernel function that satisfies particular discrete moment conditions. This paper shows that the same approach can be used to construct one-sided kernel functions (kernel functions are referred to as generating functions in the MLS literature). We also examine the performance of the new approach for a family of kernel functions introduced by Peskin. It is demonstrated that the one-sided MLS construction tends to generate non-monotone interpolation kernels with large over- and undershoots. We present two simple weight shifting strategies to construct generating functions that are positive and monotone, which enhances the stability of the resulting IB methodology. Benchmark cases are used to test the order of accuracy and verify the one-sided IB/MLS simulations in both two and three spatial dimensions. This new IB/MLS method is also used to simulate flow over the Ahmed car model, which highlights the applicability of this methodology for modeling complex engineering flows.