Abstract This paper presents an immersed boundary (IB) method for fluid–structure–acoustics interactions involving large deformations and complex geometries. In this method, the fluid dynamics is solved by a finite difference method where the temporal, viscous and convective terms are respectively discretized by the third-order Runge–Kutta scheme, the fourth-order central difference scheme and a fifth-order W/TENO (Weighted/Targeted Essentially Non-oscillation) scheme. Without loss of generality, a nonlinear flexible plate is considered here, and is solved by a finite element method based on the absolute nodal coordinate formulation. The no-slip boundary condition at the fluid–structure interface is achieved by using a diffusion-interface penalty IB method. With the above proposed method, the aeroacoustics field generated by the moving boundaries and the associated flows are inherently solved. In order to validate and verify the current method, several benchmark cases are conducted: acoustic waves scattered from a stationary cylinder in an inviscid quiescent flow, sound generation by a stationary and a rotating cylinder in a uniform flow, sound generation by an insect in hovering flight, deformation of a red blood cell induced by acoustic waves and acoustic waves scattered by a stationary sphere. The comparison of the sound scattered by a cylinder shows that the present IB–WENO scheme, a simple approach, has an excellent performance which is even better than the implicit IB–lattice Boltzmann method. For the sound scattered by a sphere, the IB–TENO scheme has a lower dissipation compared with the IB–WENO scheme. Applications of this technique to model fluid–structure-acoustics interactions of flapping foils mimicking an insect wing section during forward flight and flapping foil energy harvester are also conducted, considering the effects of foil shape and flexibility. The difference of the force and sound generations of the foils are compared. For wing during forward flight, the results show that flexible wing generates larger thrust with higher acoustic pressure. In terms of the energy harvester, the current results show that the geometrical shape has no significant effects on the force and sound generation, and the flexibility of the plate tends to deteriorate the power extraction efficiency. The flexible plate also induces larger fluctuating pressure at the frequency of 2 f ( f is the flapping frequency) and weaker sound at the frequencies of f and 3 f . The successful validations and applications show that the IB method handled by delta function, whose accuracy is generally lower than that of the internal flow solver, is accurate for predicting the dilatation and acoustics, and thus is an attractive alternative for modeling fluid–structure–acoustics interactions involving large deformations and complex geometries.

中文翻译：

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涉及大变形和复杂几何形状的流体-结构-声学相互作用的浸入边界方法

摘要 本文提出了一种用于涉及大变形和复杂几何形状的流体-结构-声学相互作用的浸入边界 (IB) 方法。在该方法中，流体动力学通过有限差分法求解，其中时间项、粘性项和对流项分别通过三阶 Runge-Kutta 格式、四阶中心差分格式和五阶 W/TENO 离散化（加权/目标基本非振荡）方案。不失一般性，这里考虑非线性柔性板，并通过基于绝对节点坐标公式的有限元方法求解。流固界面的无滑移边界条件是通过使用扩散界面惩罚 IB 方法实现的。通过上面提出的方法，由移动边界和相关流动产生的气动声学场得到了固有的解决。为了验证和验证当前​​方法，进行了几个基准案例：从静止圆柱体在无粘性静止流中散射的声波，均匀流中静止圆柱体和旋转圆柱体的声音，悬停昆虫的声音。飞行，由声波和静止球体散射的声波引起的红细胞变形。通过圆柱体散射声音的比较表明，本 IB-WENO 方案，一种简单的方法，具有优异的性能，甚至优于隐式 IB-格子 Boltzmann 方法。对于球体散射的声音，IB-TENO 方案与 IB-WENO 方案相比具有更低的耗散。考虑到箔片形状和柔韧性的影响，还进行了该技术在模拟向前飞行过程中模仿昆虫翅膀部分的扑翼箔片和扑翼箔片能量收集器的流体-结构-声学相互作用建模的应用。比较了箔的力和声音产生的差异。对于前飞过程中的机翼，结果表明柔性机翼产生更大的推力和更高的声压。就能量收集器而言，目前的结果表明，几何形状对力和声音的产生没有显着影响，板的柔韧性往往会降低功率提取效率。柔性板还在 2 f 频率（f 是拍动频率）处产生较大的波动压力，并在 f 和 3 f 频率处产生较弱的声音。成功的验证和应用表明，由 delta 函数处理的 IB 方法，其精度通常低于内部流动求解器的精度，对于预测膨胀和声学是准确的，因此是流体-结构-声学建模的一种有吸引力的替代方法涉及大变形和复杂几何形状的相互作用。