The volume-filtering immersed boundary method
The volume-filtering immersed boundary method
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DOI：
10.1016/j.jcp.2023.112136
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发表时间：
2022-10
期刊：
影响因子：
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通讯作者：
H. Dave;M. Herrmann;M. H. Kasbaoui
中科院分区：
文献类型：
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作者：
H. Dave;M. Herrmann;M. H. Kasbaoui
我们提出了一种新的框架来处理静态和运动的浸没边界(IB)。在这种名为体积滤波浸没边界(VFIB)的方法中，输运方程是通过对Navier-Stokes方程进行滤波并考虑固液界面上的应力而得到的。其结果是，通常应用于固体-流体界面的边界条件被转换为应用于过滤后的输运方程右侧的体力。在此方法中，滤镜宽度充当控制分辨率级别的参数。如果过滤器的宽度远小于界面的特征波纹尺度，则认为IB分辨率很好。这种IB方法有几个创新之处。首先，它阐明了在IB内部求解输运方程时产生的内部流动的作用。我们证明，为了得到准确的力，必须分离外部和内部流体产生的应力，并提供了一种这样做的方法。其次，我们证明了与边界上的拉格朗日强迫点相关的体积依赖于曲面的局部拓扑。我们提供了一种使用界面的三角形镶嵌和表面密度函数来计算这些体积的直接方法。第三，我们提供了一种计算固体体积分数的有效方法，从而能够对内部/外部单元进行标记。该体积分数也包括在将外部流体引起的应力与总应力分离的过程中。第四，我们指出了将VFIB方法扩展到包含IBS的大涡模拟的途径。最后，我们将VFIB应用于二维和三维静态和运动IBS的数值试验。与以往的IB方法相比，我们的结果有了很大的改善。此外，我们测试了几个过滤器核，并表明，对于分辨率较好的IBS，核的选择几乎不起作用。
We present a novel framework to deal with static and moving immersed boundaries (IB) based on volume-filtering. In this strategy, called Volume-Filtering Immersed Boundary (VFIB) method, transport equations are derived by filtering the Navier-Stokes equations and accounting for stresses at the solid-fluid interface. The result is that boundary conditions that normally apply on the solid-fluid interface are transformed into bodyforces that apply on the right-hand side of the filtered transport equations. In this method, the filter width acts as a parameter that controls the level of resolution. The IB is considered well-resolved if the filter width is much smaller than the characteristic corrugation scale of the interface. There are several innovations in this IB method. First, it sheds light on the role of the internal flow which arises when the transport equations are solved inside the IB. We show that, it is essential to separate stresses due to the external and internal fluids in order to get accurate forces, and provide a method to do so. Second, we show that the volumes associated with Lagrangian forcing points on the boundary depend on the local topology of the surface. We provide a straightforward way to compute these volumes using a triangle tessellation of the interface and the surface density function. Third, we provide an efficient procedure to compute the solid volume fraction, thus, enabling tagging interior/exterior cells. This volume fraction is also involved in the procedure to separate stresses due to the external fluid from the total stresses. Fourth, we show a path forward to extend the VFIB method to Large Eddy Simulations involving IBs. Lastly, we apply the VFIB in several numerical tests involving two- and three-dimensional static and moving IBs. We show greatly improved results compared to prior IB methods. Further, we test several filter kernels and show that, for well-resolved IBs, the choice of the kernel plays little role.