论文标题
带有亚种植分辨率和改进数值稳定性的沉浸边界方法应用于史基斯流中的细长身体
An immersed boundary method with subgrid resolution and improved numerical stability applied to slender bodies in Stokes flow
论文作者
论文摘要
沉浸式边界方法是用于解决流体结构相互作用问题的数值和数学公式。它依赖于在欧拉流体网格上求解流体方程，并插入所得速度回到浸入式结构上。要解决细长的纤维，网格间距必须在光纤半径的顺序上，因此沿细丝所需的网格点的数量必须与纵横比的顺序相同。因此，使用IB方法对细长物体进行仿真可能是棘手的。提出了一种在Stokes流的背景下解决此问题的技术。结构的速度分为来自基础流体网格的组件，该分量比通常所需的较粗，并且与力成正比（拖放项）。设置阻力系数，以使单个球体完全表示在任意网格的网格上。阻力术语的隐式处理消除了通常与IB方法相关的一些稳定限制。尽管进行了测试，但可以在更粗的网格上获得相对精度的1-2位数字的测试，但这是丧失精度。测试其准确性和稳定性后，将方法应用于两个现实世界的例子：剪切流中的纤维和纤维悬浮液。这些示例表明，该方法可以重现现有结果，并就对齐纤维悬浮液的粘度做出合理的预测。
The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto immersed structures. To resolve slender fibers, the grid spacing must be on the order of the fiber radius, and thus the number of required grid points along the filament must be of the same order as the aspect ratio. Simulations of slender bodies using the IB method can therefore be intractable. A technique is presented to address this problem in the context of Stokes flow. The velocity of the structure is split into a component coming from the underlying fluid grid, which is coarser than normally required, and a component proportional to the force (a drag term). The drag coefficient is set so that a single sphere is represented exactly on a grid of arbitrary meshwidth. Implicit treatment of the drag term removes some of the stability restrictions normally associated with the IB method. This comes at a loss of accuracy, although tests are conducted that show 1-2 digits of relative accuracy can be obtained on coarser grids. After its accuracy and stability are tested, the method is applied to two real world examples: fibers in shear flow and a suspension of fibers. These examples show that the method can reproduce existing results and make reasonable predictions about the viscosity of an aligned fiber suspension.
