SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page B847-B868, January 2020.
The immersed boundary (IB) 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.

中文翻译：

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具有细网格分辨率和改进的数值稳定性的沉浸边界方法在斯托克斯流中的细长体中的应用

SIAM科学计算杂志，第42卷，第4期，第B847-B868页，2020年1月。
浸入边界（IB）方法是解决流固耦合问题的数值和数学公式。它依赖于求解欧拉流体网格上的流体方程，并将所得速度插值回浸入式结构中。为了分解纤细的纤维，网格间距必须在纤维半径的数量级上，因此沿着长丝的所需网格点的数量必须与纵横比相同。因此，使用IB方法进行细长体的模拟可能很棘手。提出了一种在斯托克斯流环境中解决该问题的技术。结构的速度分为一个来自下面的流体网格的分量，该分量比正常情况下要粗糙，一个与力成比例的分量（一个阻力项）。设置阻力系数，以便在任意网格宽度的网格上精确表示单个球体。拖曳项的隐式处理消除了通常与IB方法相关的一些稳定性限制。尽管进行的测试表明可以在较粗的网格上获得1--2位数的相对精度，但这会损失准确性。在测试其准确性和稳定性之后，将该方法应用于两个实际示例：剪切流中的纤维和纤维的悬浮液。这些示例表明，该方法可以重现现有结果，并可以对对齐的纤维悬浮液的粘度做出合理的预测。尽管进行的测试表明可以在较粗的网格上获得1--2位数的相对精度，但这会损失准确性。在测试其准确性和稳定性之后，将该方法应用于两个实际示例：剪切流中的纤维和纤维的悬浮液。这些示例表明，该方法可以重现现有结果，并可以对对齐的纤维悬浮液的粘度做出合理的预测。尽管进行的测试表明可以在较粗的网格上获得1--2位数的相对精度，但这会损失准确性。在测试其准确性和稳定性之后，将该方法应用于两个实际示例：剪切流中的纤维和纤维的悬浮液。这些示例表明，该方法可以重现现有结果，并可以对对齐的纤维悬浮液的粘度做出合理的预测。