The goal of this paper is to examine the evaluation of interfacial stresses using a standard, finite difference based, immersed boundary method (IMBM). This calculation is not trivial for two fundamental reasons. First, the immersed boundary is represented by a localized boundary force which is distributed to the underlying fluid grid by a discretized delta function. Second, this discretized delta function is used to impose a spatially averaged no-slip condition at the immersed boundary. These approximations can cause errors in interpolating stresses near the immersed boundary.To identify suitable methods for evaluating stresses, we investigate three model flow problems at very low Reynolds numbers. We compare the results of the immersed boundary calculations to those achieved by the boundary element method (BEM). The stress on an immersed boundary may be calculated either by direct evaluation of the fluid stress (FS) tensor or, for the stress jump, by direct evaluation of the locally distributed boundary force (wall stress or WS). Our first model problem is Poiseuille channel flow. Using an analytical solution of the immersed boundary formulation in this simple case, we demonstrate that FS calculations should be evaluated at a distance of approximately one grid spacing inward from the immersed boundary. For a curved immersed boundary we present a procedure for selecting representative interfacial fluid stresses using the concepts from the Poiseuille flow test problem. For the final two model problems, steady state flow over a bump in a channel and unsteady peristaltic pumping, we present an 'exclusion filtering' technique for accurately measuring stresses. Using this technique, these studies show that the immersed boundary method can provide reliable approximations to interfacial stresses.

中文翻译：

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使用浸入边界法评估界面流体动态应力。

本文的目的是使用标准的、基于有限差分的浸入边界法 (IMBM) 来检查界面应力的评估。由于两个基本原因，这种计算并非微不足道。首先，浸入边界由局部边界力表示，该力通过离散化 delta 函数分布到底层流体网格。其次，这个离散的 delta 函数用于在浸没边界处施加空间平均的无滑移条件。这些近似值可能会导致浸入边界附近的应力内插错误。为了确定评估应力的合适方法，我们研究了雷诺数非常低的三个模型流动问题。我们将浸入边界计算的结果与边界元法 (BEM) 的结果进行比较。浸入边界上的应力可以通过直接评估流体应力 (FS) 张量来计算，或者对于应力跳跃，可以通过直接评估局部分布的边界力（壁应力或 WS）来计算。我们的第一个模型问题是 Poiseuille 通道流。在这个简单的情况下使用浸入边界公式的解析解，我们证明应该在从浸入边界向内大约一个网格间距的距离处评估 FS 计算。对于弯曲的浸入边界，我们提出了使用泊肃叶流测试问题中的概念选择代表性界面流体应力的程序。对于最后两个模型问题，通道中凸起的稳态流动和非稳态蠕动泵送，我们提出了“排除过滤” 准确测量应力的技术。使用这种技术，这些研究表明浸入边界法可以提供可靠的界面应力近似值。