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首页> 外文期刊>Journal of Computational Physics >Validation of a simple method for representing spheres and slender bodies in an immersed boundary method for Stokes flow on an unbounded domain
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Validation of a simple method for representing spheres and slender bodies in an immersed boundary method for Stokes flow on an unbounded domain

机译：浸没边界法中无界域上斯托克斯流的表示球体和细长体的简单方法的验证

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摘要

We test the efficacy of using a single Lagrangian point to represent a sphere, and a one-dimensional array of such points to represent a slender body, in a new immersed boundary method for Stokes flow. A numerical parameter, the spacing of the Eulerian grid, is used to determine the effective radius of the immersed sphere or slender body. Such representations are much less expensive computationally than those with two or three-dimensional meshes of Lagrangian points. To perform this test, we develop a numerical method to solve the discretized Stokes equations on an unbounded Eulerian grid which contains an arbitrary configuration of Lagrangian points that apply force to the fluid and that move with the fluid. We compare results computed with this new immersed boundary method to known results for spheres and rigid cylinders in Stokes flow in R-3. We find that, for certain choices of parameters, the interactions with the fluid of a single Lagrangian point accurately replicate those of a sphere of some particular radius, independent of the location of the point with respect to the Eulerian grid. The interactions of a linear array of Lagrangian points, for certain choices of parameters, accurately replicate those of a cylinder of some particular radius, independent of the position and orientation of the array with respect to the Eulerian grid. The effective radius of the sphere and the effective radius of the cylinder turn out to be related in a simple and natural way. Our results suggest recipes for choosing parameters that should be useful to practitioners. One surprising result is that one must not use too many Lagrangian points in an array. Another is that the approximate delta functions traditionally used in the immersed boundary method perform much better than higher order delta functions with the same support. (c) 2008 Elsevier Inc. All rights reserved.
机译：在斯托克斯流的一种新的浸入边界方法中，我们测试了使用单个拉格朗日点表示球体以及此类点的一维数组表示细长体的功效。数值参数，即欧拉网格的间距，用于确定沉浸球体或细长物体的有效半径。这样的表示在计算上比具有拉格朗日点的二维或三维网格的表示便宜得多。为了执行此测试，我们开发了一种数值方法来求解无界欧拉网格上离散的Stokes方程，该欧拉网格包含任意拉格朗日点配置，这些拉格朗日点向流体施加力并随流体移动。我们将用这种新的浸入边界方法计算的结果与R-3中斯托克斯流中的球体和刚性圆柱体的已知结果进行比较。我们发现，对于某些特定的参数选择，与单个拉格朗日点的流体的相互作用准确地复制了某个特定半径的球体的相互作用，而与点相对于欧拉网格的位置无关。对于某些参数选择，拉格朗日点的线性阵列的相互作用可以精确地复制具有某些特定半径的圆柱体的相互作用，而与阵列相对于欧拉网格的位置和方向无关。球的有效半径和圆柱的有效半径被证明以简单自然的方式相关。我们的结果提出了选择参数的方法，这些参数应该对从业者有用。一个令人惊讶的结果是，一个数组中不能使用太多的拉格朗日点。另一个是在浸没边界方法中传统使用的近似增量函数比具有相同支持的高阶增量函数要好得多。 （c）2008 Elsevier Inc.保留所有权利。

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