基于径向基函数（RBF）的正则化Stokeslets方法中闭曲线和开曲线参数模型
Radial Basis Function (RBF)-based Parametric Models for Closed and Open Curves within the Method of Regularized Stokeslets
摘要：
正则化Stokeslets（MRS）方法是一种利用正则化基本解来计算粘性流体中物体引起的流动的数值方法，其惯性效应可以忽略。弹性物体被表示为拉格朗日结构，在流体上施加点力。结构上的力通常由弯曲或张力模型确定，先前使用有限差分近似计算。在本文中，我们研究了球基函数（SBF），径向基函数（RBF）和拉格朗日-切比雪夫参数模型来表示和计算力的弹性结构，可以表示为一个开放的曲线，纤毛和鞭毛的研究的动机。静态开放曲线的不同插值的评价误差，以及使用不同类型的聚类参数节点计算法线和二阶导数的误差，给出了一个开放的平面曲线的情况。我们确定，建立在集群节点上的SBF和RBF插值与拉格朗日-切比雪夫插值建模二次可微的开放平面曲线的竞争力。我们建议在MRS中使用SBF和RBF参数模型来评估和更新弹性结构。开放和封闭的弹性结构浸入在二维流体的结果，显示RBF-Stokeslets方法的有效性。
英文摘要：
The method of regularized Stokeslets (MRS) is a numerical approach using regularized fundamental solutions to compute the flow due to an object in a viscous fluid where inertial effects can be neglected. The elastic object is represented as a Lagrangian structure, exerting point forces on the fluid. The forces on the structure are often determined by a bending or tension model, previously calculated using finite difference approximations. In this paper, we study Spherical Basis Function (SBF), Radial Basis Function (RBF) and Lagrange-Chebyshev parametric models to represent and calculate forces on elastic structures that can be represented by an open curve, motivated by the study of cilia and flagella. The evaluation error for static open curves for the different interpolants, as well as errors for calculating normals and second derivatives using different types of clustered parametric nodes, are given for the case of an open planar curve. We determine that SBF and RBF interpolants built on clustered nodes are competitive with Lagrange-Chebyshev interpolants for modeling twice-differentiable open planar curves. We propose using SBF and RBF parametric models within the MRS for evaluating and updating the elastic structure. Results for open and closed elastic structures immersed in a 2D fluid are presented, showing the efficacy of the RBF-Stokeslets method.
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