Radial basis function (RBF)‐based parametric models for closed and open curves within the method of regularized stokeslets. (26th May 2015)

• Record Type: Journal Article
• Authors: Shankar, Varun; Olson, Sarah D.
• Is Part Of: International journal for numerical methods in fluids. Volume 79:Number 6(2015)
• Page Start: 269
• Page End: 289
• Publication Date: 2015-05-26
• Subjects: radial basis functions -- regularized stokeslet -- parametric model -- immersed boundary; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4048
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: 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, is 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. Copyright © 2015 John Wiley & Sons, Ltd. Abstract : We present a comparison of spherical basis function (SBF) and radial basis function (RBF) parametric models for the modeling of open elastic curves immersed in viscous fluids. We present convergence results on static test problems using parametric collocation at Chebyshev and Mapped Chebyshev nodes. We then extend the method of regularized Stokeslets (MRS) with the SBF and RBF geometric models and present the result of time‐dependent fluid‐structure interaction simulations of both open and closed elastic structures.