Radial Basis Function (RBF)-based Parametric Models for Closed and Open Curves within the Method of Regularized Stokeslets

摘要

The method of regularized Stokeslets (MRS) is a numerical approach usingregularized fundamental solutions to compute the flow due to an object in aviscous fluid where inertial effects can be neglected. The elastic object isrepresented as a Lagrangian structure, exerting point forces on the fluid. Theforces on the structure are often determined by a bending or tension model,previously calculated using finite difference approximations. In this paper, westudy Spherical Basis Function (SBF), Radial Basis Function (RBF) andLagrange-Chebyshev parametric models to represent and calculate forces onelastic structures that can be represented by an open curve, motivated by thestudy of cilia and flagella. The evaluation error for static open curves forthe different interpolants, as well as errors for calculating normals andsecond derivatives using different types of clustered parametric nodes, aregiven for the case of an open planar curve. We determine that SBF and RBFinterpolants built on clustered nodes are competitive with Lagrange-Chebyshevinterpolants for modeling twice-differentiable open planar curves. We proposeusing SBF and RBF parametric models within the MRS for evaluating and updatingthe elastic structure. Results for open and closed elastic structures immersedin a 2D fluid are presented, showing the efficacy of the RBF-Stokeslets method.