We present a new computational method by extending the Immersed Boundary (IB) method with a geometric model based on parametric Radial Basis Function (RBF) interpolation of the Lagrangian structures. Our specific motivation is the modeling of platelets in hemodynamic flows, though we anticipate that our method will be useful in other applications involving surface elasticity. The efficacy of our new RBF-IB method is shown through a series of numerical experiments. Specifically, we test the convergence of our method and compare our method with the traditional IB method in terms of computational cost, maximum stable time-step size and volume loss. We conclude that the RBF-IB method has advantages over the traditional Immersed Boundary method, and is well-suited for modeling of platelets in hemodynamic flows.
This is an author-produced, peer-reviewed version of this article. The final, definitive version of this document can be found online at International Journal for Numerical Methods in Fluids, published by John Wiley & Sons, Inc. Copyright restrictions may apply. doi: 10.1002/fld.4061
Shankar, Varun; Wright, Grady B.; Kirby, Robert M.; and Fogelson, Aaron L.. (2015). "Augmenting the Immersed Boundary Method with Radial Basis Functions (RBFs) for the Modeling of Platelets in Hemodynamic Flows". International Journal for Numerical Methods in Fluids, 79(10), 536-557. https://doi.org/10.1002/fld.4061