Augmenting the immersed boundary method with Radial Basis Functions (RBFs) for the modeling of platelets in hemodynamic flows

Summary 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, although we antic...

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Bibliographic Details
Published in:International journal for numerical methods in fluids 2015-12, Vol.79 (10), p.536-557
Main Authors: Shankar, Varun, Wright, Grady B., Kirby, Robert M., Fogelson, Aaron L.
Format: Article
Language:English
Subjects:
Boundaries
Computational efficiency
Computer simulation
Convergence
Hemodynamics
immersed boundary methods
Mathematical models
platelet modeling
Platelets
Radial basis function
radial basis functions
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Summary:Summary 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, although 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 IB method and is well‐suited for modeling of platelets in hemodynamic flows. Copyright © 2015 John Wiley & Sons, Ltd. We present an application of our radial basis function (RBF)‐based parametric geometric model to the simulation of platelets in hemodynamic flows by the immersed boundary (IB) method. We test the convergence, area conservation and energy‐dissipation properties, and time‐step restrictions of our new RBF‐IB method on a fluid–structure interaction problem. We compare the computational cost of the RBF‐IB method with that of the traditional IB method for platelet simulations, and present the results of a platelet aggregation simulation accomplished with the RBF‐IB method.
ISSN:0271-2091
1097-0363
DOI:10.1002/fld.4061