A Study of Different Modeling Choices For Simulating Platelets Within the Immersed Boundary Method

TL;DR

This paper compares different mathematical representations for modeling platelets in fluid-structure interaction simulations using the Immersed Boundary method, focusing on accuracy and computational efficiency.

Contribution

It introduces and evaluates radial basis functions and Fourier-based models as alternatives to traditional piecewise-linear approximations for platelet simulation.

Findings

Radial basis functions reduce geometric modeling errors.

Fourier-based models improve force computation accuracy.

Trade-offs identified between computational cost and accuracy.

Abstract

The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid-structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a Lagrangian representation of structural objects. Operators are defined for transmitting information (forces and velocities) between these two representations. Most IB simulations represent their structures with piecewise-linear approximations and utilize Hookean spring models to approximate structural forces. Our specific motivation is the modeling of platelets in hemodynamic flows. In this paper, we study two alternative representations - radial basis functions (RBFs) and Fourier-based (trigonometric polynomials and spherical harmonics) representations - for the modeling of platelets in two and three dimensions within the IB framework, and compare our results with the traditional piecewise-linear approximation methodology. For different representative shapes, we examine the geometric modeling errors (position and normal vectors), force computation errors, and computational cost and provide an engineering trade-off strategy for when and why one might select to employ these different representations.