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A study of different modeling choices for simulating platelets within the immersed boundary method

Authors
Journal
Applied Numerical Mathematics
0168-9274
Publisher
Elsevier
Volume
63
Identifiers
DOI: 10.1016/j.apnum.2012.09.006
Keywords
  • Immersed Boundary Methods
  • Radial Basis Functions
  • Fourier-Based Methods
  • Platelet Modeling
Disciplines
  • Computer Science
  • Engineering
  • Mathematics
  • Musicology

Abstract

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.

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