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

  • Authors:

  • Varun Shankar;Grady B. Wright;Aaron L. Fogelson;Robert M. Kirby

  • Affiliations:

  • School of Computing, Univ. of Utah, Salt Lake City, UT, USA;Department of Mathematics, Boise State Univ., Boise, ID, USA;Departments of Mathematics and Bioengineering, Univ. of Utah, Salt Lake City, UT, USA;School of Computing, Univ. of Utah, Salt Lake City, UT, USA

  • Venue:
  • Applied Numerical Mathematics
  • Year:
  • 2013

Quantified Score

Hi-index 0.00

Visualization

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.