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About SIAM
The Society for Industrial and Applied Mathematics (SIAM) aims to advance the application of mathematics and computational science to engineering, industry, science, and society.

About the Chapter
The SIAM student chapter at the University of Illinois at Urbana-Champaign was created in the fall of 2006, is supported by the SIAM parent organization, and is a registered student organization at UIUC.

SIAM Student Chapter Colloquium

Simulation of cellular blood flow in complex geometry microvessels

Prof. Jonathan Freund, University of Illinois at Urbana-Champaign


  • Monday 9/28/2009 at 1PM
  • Siebel Center 4405


A spectral boundary integral method for simulating large numbers of blood cells flowing in complex geometries is developed and demonstrated. The blood cells are modeled as finite-deformation linear elastic membranes containing a higher viscosity fluid than the surrounding plasma, but the solver itself is independent of the particular constitutive model employed for the cell membranes. The surface integrals developed for solving the viscous flow, and thereby the motion of the massless membrane, is evaluated using an O(N log N) particle-mesh Ewald (PME) approach. The cell shapes, which can become highly distorted under physiologic conditions, are discretized with spherical harmonics. The resolution of these global basis functions is, of course, excellent, but more importantly they facilitate an approximate de-aliasing rocedure that stabilizes the simulations without adding any numerical dissipation or restricting the permissible numerical time step. Complex geometry no-slip boundaries are included using a constraint method that is coupled into an implicit system that is solved as part of the time advancement routine. The implementation is verified against solutions for axisymmetric flows reported in the literature. It is also used to simulate flow of blood cells at 30% volume fraction in tubes between 4.9um and 16.9um in diameter. For these, it is shown to reproduce the well-known non-monotonic dependence of the effective viscosity on the tube diameter. It is also demonstrated for the flow of cells over a spherical occlusion in a microvessel, transport of a white blood cell, and for a triply branched microvessel network.

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Siebel Center for Computer Science
University of Illinois at Urbana-Champaign
201 N. Goodwin Ave.
Urbana, IL 61801

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