# American Institute of Mathematical Sciences

June  2011, 15(4): 1065-1076. doi: 10.3934/dcdsb.2011.15.1065

## Boundary integral and fast multipole method for two dimensional vesicle sets in Poiseuille flow

 1 Laboratoire d'Ingénierie Mathématique, Ecole Polytechnique de Tunisie, Université de Carthage, B.P. 743 - 2078 La Marsa, Tunisia 2 Laboratoire Interdisciplinaire de Physique, 140, rue de la Physique, 38402 Saint Martin d'Hères, France, France

Received  January 2010 Revised  March 2010 Published  March 2011

Two dimensional numerical simulations of sets of vesicles in a Poiseuille flow are presented. Vesicles are a simple model to describe the dynamics of red cells in blood flow. At the scale of vesicles, the hydrodynamics is well described by the Stokes equation, whose linearity allows the use of Green's functions via the boundary integral method. This is coupled with the fast multipole method to acheive optimal scaling with respect to the number of discretization points. Results are presented for sets of different number of vesicles, showing their spatial organization. Vesicles assume a parachute-like shape and align one to the other in the centre of the parabolic profile. The relative distances depend on the total number of vesicles and on the position in the set.
Citation: Hassib Selmi, Lassaad Elasmi, Giovanni Ghigliotti, Chaouqi Misbah. Boundary integral and fast multipole method for two dimensional vesicle sets in Poiseuille flow. Discrete & Continuous Dynamical Systems - B, 2011, 15 (4) : 1065-1076. doi: 10.3934/dcdsb.2011.15.1065
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