3:30 pm Thursday, December 2, 2010
ICES Seminar: A fast method for Stokesian particulate flows by George Biros (Georgia Tech) in ACES 2.302 (Avaya Auditorium)
I will introduce a fast method for simulation of Stokesian particulate flows, and discuss its application to blow flow simulation. The method is an extension to general non-axisymmetric vesicle flows in three dimensions of our earlier work on axisymmetric vesicles (S. K. Veerapaneni, D. Gueyffier, G. Biros and D. Zorin, "A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flow," Journal of Computational Physics, Vol. 228(19), 2009). Although the main components are similar in spirit to the axisymmetric case (spectral approximation in space, semi-implicit time-stepping scheme), important new elements need to be introduced for a full 3D method. In particular, spatial quantities are discretized using spherical harmonics, and quadrature rules for singular surface integrals need to be adapted to this case; an algorithm for surface reparameterization is needed to ensure stability of the time-stepping scheme, and spectral filtering is introduced to maintain reasonable accuracy while minimizing computational costs. To characterize the stability of the scheme and to construct preconditioners for the iterative linear system solvers used in the semi-implicit time-stepping scheme, we perform a spectral analysis of the evolution operator on the unit sphere. By introducing these algorithmic components, we obtain a time-stepping scheme that, in our numerical experiments, is unconditionally stable. I present results to analyze the overall cost and convergence rates of the method. I will also report on numerical experiments that have resulted in new understanding of viscoelastic rheological effects, including shape equilibria in shear flows, migration in flows with "curvature," and pattern formation in confined flows. This work is joint with Shravan K. Veerapaneni, Abtin Rahimian, and Denis Zorin. Submitted by
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