Dr. Roland Glowinski Cullen Professor of Mathematics and Mechanical Engineering
University of Houston

Title: Particle clustering in rotating cylinders
Abstract: In this lecture, we return, in some sense, to one of the Magnus Lectures given some years ago by Tom Mullin, and offer a computational science perspective to this former speaker exciting presentation. Indeed, in this lecture, we investigate computationally the clustering of rigid solid particles in rotating cylinders containing an incompressible viscous fluid, for particle populations ranging from 10 to more than 100. We study in particular the influence of the angular velocity on these clustering phenomena. The presentation will be illustrated by animations visualizing these truly threedimensional phenomena, which to the best of our knowledge are not fully understood, as of today. The presentation will include a description of the numerical methodology retained for the solution of the differential system coupling the NavierStokes equations modeling the flow, with the NewtonEuler equations describing the particle motion.
Prior to the seminar, please join Dr. Glowinski and the Department of Mathematics for coffee in Weber 117 at 3:30 pm.
Title: Adventures in Computing
Abstract: The main goal of this lecture is to present real life situations where Applied & Computational Mathematics can significantly contribute, via numerical simulation inparticular, to progress beneficial to Society. This presentation will be illustrated by examples related to real life applications, in CardioVascular Medicine in particular, an area where methods developed by the speaker have found applications.
Please join Dr. Glowinski at a reception following his lecture.
Title: A LeastSquares/Fictitious Domain Method for Linear Elliptic Boundary Value Problems with Neumann or Robin Boundary Conditions: A Virtual Control Approach
Abstract: Motivated by the numerical simulation of particulate flow with slipboundary conditions at the interface fluidparticles, we are going to address in this lecture the solution of the following elliptic problem
(1)
(2)
by a fictitious domain method (new to the best of our knowledge); in (1), (2), Ω denotes a bounded domain of Rd and ω a subdomain of Ω. Our approach relies essentially on the transformation of (1), (2) in a (virtual) control problem (in the sense of J.L. Lions), involving an extension of (1) (completed by u =g0 on ∂Ω) on the whole Ω, the restriction of the extended solution to being the solution of (1), (2). From an algorithmic point of view, one solves the control problem by a leastsquares/conjugate gradient algorithm whose finite element implementation is rather easy, even if the mesh associated with Ω does not match the geometry of ω.
Numerical experiments, including the generalization to the solution of parabolic equations with moving ω, suggest optimal orders of convergence.
Prior to the seminar, please join Dr. Glowinski and the Department of Mathematics for coffee in Weber 117 at 3:30 pm.
The Arne Magnus Lectures are given annually in the Department of Mathematics at Colorado State University in honor of Dr. Arne Magnus, our friend and colleague for 25 years.
The lectures are supported by the Arne Magnus Lecture Fund and the Albert C. Yates Endowment in Mathematics.
Contributions to the Magnus Fund are greatly appreciated and may be made through the Department of Mathematics. Please contact Sheri Hofeling (hofeling@math.colostate.edu) at at (970)4917047 for specific information.
All lectures are free and open to the public.