I will present a parallel dynamic mesh Lagrangian method for flows with dynamic interfaces that we have been developing at CMU. We take an aggressive approach to dynamic meshing by triangulating the propagating grid points at every time step using a scalable parallel Delaunay algorithm. Contrary to conventional wisdom, I will provide evidence that the costs of the geometric components (triangulation, coarsening, refinement, and partitioning) can be made small relative to the flow solver. For example, in a 2D simulation of 10 interacting viscous cells with 500,000 unknowns on 64 processors of a Cray T3E, dynamic meshing consumes less than 5% of a time step. Moreover, our experiments on up to 128 processors show that the computational geometry scales about as well as the flow solver.
I will discuss the application of our dynamic mesh Lagrangian method to microstructural simulation of blood flow, which is essentially a problem in modeling the interaction of fluid-solid mixtures. The model is termed "microstructural" because it distinguishes the fluid (blood plasma and hemoglobin) from the solid (cell membrane) at micron scales, and computes the momentum exchange between them -- in contradistinction to typical macroscopic models that treat blood as a homogeneous generalized Newtonian medium with phenomenological incorporation of cellular effects. I will conclude with a discussion of the prospects for microstructural modeling of blood flow at scales of interest in the design of artificial heart devices.
This work is joint with former graduate student Ivan Malcevic (now at GE); graduate students Eiris Borner, Judy Hill, and Clemens Kadow; CMU colleagues Guy Blelloch, Gary Miller, and Noel Walkington; and University of Pittsburgh Medical Center collaborator Jim Antaki.
Omar Ghattas is Professor of Civil & Environmental Engineering and Bioengineering, and Director of the Mechanics, Algorithms, and Computing Laboratory, at Carnegie Mellon University. He received his BS, MS, and PhD from Duke University in 1984, 1986, and 1988, respectively. He joined CMU in 1989 after serving as a postdoctoral research associate at Duke. He has been a visiting scientist at the Institute for Computer Applications in Science and Engineering (ICASE) at NASA-Langley Research Center; the Computer Science Research Institute (CSRI) at Sandia National Laboratories; and the Center for Applied Scientific Computing (CASC) at Lawrence Livermore National Laboratory. Ghattas has general research interests in high performance scientific computation, with particular emphasis on simulation and optimization of complex systems governed by fluid- and solid-mechanical phenomena.