 
Summary: A PARALLEL DYNAMICMESH LAGRANGIAN METHOD
FOR SIMULATION OF FLOWS WITH DYNAMIC INTERFACES
JAMES F. ANTAKIy, GUY E. BLELLOCHz, OMAR GHATTASx
IVAN MALCEVI´Cx, GARY L. MILLER , AND NOEL J. WALKINGTONk
Abstract. Many important phenomena in science and engineering, including our motivating problem of microstructural blood flow, can be
modeled as flows with dynamic interfaces. The major challenge faced in simulating such flows is resolving the interfacial motion. Lagrangian
methods are ideally suited for such problems, since interfaces are naturally represented and propagated. However, the material description of
motion results in dynamic meshes, which become hopelessly distorted unless they are regularly regenerated. Lagrangian methods are particularly
challenging on parallel computers, because scalable dynamic mesh methods remain elusive. Here, we present a parallel dynamic mesh Lagrangian
method for flows with dynamic interfaces. We take an aggressive approach to dynamic meshing by triangulating the propagating grid points at
every timestep using a scalable parallel Delaunay algorithm. Contrary to conventional wisdom, we show 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 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 64 processors show that the computational geometry scales about as well as the flow solver. Therefore we anticipate that
overall scalability on larger problems will be as good as the flow solver's.
1. Motivation. Flows with dynamic interfaces arise in many fluidsolid and fluidfluid interaction problems, and
are among the most difficult computational problems in continuum mechanics. Examples abound in the aerospace,
automotive, biomedical, chemical, marine, materials, and wind engineering sciences. These include largeamplitude
vibrations of such flexible aerodynamic components as high aspect ratio wings and blades; flows of mixtures and
slurries; windinduced deformation of towers, antennas, and lightweight bridges; hydrodynamic flows around offshore
