A Parallel Dynamic-Mesh Lagrangian Method for Simulation of Flows with Dynamic Interfaces

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.