On Efficient Multigrid Methods for Flows with Small Particles.

Boris Diskin

National Institute of Aerospace, 144 Research Drive, Hampton, VA 23666

Vasyl M. Harik
Swales Materials Group, Mail Stop 186A, NASA Langley Research Center, Hampton, VA 23681


Multiscale modeling of materials requires simulations of multiple levels of structural hierarchy. The computational efficiency of numerical methods becomes a critical factor for simulating large physical systems with highly desperate length scales. A flow with small particles represents a particularly difficult problem for efficient multigrid solution. These particles are often so small, occupying just a few points on the fine grid, that they cannot be properly incorporated into a coarse-grid formulation. Efficiency, i.e., convergence rate, of classical multigrid solvers deteriorates significantly because of the poor accuracy of coarse-grid approximations.
In this talk, I am planning to overview and evaluate several existing multigrid approaches to solving problems with small particles. A new multigrid method based on a modified local Galerkin coarsening scheme will be presented. Numerical tests confirm recovering the optimal (Laplace-like) efficiency in solution of practically interesting problems.