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

Abstract

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.