Unstructured multigrid techniques for relieving the
stiffness associated with high-Reynolds number
viscous flow simulations on extremely stretched grids are investigated.
One approach consists of employing a
semi-coarsening or directional-coarsening technique,
based on the directions of strong coupling within the mesh,
in order to construct more optimal coarse grid levels.
An alternate approach is developed which
employs directional implicit smoothing with
regular fully coarsened multigrid levels.
The directional implicit smoothing is obtained
by constructing implicit lines in the unstructured mesh
based on the directions of strong coupling.
Both approaches yield large increases in convergence
rates over the traditional explicit full-coarsening
multigrid algorithm. However, maximum benefits
are achieved by combining the two approaches
in a coupled manner into a single algorithm.
An order of magnitude increase in convergence rate over the
traditional explicit full-coarsening algorithm is demonstrated,
and convergence rates for high-Reynolds number viscous flows
comparable to those achieved for inviscid flows are obtained.
Furthermore, convergence rates which are insensitive to the
degree of anisotropy in the mesh are demonstrated on meshes
with aspect ratios up to 10,000:1.