Under-resolution, Adaptive Mesh Refinement, and Computing
                 Singularities in Boussinesq Convection

                                   by

                             Michael Minion

               JWB 335, 3:15pm  Monday, February 26, 1996

                                Abstract

  There are many numerical methods for incompressible flow that allow
  the user to compute stable solutions of flows for which the smallest
  physical scales are not resolved.  It is important to be able to
  recognize and if possible avoid any unphysical effects the
  under-resolution may cause.

  Numerical studies will be presented showing that a wide variety of
  numerical methods produce spurious vortices when under-resolving
  strong shear layers. Use of local grid refinement can remedy the
  problem of under-resolution, but the question of where and when to add
  resolution is not well understood.  Examples showing how poorly
  implemented grid refinement can actually hurt calculations will be
  shown.

  These topics take on fundamental importance if one is attempting to
  extract information about a physical system from marginally resolved
  or under-resolved numerical computations.  As an example, numerical
  experiments designed to address the open question of whether or not
  finite time singularities can occur in 2-D Boussinesq convection will
  be discussed.

Requests for preprints and reprints: rmm@math.utah.edu, Attn: Michael Minion
This source can be found at http://www.math.utah.edu/research/