A two-weight scheme for a time-dependent advection-diffusion problem
Naresh M. Chadha and
Niall Madden,
Abstract
We consider a family of two-weight finite difference
schemes for a time-dependent advection-diffusion problem.
For a given uniform grid-spacing in time and space, and for a fixed
value of advection and diffusion parameters, we demonstrate how to
optimally choose these weights by means of the notion of an equivalent
differential equation. We also provide a geometric interpretation
of the weights.
We present numerical results that demonstrate that the approach is
superior to other commonly used methods that also fit into the
framework of a two-weight scheme.
This material is based upon works supported by the Science Foundation
Ireland under Grant No. 08/RFP/CMS1205.
Published as: N.M. Chadha and N. Madden,
A two-weight scheme for a time-dependent advection-diffusion problem,
In C. Carmelo, J. L. Gracia, and F. J. Lisbona, (eds), BAIL 2010 -
Boundary and Interior Layers, Computational and Asymptotic Methods,
Vol 81 of Lect. Notes Comput. Sci. Eng., 99--108. Springer, 2011.