Chadha and Madden - "A two-weight scheme for a time-dependent advection-diffusion problem"

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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.

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