A two-weight scheme for a time-dependent advection-diffusion problem
Chadha, Naresh M.
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Naresh M. Chadha and Niall Madden (2011) 'A two-weight scheme for a time-dependent advection-diffusion problem'. Lecture Notes In Computational Science And Engineering, 85 :99-108.
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.