A finite volume method with a modified ENO scheme using a Hermite interpolation to solve advection-diffusion equations

In this paper we have developed a finite volume ENO scheme, third-order acc urate, based on cell averages and a TVD Runge-Kutta time discretization to solve advection-diffusion equations in a two-dimensional spatial domain. We have designed a special interpolating polynomial based on a modified ENO s cheme and a Hermite procedure which avoids the excessive smearing in region s with sharp concentration fronts and the overcompression effects produced by the modified ENO technique. These modifications do not affect the non-os cillatory philosophy since we compare divided differences in the modified E NO scheme and in the evaluation of the Hermite polynomial derivatives. Nume rical results compare favourably with their respective analytical solutions . Copyright (C) 2001 John Wiley & Sons, Ltd.