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 nite volume ENO scheme, third-order accurate, based on cell averages and a TVD Runge{Kutta time discretization to solve advection{di usion equations in a two- dimensional spatial domain. We have designed a special interpolating polynomial based on a modi ed ENO scheme and a Hermite procedure which avoids the excessive smearing in regions with sharp concentration fronts and the overcompression e ects produced by the modi ed ENO technique. These modi cations do not a ect the non-oscillatory philosophy since we compare divided di erences in the modi ed ENO scheme and in the evaluation of the Hermite polynomial derivatives. Numerical results compare favourably with their respective analytical solutions