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

Resumen

Abstract In this paper we have developed a finite volume ENO scheme, third‐order accurate, 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 scheme and a Hermite procedure which avoids the excessive smearing in regions with sharpconcentration fronts and the overcompression effects produced by the modified ENO technique. Thesemodifications do not affect the non‐oscillatory philosophy since we compare divided differences inthe modified ENO scheme and in the evaluation of the Hermite polynomial derivatives. Numericalresults compare favourably with their respective analytical solutions. Copyright © 2001 John Wiley & Sons, Ltd.