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A finite volume method with a modified ENO scheme using a Hermite interpolation to solve advection diffusion equations
Author(s) -
Balaguer A.,
Conde C.,
López J. A.,
Martínez V.
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.123
Subject(s) - hermite polynomials , finite volume method , hermite interpolation , discretization , mathematics , advection , interpolation (computer graphics) , polynomial , diffusion , scheme (mathematics) , mathematical analysis , computer science , physics , mechanics , motion (physics) , thermodynamics , artificial intelligence
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.