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TitleA very high-order finite volume method for the time-dependent convection-diffusion problem with Butcher tableau extension
Author(s)Clain, Stéphane
Machado, Gaspar J.
KeywordsFinite volume
Very high-order
Polynomial reconstruction
Butcher Tableau
Issue date2014
JournalComputers and Mathematics With Applications
Abstract(s)The time discretization of a very high-order finite volume method may give rise to new numerical difficulties resulting into accuracy degradations. Indeed, for the simple one-dimensional unstationary convection-diffusion equation for instance, a conflicting situation between the source term time discretization and the boundary conditions may arise when using the standard Runge-Kutta method. We propose an alternative procedure by extending the Butcher Tableau to overcome this specific difficulty and achieve fourth-, sixth- or eighth-order of accuracy schemes in space and time. To this end, a new finite volume method is designed based on specific polynomial reconstructions for the space discretization, while we use the Extended Butcher Tableau to perform the time discretization. A large set of numerical tests has been carried out to validate the proposed method.
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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