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TitleNew cell-vertex reconstruction for finite volume scheme : application to the convection-diffusion-reaction equation
Author(s)Costa, Ricardo Daniel Pereira
Clain, Stéphane
Machado, Gaspar J.
Finite volume method
Cell-vertex interpolation
Second-order accuracy
Issue date2014
JournalComputers and Mathematics With Applications
Abstract(s)The design of efficient, simple, and easy to code, second-order finite volume methods is an important challenge to solve practical problems in physics and in engineering where complex and very accurate techniques are not required. We propose an extension of the original Frink's approach based on a cell-to-vertex interpolation to compute vertex values with neighbor cell values. We also design a specific scheme which enables to use whatever collocation point we want in the cells to overcome the mass centre point restrictive choice. The method is proposed for two- and three-dimension geometries and a second-order extension time-discretization is given for time-dependent equation. A large number of numerical simulations are carried out to highlight the performance of the new method.
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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