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Title6th-order finite volume approximations for the stokes equations with a curved boundary
Author(s)Costa, Ricardo Daniel Pereira
Clain, Stéphane
Machado, Gaspar J.
Keywordsfinite volume
sixth-order approximation
Stokes equation
curved boundary
Issue date2015
PublisherAssociação Portuguesa de Mecânica Teórica, Aplicada e Computacional (APMTAC)
Abstract(s)A new solver for the Stokes equations based on the finite volume method is proposed using very accurate polynomial reconstruction to provide a 6th-order scheme. We face two main difficulties: the gradient-divergence duality where the divergence free condition will impose the pressure gradient, and on the other hand, we assume that the domain has a regular curved boundary. The last point implies that a simple approximation of the boundary using piecewise segment lines dramatically reduces the scheme accuracy to at most a second-order one. We propose a new and simple technology which enables to restore the full scheme accuracy based on a specific polynomial reconstruction only using the Gauss points of the curved boundary and does not require any geometrical transformation.
TypeConference paper
AccessOpen access
Appears in Collections:CMAT - Artigos em atas de conferências e capítulos de livros com arbitragem / Papers in proceedings of conferences and book chapters with peer review

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