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|Title:||6th-order finite volume approximations for the stokes equations with a curved boundary|
|Author(s):||Costa, Ricardo Daniel Pereira|
Machado, Gaspar J.
|Publisher:||Associação 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.|
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