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TitleA sixth-order finite volume scheme for the steady-state incompressible Stokes equations on staggered unstructured meshes
Author(s)Costa, Ricardo
Clain, Stéphane
Machado, Gaspar J.
KeywordsStokes equations
Incompressible fluid
Finite volume
High-order scheme
Issue date2017
PublisherAcademic Press
JournalJournal of Computational Physics
Abstract(s)We propose a new sixth-order finite volume scheme to solve the bidimensional linear steady-state Stokes problem on staggered unstructured meshes and complex geometries. The method is based on several classes of polynomial reconstructions to accurately evaluate the diffusive fluxes, the pressure gradient, and the velocity divergence. The main difficulty is to handle the div-grad duality to avoid numerical locking and oscillations. A new preconditioning technique based on the construction of a pseudo-inverse matrix is also proposed to dramatically reduce the computational effort. Several numerical simulations are carried out to highlight the performance of the new method.
AccessRestricted access (Author)
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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