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Collocated finite volume schemes for the simulation of natural convective flows on unstructured meshes. (English) Zbl 1133.76028

Summary: We describe here a collocated finite volume scheme that was recently developed for the numerical simulation of the incompressible Navier-Stokes equations on unstructured meshes, in two or three space dimensions. We recall its convergence in the case of linear Stokes equations, and we prove a convergence theorem for the case of Navier-Stokes equations under Boussinesq hypothesis. We then present several numerical studies. A comparison between a cluster-type stabilization technique and the more classical Brezzi-Pitkäranta method is performed, the numerical convergence properties are presented on both analytical solutions and benchmark problems, and the scheme is finally applied to the study of natural convection between two eccentric cylinders.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76R10 Free convection
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