Numerical Results for a Colocated Finite-Volume Scheme on Voronoi Meshes for Navier-Stokes Equations
V.C. Mariani; E.E.M. Alonso; and S. Peters

doi:10.3970/cmes.2008.029.015
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 29, No. 1, pp. 15-28, 2008
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Keywords Newton method, Voronoi Diagram, Navier-Stokes equations, cavity.
Abstract An application of Newton's method for linearization of advective terms given by the discretization on unstructured Voronoi meshes for the incompressible Navier-Stokes equations is proposed and evaluated in this article. One of the major advantages of the unstructured approach is its application to very complex geometrical domains and the mesh is adaptable to features of the flow. Moreover, in this work comparisons with the literature results in bi-dimensional lid-driven cavities for different Reynolds numbers allow us to assess the numerical properties of the new proposed finite-volume scheme. Results for the components of the velocity, and the pressure collocated at the centers of the control volumes are presented and discussed. On the basis of the numerical experiments reported in this article is seems that the method under investigation has no difficulty at capturing the formation of primary and secondary vortices as Reynolds number increases.
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