A new finite volume scheme is used for the approximation of the Navier-Stokes equations on general grids, including non matching grids. It is based on a discrete approximation of the weak form and on the definition of discrete gradient and divergence operators on each control volume. A sketch of the convergence proof is given, and the results of a numerical implementation on a non matching grids are shown. A byproduct is a finite volume scheme that is convergent for diffusion problems on general grids. To cite this article: R. Eymard, R. Herbin, C. R. Acad. Sci. Paris, Ser. I 344 (2007). © 2007 Académie des sciences.
Eymard, R., & Herbin, R. (2007). A new colocated finite volume scheme for the incompressible Navier-Stokes equations on general non matching grids. Comptes Rendus Mathematique, 344(10), 659–662. https://doi.org/10.1016/j.crma.2007.03.025