Finite volume discretization and multilevel methods in flow problems

Abstract : This article is intended as a preliminary report on the implementation of a finite volume multilevel scheme for the discretization of the incompressible Navier-Stokes equations. As is well known, the use of staggered grids (e.g., MAC grids [M. Perić, R. Kessler and G. Scheuerer, Comput. & Fluids 16 (1988), no. 4, 389-403; Zbl 0672.76018]) is a serious impediment for the implementation of multilevel schemes in the context of finite differences. This difficulty is circumvented here by the use of a colocated finite volume discretization [S. Faure, J Laminie and R. Temam, "Colocated finite volume schemes for fluid flows'', submitted; M. Perić, R. Kessler and G. Scheuerer, op. cit.], for which the algebra of multilevel methods is much simpler than in the context of MAC type finite differences. The general ideas and the numerical simulations are presented in this article in the simplified context of a two-dimensional Burgers equation; the two- and three-dimensional Navier-Stokes equations, which introduce new difficulties related to the incompressibility condition and the time discretization, will be considered elsewhere [see S. Faure, J Laminie and R. Temam, op. cit.; "Finite volume discretization and multilevel methods for the Navier-Stokes equations'', in preparation].
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https://hal.archives-ouvertes.fr/hal-00730193
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Submitted on : Friday, September 7, 2012 - 5:44:35 PM
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Jacques Laminie, Sylvain Faure, Roger Temam. Finite volume discretization and multilevel methods in flow problems. Journal of Scientific Computing, Springer Verlag, 2005, 25 (1-2), pp.231-261. ⟨hal-00730193⟩

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