Éditeur(s) : HAL CCSD Global Science Press
Résumé : International audience
In this paper, the authors present two different time-discretization schemes combined with a finite-volume space discretization for the incompressible Navier-Stokes equations. They show that the collocated space discretization, usually used with a projection method, can also be extended to other time discretizations over previous projection methods, like the splitting methods. The main advantage of this splitting method is that the pressure approximation is truly of second order. In the first and second parts of this article, two different time-discretization schemes are considered with a collocated space discretization and it is explained how the unknown can be correctly coupled. Numerical simulations are presented in the last part. Tests of spatial and time accuracies are made. The numerical results when the Navier-Stokes problem is solved are shown, in the model problem of the driven cavity.
ISSN: 1815-2406

hal-00730191
https://hal.archives-ouvertes.fr/hal-00730191

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
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].
ISSN: 0885-7474

hal-00730193
https://hal.archives-ouvertes.fr/hal-00730193