Colocated finite volume schemes for fluid flows

Jacques Laminie (1) , Sylvain Faure (2) , Roger M. Temam (3)

1 LAMIA - Laboratoire de Mathématiques Informatique et Applications
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 ISC - Institute for Scientific Computing and Applied Mathematics

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.

Domaines: Analyse numérique [math.NA]

Jacques Laminie, Sylvain Faure, Roger M. Temam. Colocated finite volume schemes for fluid flows. Communications in Computational Physics, 2008, 4 (1), pp.1 - 25. ⟨hal-00730191⟩