Preconditioning Navier Stokes Problem Dis cretized by Discrete Duality Finite Volume schemes

Preconditioning Navier-Stokes Problem Dis- cretized by Discrete Duality Finite Volume schemes 1 Sarah Delcourte * — Delphine Jennequin ** * NACHOS Project, INRIA Sophia-Antipolis, France, ** DASSAULT SYSTEM, Suresnes, France, ABSTRACT. We focus on the Discrete Duality Finite Volume (DDFV) method whose particular- ity is to allow the use of unstructured or nonconforming meshes. We discretize the non-linear Navier-Stokes problem, using the rotational formulation of the convection term, associated with the Bernoulli pressure. With an iterative algorithm, we are led to solve a saddle-point problem at each iteration. We give a particular interest to this linear problem by testing some precondi- tioners issued from finite elements, which we adapt to the DDFV method. KEYWORDS: finite volumes, preconditioners, saddle-point, Navier-Stokes equations 1. Introduction Let be ? an open bounded connected domain of R2 with a Lipschitz boundary denoted by ?. We consider the numerical resolution of the bidimensional stationnary Navier-Stokes equations: given f , find (u, p) such that 8 > < > : ??∆u+ u ·?u+?p = f in ?, ? · u = 0 in ?, u = 0 on ?, R ? p(x) dx = 0.

• uj ·


• ?ti2 ? ?ti1


• dual cells


• discrete duality


• navier stokes equations


• finite volume


• delaunay-voronoi meshes