We present finite volume schemes for Stokes and Navier-Stokes equations. These schemes are based on the mixed finite volume introduced in Droniou and Eymard, Numer Math 105 (2006), 35-71, and can be applied to any type of grid (without orthogonality assumptions as for classical finite volume methods) and in any space dimension. We present numerical results on some irregular grids, and we prove, for both Stokes and Navier-Stokes equations, the convergence of the scheme toward a solution of the continuous problem.
|Pages (from-to)||137 - 171|
|Number of pages||35|
|Journal||Numerical Methods for Partial Differential Equations|
|Publication status||Published - 2009|