Saddle point preconditioners for linearized Navier–Stokes equations discretized by a finite volume method

We are interested in the numerical resolution of the Navier–Stokes problem discretized by a finite-volume method, named DDFV (Discrete Duality Finite Volume method), whose particularity is to work with unstructured and non-conforming meshes. The initial non-linear system may be transformed into a sequence of Oseen-type problems in rotational form which take the form of saddle-point problems. Some efficient preconditioners have been studied when this kind of Oseen-type problem is discretized by a finite element or a finite difference method but they have not been extended to matrices obtained from finite volume methods. In the present work, we will focus on the adaptation of the most efficient preconditioning techniques to our finite-volume scheme.