Reliable flow solver based on the high order control volume Padé-type differences

The problem of reliable implementation of the high order control volume Pade-type difference schemes for the numerical simulation of the incompressible fluid flows in complex geometries is considered. We analyze the following issues: (1) the formulation in the curvilinear coordinates; (2) the constructive grid non-degeneracy conditions which allow to build the barrier variational grid generator; (3) construction and properties of the fully implicit solution technique; (4) the grid refinement results for the model problems.