Keywords : Navier-Stokes, incompressible, 2D geometry, Finite Elements Methods (finite element method, finite element method, finite elements method), Domain Decomposition Methods, Dynamical Multi-Level Methods.
The DDNS2 code is a parallel solver for unsteady incompressible Navier-Stokes flows in 2D geometries and primitive variables written in Fortran 95 with MPI as a message-passage library. Mixed finite element methods, with hierarchical basis, are used to discretize the equations and a non overlapping domain decomposition approach leads to an interface problem which involves a Lagrange multiplier corresponding to the velocity (the FETI approach). A dynamical multilevel method is developed locally on each subdomain. Several numerical estimates on the evolution of linear and nonlinear terms allow to construct the multilevel strategy which produces auto-adaptive cycles in time during which different mesh sizes, one for each subdomain, can be considered.