Simulações numéricas de problemas descritos pelas equações de Navier-Stokes incompressíveis Via Biblioteca FeniCS

Abstract

This work aims to study the Navier-Stokes equations solved by the finite element method using the FEniCS public domain library. A comparative study of projection and stabilized methods is presented. The projection methods implemented were: non-incremental pressure correction scheme (Chorin), incremental pressure correction scheme (IPCS) and consistent splitting scheme (CSS). The adaptive choice of time step scheme, PID, is considered in the projection and stabilized methods. In addition, fluid-structure interaction problems are investigated through the coupled momentum method for FSI (CMM-FSI). The CMM-FSI method considers the conventional formulation of finite elements for the Navier-Stokes equations in a rigid domain, adding modifications in such a way that the membrane deformation is considered. For the variable formulation of the Navier-Stokes equations a stabilized Stremline-Upwind/Petrov-Galerkin (SUPG) formulation is considered for the velocity and stabilized Pressure-Stabilizing/Petrov-Galerkin (PSPG) formulation for the pressure enriched with Least-Squares on Incompressibility Constraint (LSIC) stabilization. The FEniCS library demonstrated efficiency in the treatment of the Navier-Stokes equations in general and in solution of fluid-structure interaction problems by the CMM-FSI method.