Among the main problems in the field of Computational Fluid Dynamics (CFD), there is the two-dimensional laminar flow in a transient regime of an incompressible fluid modeled by Navier-Stokes equations. Among the decoupled solutions for this equation system, that is, solutions for velocity regardless to pressure, there are the Projection methods, which separate the solution in three parts, solved in each time steps applying an iterative process regardless to the iterative process for the other variables. It may result, according to the Projection method applied, in two Reaction-Diffusion equations and one Poisson equation to be solved in each time step. This paper sought to develop an algorithm to solve the Navier-Stokes equation, applying the Finite Volume Method (FVM) with second order approximation scheme (CDS), beside a Projection method with incremental pressure-correction scheme, so that each Reaction-Diffusion and the Poisson equation are solved efficiently. Therefore, several solvers were tested for each equation, resulting in an algorithm with the combination that achieved the best result for each equation, with the preconditioned Conjugate Gradient method (PCG) with the Multigrid method (MG) and ILU solver (Incomplete LU factorization) being the methodology used in the whole problem solving process. The geometric Multigrid with V cycle, the correction scheme (CS), the full weighting restriction, the prolongation through bilinear interpolation and the maximum number of levels for the studied cases were utilized. The results achieved were satisfactory, since the proposed methodology accelerated the iterative process considerably in relation to the classical methods available in the literature.
Abstract Among the main problems in the field of Computational Fluid Dynamics (CFD), there is the two-dimensional laminar flow in a transient regime of an incompressible fluid modeled [...]
Solution of the Navier-Stokes equations using projection method and preconditioned conjugated gradient with multigrid and ILU solver 
