Contribuição para a solução numérica monolítica do modelo matemático diferencial para a fluidodinâmica incompressível newtoniana

Abstract

The development of a incompressible fluid flow parallel simulation software is presented. Many aspects of the tool's development are discussed, including the solving of linear systems, data output, domain partitioning and load balancing among multiple MPI processes. The problem is formulated in terms of primary variables through the Navier-Stokes equations, which are discretized using the finite differences method. A framework for solving the discrete equations for the problem in a fully-coupled way applicable to structured staggered grids is developed. Multiple advection schemes and multiple non-linearity treatment techniques are evaluated, including the full Newton-Raphson method, where the Jacobian is explicitly built. The turbulence is treated through large eddy simulation, where the eddy viscosity is calculated via the Smagorinsky model, damped with the van Driest function. Linear systems are solved iteratively through the Schur complement, enabling the handling of the kind of matrices arising naturally from the problem, which contains zeros on the main diagonal, and can not be solved through ordinary iterative methods.