Simulação numérica de escoamentos de fluidos incompressíveis a baixo Reynolds utilizando o método de Galerkin descontínuo h-adaptativo

Abstract

In several engineering applications the knowledge of the speed and pressure fields favors the understanding of physical processes that represent the problem. The study of fluid flow behavior can be modeled by Navier-Stokes equations. These equations, in its complete form, have no analytical solution and it is necessary to use approximation methods to obtain an approximate solution. The most classical approximation methods obtain the result from first order precision schemes, which may not represent with good precision the physical phenomenon studied. Results with greater precision are obtained with methods of high order of precision. Recently, the Discontinuous Galerkin Method has been explored in large scale in fluid dynamics applications, presenting excellent results. In this method, high-grade polynomials (p) are used to interpolate the solution considering the discontinuity between elements. On the other hand, meshes with adaptive refinement (h) also offer good precision to the results considering the regions of greatest variation of the solution. Adaptive meshes can be obtained from the definition of an optimal mesh criterion, for example, seeking to increase the accuracy of a given approximate solution by increasing the amount of elements only in the regions that have the highest gradients in the solution. Such an approach can significantly reduce the computational cost when compared to a homogeneous mesh refining required to obtain the same approximation error. The hp union represents a solution strategy capable of combining the attractiveness of the solution obtained with high-grade polynomials together with the adaptive refinement of the mesh in the critical regions of the domain. This work uses the h-adaptive discontinuous Galerkin method as a numerical tool in order to explore the precision of the results together with an optimized strategy for the generation of meshes in the domain. Initially, the problem is validated considering known analytical solutions in steady and transient regimes. The Reynolds low transient flow around the two-dimensional cylinder is used to verify the accuracy of the results from the h-adaptive schema. In all cases analyzed in this work, the h-adaptive discontinuous Galerkin method presented excellent results regarding validation and its comparison with classical literature results.