Solução numérica das Equações de Navier-Stokes usando uma hibridação das metodologias Fronteira Imersa e Pseudo-Espectral de Fourier

Abstract

In the present these a new methodology is developed for incompressible Navier-Stokes equations applied in flow over complex geometries. This methodology is supported by coupling of Fourier pseudo-spectral methodology (FPSM) and immersed boundary methodology (IBM). The main features of FPSM is high numerical accuracy combined with high computational efficiency, since is not necessary to solve the linear system for pressure-velocity coupling. However, it is restricted to problems with periodic boundary conditions. In order to expand the FPSM applicability in Computational Fluid Dynamics (CFD) it is coupled with IBM. The IBM was carried out to solve flows over complex and moving geometries using a cartesian mesh. Generally, IBM reach only low accuracy in solution near of immersed interface. Using the hybridation proposed in the present work, the accuracy increase in results near of boundary. In the present work are shown verification and validation results of hybrid methodology. Manufactured solutions technique is used in order to verify the IMERSPEC methodology. Fourth order convergence rate is obtained. For validation of methodology classical CFD benchmarks flows are simulated: flow over a backward-facing step 2D and 3D and flow over a cylinders. In order to demonstrate the methodology capabilities are also simulated the free fall of rigid body, which is a fluid-structure interaction problem. The results of all benchmark problems are in agreement with literature data.