Modelagem matemática de jatos em desenvolvimento espacial usando a metodologia pseudoespectral de Fourier

Abstract

The search for numerical methods aiming at the solution of solve the Navier-Stokes equations accurately and with a high convergence rate represents a major area of interest for CFD researchers. Such a quest is motivated by physical phenomena, like turbulence in fluids, in which only accurate methodologies with high convergence rate may allow to satisfactorily obtain a physical solution that characterizes the problem. One of the main difficulties in obtaining high accuracy in the numerical solution of the Navier-Stokes equations is the high computational cost. In order to circumvent such a drawback, in the MFLab, a new methodology has began to be developed with the works of Mariano (2007), Moreira (2007), Mariano (2011). Such a methodology is based on the coupling of the Fourier pseudo-spectral (FPSM) and immersed boundary methodologies (IBM). A main characteristic of the FPSM is the high numerical accuracy associated to a relative low computational cost, since solving the linear system of the pressure-velocity coupling is not necessary. However, the FPSM methodology has its applicability restricted only to problems with periodic boundary conditions. In order to expanding the range of problems to which the FPSM can be applied more complex problems of the Computational Fluid Dynamics (CFD), the FPSM methodology is coupled with the IBM. The IBM is a methodology developed to simulate flows over complex, moving geometries, based on a cartesian-type grid. Normally, the IBM presents a low accuracy in regions near the immersed interface. The present work proposes to continue the developments of the hybrid FPSM-IBM methodology, focusing in the solution of the Navier-Stokes equations in its isothermal and incompressible form. The present work, as an evolution of the developments of Mariano (2011) , solves the Navier-Stokes equations in its three-dimensional form. The numerical code developed is capable of Large Eddy Simulations also. The method of manufactured solutions was used in the verification of the numerical code developed, and a spectral convergence rate is achieved. In the process of validation of the FPSM methodology, a isotropic turbulence flow was simulated and the results obtained are consistent from a physical point of view. Finally, the FPSM-IBM methodology was used in the simulation of turbulent jet in spatial development. The results obtained are compared with experimental data, and present a good agreement, both qualitative and quantitatively. It was observed that the FPSM-IBM implemented allows obtaining high accuracy, spectral convergence rates, computational efficiency, and allows the integrally Fourier-spectral solution of non-periodic problems.