Desenvolvimento e implementação da metodologia combinada fronteira imersa térmica e pseudoespectral de Fourier

Abstract

A novel methodology combining Fourier pseudospectral and immersed boundary methods - IMERSPEC - has been developed for heat transfer problems, using Navier-Stokes, mass conservation and energy equations for incompressible flows. The numerical algorithm consists of a Fourier pseudospectral collocation method, used for flow solution and thermal heat transfer, while the immersed boundary method (multi-direct forcing method) is used only to apply the thermal boundary conditions. The IMERSPEC methodology has been developed in the fluid mechanic laboratory (MFLab) to solve isothermal fluid flows problems. In the present work, a new formulation for first (Dirichlet), second (Neumann) and third (Robin) boundary conditions types is proposed. The verification and validation of the methodology are presented for every boundary conditions and the results show a good agreement with the literature. Furthemore, the methodology convergence when applied to mathematical problems with synthesized analytical solutions shows accuracy machine and four order to rate of convergence for non coincidents nodes. Whilst for physical problems, the presented methodology provides second order rate of convergence for the energy equation and the Navier-Stokes equations. The computational cost has been analyzed and it is shown that runtime presents Nlog2N order, expected result to Fourier method