Modelagem matemática de escoamentos bifásicos usando o Meto- Do Espectral de Fourier

Abstract

Numerical simulations of two-phase ow require high accuracy in order to obtain detailed information of the ow. Low computational cost is also very important, because in general, numerical simulation require a high grid renement, which makes them onerous. Thus, in the present work the authors propose the use of Fourier pseudo-spectral method to solve multiphase ow problems. This method presents high order numerical convergence and low computational cost, due to the algorithm called FFT (Fast Fourier Transform). In addition, when this method is applied to solve the Navier-Stokes equations, decouples the pressure and velocity through the projection method, without the need to solve the pressure Poisson equation. To handle the two-phase ow with moving and deformable geometries, Fourier pseudo-spectral method coupled with the hybrid method Front-Tracking/ Front-Capturing. This hybrid method works with two elds, one Eulerian, where the Navier-Stokes and continuity equations are solved for the uid and the Lagrangean equations are solved for interfaces. For this method, both domains are coupled by interpolation and distribution process. Nevertheless, the lagrangean interface are transported through the Eulerian domain. The verication and validation is presented using manufactured solution. Spurious currents and vortex ow were simulated and good results were obtained. The results for the rise of a single bubble are presented and compared with experimental data Clift, Grace e Weber (1978).