Abstract: In the present work the dynamics of a non-isothermal fluid flow in a fractal domain is analysed. This domain is a cavity in which the edges are pre-fractals of the Koch square curve. Simulations were carried out considering the pre-fractals of level 0 (square cavity), 1 and 2. The natural convection simulation were performed on a structured staggered grid using a finite volume method, as in our previous work [1]. For the level-0 fractal, the numerical code reproduces the results found in the literature (see [3], page 140). For isothermal flow some scillations were detected at the kinetic energy for Reynolds number between 400 and 1000, but they are not verified for standard cavity under the same conditions. Such oscillations were observed by Goodrich [2], but for a deep cavity (aspect ratio equal 2) and for Reynolds number interval between 5000 and 10000.

References:

1. E. Doescher, H.F. Campos Velho, F.M. Ramos (2001): Isothermal Fluid Flow in Fractal Domains, Computational and Applied Mathematics (submitted).

2. J.W. Goodrich, K. Gustafson, K. Halasi (1990): Hopf Bifurcation in the Driven Cavity, Journal of Computational Physics, 90, 219-261.

3. M. Griebel, T. Dornseifer, T. Neunhoeffer (1998): Numerical Simulation in Fluid Dynamics: A Practical Introduction, SIAM, Philadelphia (PA), USA.