Desenvolvimento de programa para simulação de escoamentos incompressíveis com fronteira móvel

Abstract

In this work we develop a computational code for incompressible flows with moving boundaries based on the finite element method. Such problems are found in engineering in several ways. As example one may cite the free surface flows and the fluid-structure problems. However there is no satisfactory analytical solution and even numerical solutions are challenging. In this sense, in the last decades, approximate methods, such as the finite element method, have been widely employed in this context. In our code we employ implicit temporal integration and mixed stable finite elements with linear shape functions for pressure and quadratic for velocities. The fluid dynamics governing equations are described in the arbitrary Lagrangian-Eulerian (ALE) way, enabling mesh moving to accommodate the boundary movement. Finally, the program is tested by numerical classical examples which are compared to the literature and we also present one example of transient moving boundary problem.