Modelagem matemática tridimensional para problemas de interação fluido-estrutura

Abstract

The mathematical modeling and the three-dimensional numerical simulation of flows around complex moving geometries have been one of the greatest challenges in today engineering problems. The discretization of three-dimensional domains requires, very often, huge amount of data processing and storing which, with the frequently local mesh refinements, make the computations an extremely expensive issue. Representing complex geometries by generalized coordinates grids, may impose mathematical or numerical difficulties, hence a limited range of use. The immersed boundaries methodologies have been developed aiming to cope with this problem by separating it in two domains: a Lagrangian domain to represent the solid/fluid interface and an Eulerian domain to the flow counterpart. This work presents an extension to three-dimensional domains of the Immersed Boundary Method, developed at the LTCM, named Virtual Physical Method. The Eulerian domain was discretized using second-order time and space approximations, by Finite Volumes in a Cartesian mesh having parallel processing capabilities. The Lagrangian domain was built employing a triangular elements mesh. The initial tests were done in order to validate, firstly, the Cartesian basis domain in order to insert, later, the immersed boundary. As the first geometry studied, a stationary sphere was chosen. Despite the geometric simplicity of the spheres, the flow around them produces very rich structures, having well reported benchmarks available in the literature. Once the methodology has been validated for a stationary geometry, it was extended to a Fluid-Structure Interaction Problem. The dynamic system chosen was composed by a sphere tethered by springs immersed in the flow. The flow past the sphere-springs system was studied. Another important contribution of this work was the development, at the LTCM, of an important know-how in parallel processing, which has resulted in a laboratory in this important field of research.