Análise de estimativa de erro aplicada a problemas de interação fluido-estrutura, com formulação totalmente euleriana, via método dos elementos finitos

Abstract

Fluid-Structure Interaction (FSI) is a subject of great importance in many domains, as engineering and biomedical sciences. Error estimates are of great relevance in numerical simulations, as they allow us to evaluate the accuracy and quality of the approximate solutions. These estimates are also essential for the application of adaptive meshes, which are currently indispensable tools for the development of efficient algorithms. This study presents a finite element method, with a fully Eulerian approach and a conforming mesh, for the analysis of FSI problems. The solid domain is modelled as neo-Hookean and the fluid is considered Newtonian, both incompressible. Error estimates for the FSI formulation are derived and employed in the implementation of an adaptive mesh. This mesh is generated through an h-adaptive refinement. The computational code is developed on FreeFem++. Two FSI problems are proposed, the results correlate well with those available in the literature. The adaptive mesh is compared with an uniform refinement. It’s shown that the former is more efficient, resulting in smaller errors for an equally sized mesh.