Finite Element Method for Fluid Structure Interaction with hp-Adaptivity

Abstract

 Abstract—Recent advances in computational studies of fluid flows with structural interactions suggest that significant contributions have been made towards reliable solutions to the problem. Achieving accurate solutions however remains a considerable task since enormous amount of computer time and memory are usually needed. This applies particularly to a partitioned approach in which structure and fluid are solved separately. This paper attempts to solve fluid-structure interaction (FSI) problems with an hp-adaptive finite element method (hp-FEM). The FSI problem is formulated based on a partitioned approach and Arbitrary Lagrangian-Eulerian (ALE) descriptions for the incompressible fluid and structure domains. The hp-adaptivity is implemented with an a posteriori error estimator and adaptation to minimize error in energy norm. The automatic mesh adaptation over the triangular mesh is achieved with red-green-blue refinement technique. A strategy for mesh refinement to occur at prescribed key points is used for effective mesh adaptivity. The hp-adaptive approach is assessed with traditional uniform mesh refinement and also an h-adaptive method on a benchmark test case. From the error convergence, the hp-adaptive method is shown to be a viable approach in acquiring accurate solution of a partitioned-based FSI analysis without significant compromise in computational time and memory. It is also found that the convergence of solution in fluid and structure domains is considerably sensitive to the aspect ratios of triangular elements.