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.Index Terms-Fluid structure interaction, finite element analysis, hp-FEM, a posteriori error estimates. I. INTRODUCTIONAnalysis of fluid flows that are being impeded by an elastic structure poses a particularly challenging task as it is a complex multiphysics problem in which fluid and structure are mutually coupled along a shared boundary. The past few years have seen growing interests in the analysis of fluid-structure interaction (FSI) problems that arise in interdisciplinary fields spanning from biomechanical to microsystems applications [1], [2]. Hence, accurate tools that provide deep understanding of the phenomenon are always of significant interests. Despite considerable advances in the computational analysis of the FSI problems, achieving reasonable accuracy of the solution without excessive computational resources remains an open challenge. This paper attempts to solve the fluid-structure interaction problem with an hp-adaptive finite element method (hp-FEM), in which a careful decision in local mesh refinement (h) combined with increase in polynomial order Manuscript received October 5, 2012; revised January 17, 2013. This work was supported in part by the Malaysia Ministry of Higher Education under its fellowships scheme.The authors are with the School of Mechanical Engineering, Universiti Sains Malaysia, 14300 Nibong Tebal, Penang, Malaysia (e-mail: aizat_abas@ yahoo.com; arahman@ eng.usm.my).(p) based on an error indicator is expected to result in highly accurate solution. I...

Adaptive FEM with Domain Decomposition Method for Partitioned-Based Fluid–Structure Interaction

“…The "Maximum" marking strategy for determining elements to be refined is chosen as it is considerably faster to compute and generally yield comparable results to "Equilibration" strategy. The following describes the construction of hp-adaptive key point strategy [18] …”

“…Hence, a numerical assessment of the performance of adaptive solvers in FSI computation is of interest to ascertain their viabilities. This paper will continue based on the initial work done on hp-adaptivity for FSI by Abas and Abdul-Rahman [18]. In terms of hp-adaptivity, the previous work can only be applied for high-order Legendre polynomial elements of up to order 3, while for the current work, major augmentation to the code allows for hp-adaptivity to reach up to order 12.…”