A Divergence-Free Immersed Boundary Method and Its Finite Element Applications. (6th August 2020)

• Record Type: Journal Article
• Authors: Zhou, Chuan; Li, Jianhua; Wang, Huaan; Mu, Kailong; Zhao, Lanhao
• Is Part Of: Journal of mechanics. Volume 36:Number 6(2020)
• Page Start: 901
• Page End: 914
• Publication Date: 2020-08-06
• Subjects: immersed boundary method -- iterative scheme -- divergence-free -- finite element framework; Mechanics, Analytic -- Periodicals; Mechanics -- Periodicals; 620.1005
• DOI: 10.1017/jmech.2020.23
• Languages: English
• ISSNs: 1727-7191

Abstract

Abstract : In order to maintain the no-slip condition and the divergence-free property simultaneously, an iterative scheme of immersed boundary method in the finite element framework is presented. In this method, the Characteristic-based Split scheme is employed to solve the momentum equations and the formulation for the pressure and the extra body force is derived according to the no-slip condition. The extra body force is divided into two divisions, one is in relation to the pressure and the other is irrelevant. Two corresponding independent iterations are set to solve the two sections. The novelty of this method lies in that the correction of the velocity increment is included in the calculation of the extra body force which is relevant to the pressure and the update of the force is incorporated into the iteration of the pressure. Hence, the divergence-free properties and no-slip conditions are ensured concurrently. In addition, the current method is validated with well-known benchmarks.