An iterative divergence-free immersed boundary method in the finite element framework for moving bodies. (15th August 2020)

• Record Type: Journal Article
• Authors: Mao, Jia; Zhao, Lanhao; Liu, Xunnan; Mu, Kailong
• Is Part Of: Computers & fluids. Volume 208(2020)
• Publication Date: 2020-08-15
• Subjects: Immersed boundary method -- Divergence-free -- No-slip -- Characteristic-based split scheme -- Oscillations -- Finite element framework; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2020.104630
• Languages: English
• ISSNs: 0045-7930

Abstract

Hightlights: A novel iterative direct-forcing immersed boundary method is proposed. Divergence-free and no-slip conditions are enforced simultaneously. Spurious force oscillations are caused by changes of the interpolation coefficient. Abstract: A novel iterative direct-forcing immersed boundary (IB) method, which meets the divergence-free and no-slip conditions simultaneously, is proposed in the finite element framework for incompressible flow problems. The coupled velocity and the pressure of the fluid field are solved by the Characteristic-based Split scheme. The formulation for the extra body force is derived according to the no-slip boundary condition. The novelty of the proposed IB method lies in that the calculation of the pressure, the iterations of the velocity, the pressure and the extra body force are accomplished in a loop at the same time. Therefore, the divergence-free and no-slip conditions are ensured fully at the same time. The accuracy of the current IB method is verified by several cases, including static and moving boundaries. Meanwhile, the contributing factors of the spurious force oscillations for moving boundaries are studied. A brand-new viewpoint is proposed, which is different with the common standpoint. The major source of spurious force oscillations pointed out in this paper is that the change of interpolation coefficients when boundaries sweep within an element, instead of the change of interpolation points when boundaries move across adjacent elements, as discussed in existing references. The oscillations which are caused by the inherent properties of the immersed boundary method cannot be avoided, while effective methods can be employed to suppress them, including refining the meshes and applying a proper discrete delta function.