Curvilinear Immersed Boundary Method for Simulating Fluid Structure Interaction with Complex 3D Rigid Bodies

By Iman Borazjani, Liang Ge, Fotis Sotiropoulos. Journal of Computational Physics, 2008

487 citations recorded by the source corpus.

The sharp-interface CURVIB approach of Ge and Sotiropoulos [L. Ge, F. Sotiropoulos, A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries, Journal of Computational Physics 225 (2007) 1782–1809] is extended to simulate fluid structure interaction (FSI) problems involving complex 3D rigid bodies undergoing large structural displacements. The FSI solver adopts the partitioned FSI solution approach and both loose and strong coupling strategies are implemented. The interfaces between immersed bodies and the fluid are discretized with a Lagrangian grid and tracked with an explicit front-tracking approach. An efficient ray-tracing algorithm is developed to quickly identify the relationship between the background grid and the moving bodies. Numerical experiments are carried out for two FSI problems: vortex induced vibration of elastically mounted cylinders and flow through a bileaflet mechanical heart valve at physiologic conditions. For both cases the computed results are in excellent agreement with benchmark simulations and experimental measurements. The numerical experiments suggest that both the properties of the structure (mass, geometry) and the local flow conditions can play an important role in determining the stability of the FSI algorithm. Under certain conditions unconditionally unstable iteration schemes result even when strong coupling FSI is employed. For such cases, however, combining the strong-coupling iteration with under-relaxation in conjunction with the Aitken’s acceleration technique is shown to effectively resolve the stability problems. A theoretical analysis is presented to explain the findings of the numerical experiments. It is shown that the ratio of the added mass to the mass of the structure as well as the sign of the local time rate of change of the force or moment imparted on the structure by the fluid determine the stability and convergence of the FSI algorithm. The stabilizing role of under-relaxation is also clarified and an upper bound of the required for stability under-relaxation coefficient is derived.

Subfields: Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/37b9ec605175d305a60406563779bd569925f393

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Citations in the corpus

An immersogeometric variational framework for fluid–structure interaction: application to bioprosthetic heart valves (2014, unknown): “Borazjani [58] compiled a current and thorough literature review and computed one of the most sophisticated and realistic heart valve analyses to date, using the curvilinear immersed boundary (CURVIB) method [59, 60].”
An immersed boundary method for fluid–flexible structure interaction (2009, methodology): “Recently, various forms and extensions of the IB method have been developed for simulating fluid–structure interaction problems [3,5–14].”
A convergence study of a new partitioned fluid-structure interaction algorithm based on fictitious mass and damping (2012, methodology): “In order to show the effect of fictitious mass and damping on the convergence of sub-iterations, we employ the mathematical analysis in [1,29], where a simplified equation describing mass-spring or string motion under external forces from fluid domains is used instead of the elastodynamic equations.”
Hydrodynamics of swimming in stingrays: numerical simulations and the role of the leading-edge vortex (2016, methodology): “…and the numerical method To simulate stingray locomotion, we use the curvilinear immersed boundary (CURVIB) method (Ge & Sotiropoulos 2007; Borazjani et al. 2008) with prescribed body motion (relative to the centre of mass) from experimental measurements (as described in the previous…”