Imposing rigidity constraints on immersed objects in unsteady fluid flows

Abstract

Imposing rigidity constraints of an immersed elastic body in a transient flow field is not trivial. It requires solution stability and accuracy. In this paper, we present an efficient and accurate algorithm implemented to enforce fluid-structure interface constraints used in the immersed finite element method (IFEM). This interface treatment is a constraint applied onto the rigid bodies based on the fluid structure interaction force evaluated from the immersed solid object. It requires no ad hoc constants or adjustments, thus providing numerical stability and avoiding unnecessary trialand-error procedures in defining the stiffness of the elastic body. This force term can be evaluated for both uniform and nonuniform fluid grids based on the higher order interpolation function adopted in the IFEM. The ability in handling nonuniform interpolations offers the convenience in modeling arbitrary geometrical shapes and provides solution refinements around interfaces. The results we obtained from flow past a rigid cylinder demonstrate that this convenient way of constraining the interface is a reliable and robust numerical approach to solve unsteady fluid flow interacting with immersed rigid bodies.

Numerical studies of blood flow in healthy, stenosed, and stented carotid arteries

“…Details of the interpolation process are given in [52]. It must be noted that this force is evaluated only at the interface since there is no internal force generated inside a rigid solid.…”

Modeling of coupled dynamics for fluid-structure interactions

“…The traction boundary condition is satisfied using Eq. (27). The traction here is evaluated using only the pressure p since the normal component of the viscous stress ( ij n j ) is very low compared to the pressure.…”

“…This problem may propagate over time and cause instabilities in the solution or convergence issues. The immersed finite element method (IFEM) [25][26][27][28] is developed to tackle this problem by representing the background viscous fluid with an unstructured finite element mesh and nonlinear finite elements for the immersed deformable solid. Similar to the immersed boundary method, the fluid domain is defined on a fixed Eulerian grid.…”

A new method for simulating rigid body motion in incompressible two‐phase flow

“…A stress is thus generated in the solid and calculated with some constitutive relationship, after which the forces are appropriately transferred back to the fluid grid for subsequent time steps. Though the methods were developed for generally deformable bodies, very stiff constitutive relationships, or other modifications, are used to approximate rigid body motion [6,7].…”