DIRECT NUMERICAL SIMULATIONS OF FLUID-STRUCTURE INTERACTION IN THE RESPIRATORY AIRWAYS

Abstract

This thesis presents recent developments in direct numerical simulations of fluid-structure interaction occurring in biological systems, with particular interest in the modeling of particle deposition within the human respiratory system. Two numerical techniques are proposed. The first one is intended for direct numerical simulations of solid high aspect ratio micro-fibers in a general Newtonian fluid flow. For efficient and accurate resolution of the microscales, a micro-grid rigidly attached to the fiber in its spatial motion is introduced. The entire problem on the micro-grid is transformed with an Arbitrary Lagrangian-Eulerian method to a fixed reference domain and then solved with a Fictitious Domain Method. Using this algorithm, rotational behavior of fibers in a linear shear flow is studied. In view of our analysis, it is suggested that respiratory tract deposition for high aspect ratio fibers with complex shapes will be enhanced compared with the deposition of simple ellipsoidal fibers. Additionally, study of deposition enhancement due to magnetic field alignment of long straight ellipsoids in realistic airway bifurcation is performed. Results indicate that magnetic alignment of such particles can increase deep lung deposition by a factor of 1.42--3.46 depending on the fiber aspect ratio. A second method is developed to allow direct numerical simulations of dynamical interaction between an incompressible fluid and a hyper-elastic incompressible solid. A Fictitious Domain Method is applied so that the fluid is extended inside the deformable solid volume and the velocity field in the entire computational domain is resolved in an Eulerian framework. Solid motion, which is tracked in a Lagrangian framework, is imposed through the body force acting on the fluid within the solid boundaries. Solid stress smoothing on the Lagrangian mesh is performed with a Zienkiewicz-Zhu patch recovery method. High-order Gaussian integration quadratures over cut elements are used in order to avoid sub-meshing within elements in the Eulerian mesh that are intersected by the Lagrangian grid. The method is validated against previously reported results on numerical simulations of 3-D rhythmically contracting alveolated ducts. Observed flow patterns and alveolus dynamics for breathing conditions and geometrical parameters corresponding to different acinar generations in the respiratory system are comparable to those reported previously. This suggests that our new formulation can be successfully applied to numerical studies of coupled dynamics of air and airway walls in distal regions of the lungs.