Date of Award

Summer 8-16-2018

Document Type


Degree Name

Doctor of Philosophy (PhD)


Computational Analysis and Modeling

First Advisor

Don Liu


Smoothed particle hydrodynamics (SPH) is a simple and effective numerical method that can be used to solve a variety of challenging problems in computational mechanics. It is a Lagrangian mesh-free method ideal for solving deformation problems. In the SPH method, the state of a system is represented by a set of particles, which possesses individual material properties and interact with each other within a specific range defined as a support domain by a weight function or smoothing function. SPH features flexibility in handling complex flow fields and in including physical effects.

In theory, the basic concept of the SPH method is introduced in this paper. Some detailed numerical aspects are discussed including the kernel approximation in continuous form and particle approximation in discrete form, the properties for the smoothing functions and some of the most frequently used ones in the SPH literature, the concept of support and interface domain, SPH formulations for Navier-Stokes equation, time integration, boundary treatment, particle interaction, artificial viscosity, laminar viscosity, shifting algorithm, and so on.

In applications, this paper presents an improved SPH method for modeling the diffusion process of a microneedle and using smoothed particle hydrodynamics (SPH) method to simulate the 25% cross-section stenosis blood vessel model and the 75% crosssection stenosis blood vessel model. The obtained numerical results are in close agreement with available theoretical and experimental results in the literature.

As an emerging transdermal drug delivery device, microneedles demonstrate some superior potential and advantages over traditional metallic needles-on-syringes in skin injection and vaccine [1]. However, very few research papers are available. This project uses a high order continuous method, the spectral element method (SEM), and a low order discrete method, the Smoothed Particle Hydrodynamics (SPH), to investigate this new drug delivery system. The incompressible Navier-Stokes equations were solved with SEM under appropriate initial and slip boundary conditions for the transport of medicine inside microneedles of rectangular and circular cross-sections. In addition, Darcy-Brinkman equations and a concentration equation were solved with SEM under appropriate initial and boundary conditions for the infiltration of medicine solution through porous media of the dermis tissue once a microneedle enters the skin. Meanwhile, the Lagrangian form of the Navier-Stokes equations were solved with the weighted interpolation approach via numerical integrations without inverting any matrices. Results from the mesh-based SEM and the mesh-free SPH simulations revealed technical details about the processes of delivery of medicine particles through microneedles and diffusion in the skin tissue, and the medicine concentration changes with space and time. The overall effect of medicine delivery under initial concentration and conditions were simulated and the effect of drug delivery were assessed.

The formation of thrombus is a complicated process. The existing literature rarely has a model for high-fidelity simulation of the effects and hazards of blood clots on blood flow. In this model, high-fidelity simulations are performed for complex human internal environments. The result of this simulation indicates high pressure area in blood vessel wall which matches the real condition of the vessel experiment.