Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Mechanical Engineering


Mechanical Engineering

First Advisor

Baskar Ganapathysubramanian

Second Advisor

Ming-Chen Hsu


We deploy the residual-based variational multi-scale (VMS) method in the sense of large-eddy simulation (LES) in finite element method to buoyancy-driven flow in enclosures and consider an extensive range of Rayleigh number from laminar ($10^3$) to turbulent ($10^{10}$) in a 2D benchmark Rayleigh--B\'enard problem. 3D simulations for a laminar and a turbulent case are performed and comparisons including mean profiles as well as fluctuation profiles with other numerical and experimental results are successfully carried out. A weakly imposed boundary conditions method is employed for both velocity and temperature, and it produces reasonable results with a much coarser mesh compared with the traditional imposition of boundary conditions. This suggests that the VMS framework with the weak imposition of boundary conditions is a computationally efficient approach to model buoyancy-driven flows in complex indoor environments.

In addition to the flow fields, we deploy the immersogeometric analysis (IMGA) method in the sense of the immersed boundary method (IBM) for objects moving in fluids onto an unstructured framework. The finite element formulation is stabilized by the VMS method in an unstructured background mesh. Weak imposition of boundary conditions is used to impose no-slip boundary condition on the immersed boundary. Adaptively refined quadrature rules are used to better capture the geometry of the immersed boundary and accurately integrate the background elements that intersect the immersed boundary. Treatment for the freshly-cleared nodes is considered. We assess the accuracy of the moving IMGA framework by analyzing object motion in a variety of flow structures, including freely dropping cylinder/sphere in viscous fluids and particle focusing in (un)obstructed channels. We show the quantities of interests are in good agreements with other analytical, numerical and experimental solutions. Advantages of this moving IMGA framework in computational cost and efficiency are indicated by the comparison with the body-fitted method using a commercial computational fluid dynamic (CFD) software. The framework of moving IMGA is capable to be deployed in applications of particle control and manipulation in microfluidic channels.

The moving IMGA on the unstructured framework is further deployed to a scalable, adaptively refined, octree-based finite element approach for a better computational performance to track object motion. This enables using a parallel, hierarchically refined octree mesh as the background mesh, with a variationally consistent IMGA formulation on this background mesh. We integrate the unstructured framework of moving IMGA to the octree-based framework. We show good scaling results of the coupled framework on Stampede2, TACC. This illustrates the potential of the moving IMGA on the coupled framework to efficiently track complex particles in flows.

Copyright Owner

Songzhe Xu



File Format


File Size

110 pages