A New Method for Modeling Free Surface Flows and Fluid-structure Interaction with Ocean Applications

The computational modeling of ocean waves and ocean-faring devices poses numerous challenges. Among these are the need to stably and accurately represent both the fluid-fluid interface between water and air as well as the fluid-structure interfaces arising between solid devices and one or more fluids. As techniques are developed to stably and accurately balance the interactions between fluid and structural solvers at these boundaries, a similarly pressing challenge is the development of algorithms that are massively scalable and capable of performing large-scale three-dimensional simulations on reasonable time scales. This dissertation introduces two separate methods for approaching this problem, with the first focusing on the development of sophisticated fluid-fluid interface representations and the second focusing primarily on scalability and extensibility to higher-order methods.

We begin by introducing the narrow-band gradient-augmented level set method (GALSM) for incompressible multiphase Navier-Stokes flow. This is the first use of the high-order GALSM for a fluid flow application, and its reliability and accuracy in modeling ocean environments is tested extensively. The method demonstrates numerous advantages over the traditional level set method, among these a heightened conservation of fluid volume and the representation of subgrid structures.

Next, we present a finite-volume algorithm for solving the incompressible Euler equations in two and three dimensions in the presence of a flow-driven free surface and a dynamic rigid body. In this development, the chief concerns are efficiency, scalability, and extensibility (to higher-order and truly conservative methods). These priorities informed a number of important choices: The air phase is substituted by a pressure boundary condition in order to greatly reduce the size of the computational domain, a cut-cell finite-volume approach is chosen in order to minimize fluid volume loss and open the door to higher-order methods, and adaptive mesh refinement (AMR) is employed to focus computational effort and make large-scale 3D simulations possible. This algorithm is shown to produce robust and accurate results that are well-suited for the study of ocean waves and the development of wave energy conversion (WEC) devices.

Scaffold-free, Human Mesenchymal Stem Cell-Based Tissue Engineered Blood Vessels.

Tissue-engineered blood vessels (TEBV) can serve as vascular grafts and may also play an important role in the development of organs-on-a-chip. Most TEBV construction involves scaffolding with biomaterials such as collagen gel or electrospun fibrous mesh. Hypothesizing that a scaffold-free TEBV may be advantageous, we constructed a tubular structure (1 mm i.d.) from aligned human mesenchymal cell sheets (hMSC) as the wall and human endothelial progenitor cell (hEPC) coating as the lumen. The burst pressure of the scaffold-free TEBV was above 200 mmHg after three weeks of sequential culture in a rotating wall bioreactor and perfusion at 6.8 dynes/cm(2). The interwoven organization of the cell layers and extensive extracellular matrix (ECM) formation of the hMSC-based TEBV resembled that of native blood vessels. The TEBV exhibited flow-mediated vasodilation, vasoconstriction after exposure to 1 μM phenylephrine and released nitric oxide in a manner similar to that of porcine femoral vein. HL-60 cells attached to the TEBV lumen after TNF-α activation to suggest a functional endothelium. This study demonstrates the potential of a hEPC endothelialized hMSC-based TEBV for drug screening.

High-speed label-free functional photoacoustic microscopy of mouse brain in action.

We present fast functional photoacoustic microscopy (PAM) for three-dimensional high-resolution, high-speed imaging of the mouse brain, complementary to other imaging modalities. We implemented a single-wavelength pulse-width-based method with a one-dimensional imaging rate of 100 kHz to image blood oxygenation with capillary-level resolution. We applied PAM to image the vascular morphology, blood oxygenation, blood flow and oxygen metabolism in both resting and stimulated states in the mouse brain.

Path Optimization in Free Energy Calculations

Free energy calculations are a computational method for determining thermodynamic quantities, such as free energies of binding, via simulation.

Currently, due to computational and algorithmic limitations, free energy calculations are limited in scope.

In this work, we propose two methods for improving the efficiency of free energy calculations.

First, we expand the state space of alchemical intermediates, and show that this expansion enables us to calculate free energies along lower variance paths.

We use Q-learning, a reinforcement learning technique, to discover and optimize paths at low computational cost.

Second, we reduce the cost of sampling along a given path by using sequential Monte Carlo samplers.

We develop a new free energy estimator, pCrooks (pairwise Crooks), a variant on the Crooks fluctuation theorem (CFT), which enables decomposition of the variance of the free energy estimate for discrete paths, while retaining beneficial characteristics of CFT.

Combining these two advancements, we show that for some test models, optimal expanded-space paths have a nearly 80% reduction in variance relative to the standard path.

Additionally, our free energy estimator converges at a more consistent rate and on average 1.8 times faster when we enable path searching, even when the cost of path discovery and refinement is considered.