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.

Probing polarization and dielectric function of molecules with higher order harmonics in scattering-near-field scanning optical microscopy

The idealized system of an atomically flat metallic surface [highly oriented pyrolytic graphite (HOPG)] and an organic monolayer (porphyrin) was used to determine whether the dielectric function and associated properties of thin films can be accessed with scanning-near-field scanning optical microscopy (s-NSOM). Here, we demonstrate the use of harmonics up to fourth order and the polarization dependence of incident light to probe dielectric properties on idealized samples of monolayers of organic molecules on atomically smooth substrates. An analytical treatment of light/sample interaction using the s-NSOM tip was developed in order to quantify the dielectric properties. The theoretical analysis and numerical modeling, as well as experimental data, demonstrate that higher order harmonic scattering can be used to extract the dielectric properties of materials with tens of nanometer spatial resolution. To date, the third harmonic provides the best lateral resolution (∼50 nm) and dielectric constant contrast for a porphyrin film on HOPG. © 2009 American Institute of Physics.