Browsing by Subject "numerical modeling"

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.

Propagation of subcritical cracks is studied in a geomaterial subject to weakening by the presence of water, which dissolves a mineral component of it. Such weakening is common when tensile micro-cracks develop, constituting sites of an enhanced mineral dissolution. Meanwhile, the dissolution process at each active site of the inter-surface is affected by the chemical properties of the environment, e.g. the PH value. In this research, a previous concept of reactive chemo-plasticity is adopted with the yield limit depending on the mineral mass dissolved and causing a chemical softening. The dissolution is described by a rate equation and is a function of a variable internal specific surface area, which in turn is assumed to be a function of the dilative plastic deformation. Two loading modes are adopted to investigate the chemical enhancement of propagation of a single crack. The behavior of the material is rigid-plastic with a chemical softening. The extended Johnson approximation is adopted, meaning that all the fields involved are axisymmetric around the crack tip with a small, unstressed cavity around it. An initial dissolution proportional to the initial porosity activates the plastic yielding. The total dissolved mass diffuses out from the process zone, and the exiting mineral mass flux can be correlated with the displacement of the crack tip. A calibration against available data will be performed in the future, followed by a series of experiments to simulate the real case.