Considered in this investigation is the three-dimensional, gravity-driven flow of a thin viscous fluid layer down an incline, and spreading over topography. Three depth-integrated models are presented and contrasted. These include an integral-boundary-layer model, a weighted-residual model and a hybrid model. A numerical solution procedure suited for solving three-dimensional flows is also proposed. Numerous simulations have been conducted using the models for various steady subcritical, and unsteady supercritical flows over several topographies. Good agreement among the three models was found. In addition, the models were also validated using experimental results, and, again, good agreement between the three models and with experiments was obtained.

Anisotropic mesh adaptation is studied for linear finite element solution of 3D anisotropic diffusion problems. The 𝕄-uniform mesh approach is used, where an anisotropic adaptive mesh is generated as a uniform one in the metric specified by a tensor. In addition to mesh adaptation, preservation of the maximum principle is also studied. Some new sufficient conditions for maximum principle preservation are developed, and a mesh quality measure is defined to server as a good indicator. Four different metric tensors are investigated: one is the identity matrix, one focuses on minimizing an error bound, another one on preservation of the maximum principle, while the fourth combines both. Numerical examples show that these metric tensors serve their purposes. Particularly, the fourth leads to meshes that improve the satisfaction of the maximum principle by the finite element solution while concentrating elements in regions where the error is large. Application of the anisotropic mesh adaptation to fractured reservoir simulation in petroleum engineering is also investigated, where unphysical solutions can occur and mesh adaptation can help improving the satisfaction of the maximum principle.

A novel and efficient photocatalyst of three dimensional (3D) Ba5Ta4O15 flower-like microsphere was synthesized via an alkaline etch under hydrothermal condition. The influence of reaction temperature, reaction time, and alkaline concentration on the morphology were investigated for the 3D Ba5Ta4O15 flower-like microsphere photocatalyst. The morphology and structure of the 3D Ba5Ta4O15 were characterized using x-ray diffraction, scanning electron microscope, transmission electron microscope, and high-resolution transmission electron microscopy. The results show that the elegant flower-like structure was composed of Ba5Ta4O15 nanosheets. The 3D Ba5Ta4O15 flower-like microspheres show a higher photocatalytic activity in the degradation of methylene blue under ultraviolet light than the bulk Ba5Ta4O15 microcrystal by the solid-state-reacted synthesized. The UV–vis diffuse reflectance spectra, photoluminescence spectra, volumetric adsorption method, and photocurrent response of the Ba5Ta4O15 photocatalyst were characterized indicated that the higher photocatalytic activity of flower-like Ba5Ta4O15 microspheres was due to the high crystallinity, large surface area and the effective charge separation.

The orientation of fibers in assemblies such as nonwovens has a major influence on the anisotropy of properties of the bulk structure and is strongly influenced by the processes used to manufacture the fabric. To build a detailed understanding of a fabric’s geometry and architecture it is important that fiber orientation in three dimensions is evaluated since out-of-plane orientations may also contribute to the physical properties of the fabric. In this study, a technique for measuring fiber segment orientation as proposed by Eberhardt and Clarke is implemented and experimentally studied based on analysis of X-ray computed microtomographic data. Fiber segment orientation distributions were extracted from volumetric X-ray microtomography data sets of hydroentangled nonwoven fabrics manufactured from parallel-laid, cross-laid, and air-laid webs. Spherical coordinates represented the orientation of individual fibers. Physical testing of the samples by means of zero-span tensile testing and z-directional tensile testing was employed to compare with the computed results.