<p>Computational Fluid Dynamic (CFD) simulations often produce datasets defined over unstructured grids with solid boundaries. Though unstructured grids allow for the flexible representation of this geometry and the refinement of the grid resolution, they suffer from high storage cost, non-trivial spatial queries, and low reconstruction smoothness. Rectilinear grids, in contrast, have a negligible memory footprint and readily support smooth data reconstruction, though with reduced geometric flexibility.</p><p>This thesis is concerned with the creation of accurate reconstruction of large unstructured datasets on rectilinear grids with the capability of representing complex boundaries. We present an efficient method to automatically determine the geometry of a rectilinear grid upon which a low-error data reconstruction can be achieved with a given reconstruction kernel. Using this rectilinear grid, we address the potential ill-posedness of the data fitting problem, as well as the necessary balance between smoothness and accuracy, through a bi-level smoothness regularization. To tackle the computational challenge posed by very large input datasets and high-resolution reconstructions, we propose a block-based approach that allows us to obtain a seamless global approximation solution from a set of independently computed sparse least-squares problems. </p><p></p><p>We endow the approximated rectilinear grid with boundary handling capabilities that allows for accommodating challenging boundaries while supporting high-order reconstruction kernels. Results are presented for several 3D datasets that demonstrate the quality of the visualization results that our reconstruction enables, at a greatly reduced computational and memory cost. Our data representation enjoys all the benefits of conventional rectilinear grids while addressing their fundamental geometric limitations.</p>

A mathematical model is developed for investigating time dependent surface deformations of a hydrostatic water volume, when it is subjected to a sudden partial collapse or rise of the sea bottom. The model solves two-dimensional Navier-Stokes Equations on a vertical plane numerically by using Marker and Cell Method (MAC) for viscous and compressible fluid including all the nonlinear effects in the solution. For demonstration, a vertical motion was given to a section in a hypothetical reservoir bed within a short time period and the resulting velocity and pressure fields and the surface profile of the water body are obtained. Computational and physical aspects are discussed.

ABSTRACT SIMULATION OF SURFACE WAVES GENERATED BY A RAPID RISE OF A BLOCK AT THE SEA BOTTOM SENOL, Nalan M.Sc., Department of Civil Engineering, Supervisor: Assoc. Prof. Dr. ismail AYDIN July 2005, 74 Pages A mathematical model is developed for investigating time dependent surface deformations of a hydrostatic water volume, when it is subjected to a sudden partial rise of the sea bottom. In the model, 2-dimensional, compressible, and viscous Navier-Stokes equations are solved by Marker and Cell (MAC) method. Variable mesh size in both horizontal and vertical directions with a staggered grid arrangement is used. Limited compressibility model is utilized for pressure. Various computational tests are done for the selection of computational parameters of the model. It is found that the amplitude of surface waves generated by vertical displacements of the sea bottom depends on size and speed of bottom displacements.