ACCURATE APPROXIMATION OF UNSTRUCTURED GRID INTO REGULAR GRID WITH COMPLEX BOUNDARY HANDLING
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.
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.
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.