Accurate Approximation of Unstructured Grid into Regular Grid with Complex Boundary Handling

Dana El-Rushaidat, Purdue University

Abstract

Unstructured grids, commonly used in computational fluid dynamics (CFD) simulations, allow for flexible point distribution and arbitrary boundary geometry. This property makes it straightforward to model complex domains and apply adaptive mesh refinement techniques. However, from a post-processing perspective, unstructured grids are expensive to process, have high storage costs, and do not support smooth data approximation. Regular grids, in contrast, are grids with implicit connectivity and geometry. They have a reduced memory footprint while supporting efficient spatial queries and smooth approximation. However, regular grids lack the flexibility to represent complex geometry due to the rigidity imposed by their structured nature. This thesis investigates the problem of creating accurate approximations of unstructured grids on regular grids. For that, a regular grid must be selected that can accommodate the varying spatial resolution of the original dataset while being as small as possible. The choice of the regular grid directly affects the computational and storage cost of the approximation. The approximation procedure must lend itself to parallel and distributed implementation to prove effective in the context of the large-scale datasets produced by high-performance computing. For unstructured grids with solid boundaries, the approximation grid needs to account for the solid boundary to yield an accurate approximation close to the body. A customized octree with hybrid refinement criteria is used to obtain the optimal rectilinear grid. The approximation of the unstructured data, solved in a least-squares fashion, typically results in an ill-posed system due to the highly non-uniform distribution of the points in the original unstructured grid. We propose a variable regularization to resolve the ill-posedness in the approximation system while maintaining low approximation error. A solid boundary handling is achieved using an approximation of the boundary geometry inside each regular grid cell cut by the boundary. The research demonstrates this using linear kernels and high-order B-spline kernels. The proposed approximation can adapt to different kernels based on the need of the visualization application. We test the method using visualization algorithms that rely heavily on interpolation. We demonstrate the effectiveness of this method using several 2D and 3D unstructured simulation datasets with solid boundaries. The evaluation shows that we can achieve qualitatively and quantitatively high accuracy in representing the original unstructured data, at least six times faster query time, and dramatically reduced file size and memory footprint. The boundary-aware rectilinear grid approximation can produce accurate visualization near the solid boundary. Results show that the approximation method proposed in this thesis provides a scalable, accurate approximation for an unstructured grid into a regular grid. Various visualization applications can benefit from the proposed approximation since the approximation can be easily integrated into almost any visualization algorithm. The proposed approximation provides high accuracy while having a smaller file size, allowing for the visualization of complex and large datasets using devices with limited storage and processing power. Naive rectilinear grids without special boundary handling capabilities suffer from a poor ability to present complex geometries. In contrast, the proposed boundary-aware approximation grid can approximate the solid boundary inside the regular cells, thus providing support for complex geometry handling that other regular grids can’t provide. The interesting part of the phenomenon presented in the simulation happens close to the solid boundary. Therefore, the ability to visualize data near the boundary is essential for achieving a high-quality visualization analysis.

Degree

Ph.D.

Advisors

Tricoche, Purdue University.

Subject Area

Fluid mechanics|Mechanics

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