| Description |
High-order cG (continuous Galerkin) and dG (discontinuous Galerkin) methods have become increasingly popular for solving real-world problems. This is due to their accuracy, the ease of massive parallelization, and the ability of the methods to handle complex geometry. One of the main disadvantages of these high-order methods is the discontinuity of the field and its derivatives at inter-element boundaries. These discontinuities make it challenging to visualize the output from the simulation data and track features reliably. In recent years, the mathematics community has attempted to postprocess simulation data and introduce continuity at the element boundaries while preserving and, at times, increasing the accuracy of the solution using a family of Smoothness Increasing and Accuracy Conserving (SIAC) filters. The Line-SIAC (L-SIAC) filter, which can be applied to simulation data from higher dimensions, is faster than two- and three-dimensional SIAC filters. This speedup is due to its lower geometric complexity while having the same properties as the high-dimensional tensor product SIAC filters. We propose to use the L-SIAC filter as a data transformation tool to treat discontinuities in the high-order simulation data while preserving accuracy. To enable the use of current visualization tools, we use L-SIAC filtering to transform high-order simulation data to low-order data. In this dissertation, we explored the L-SIAC filter as a tool for visualization, calculate derived quantities, and remove discontinuities while maintaining or improving the accuracy of the simulation data. We extend the L-SIAC filter work from uniformly structured meshes to nonuniformly unstructured meshes, enabling the use of the L-SIAC filter in practical applications. We also improved the efficiency of the L-SIAC filter to make it computationally tractable for real-world engineering applications. Finally, we packaged the L-SIAC filter as a postprocessing tool that is readily available as a part of open-source software within Nektar++. |
