Developing an ordering-based renumbering approach for triangular unstructured grids

The unstructured grid generation and employment have become very common in computational fluid dynamics applications since a few decades ago. Comparing with the structured grid data, the unstructured grid has a random data structure known as unstructured data structure (USDS). In this work, we develop a new method to convert the USDS of a triangular unstructured grid to a quasi-structured data structure (QSDS) using an ordering-based renumbering approach. In this method, the unstructured grid data is re-ordered in a manner to represent several bands in the original unstructured grid domain. Each band presents one element layer and two node lines. Then, the indices of elements and nodes are renumbered in a unified direction for the entire constructed element layers and node lines, respectively. These numbers eventually present ascending sets of element and node indices in each element layer and every node line of the resulting QSDS. This method alleviates the random USDS drawbacks because the scattered node and element numbers in the original USDS are reordered and renumbered properly. To show the robustness of the current method, we construct a few arbitrary unstructured grid distributions and convert their ordinary USDS to our innovated QSDS without requiring additional data storage.