Document Type : Research Note
Authors
Dept. of Aerospace Engineering\nSharif Universi&zwnj
Abstract
Contrary to the structured grid disadvantages, disadvantages the unstructured grid provides sufficient flexibility to generate grid in very complicated geometries and simplifies the grid adaptation, where it is necessary. In spite of termendous efferrs in improving the unstructured grid employment and despite achieving remarkable advancements, this field of research is still open to be explored by new contributors. Basically, most of unstructured grid generators grade its substructures randomly. Therefore, no global directionality can be readily found in a regular unstructured grid data structure. This can cause serious trouble for grid users, such as those in CFD, who need the knowledge of node, face, and cell neighborhood connections. Consequently, because of a quite random neighborhood numberings, the node/face/cell numbers are to be stored explicitly in large vectors and matrices. Evidently, converting this random data arrangement to an organized data structure can enhance the computational efficiency in unstructured grid applications. In this research, a very simple and computationally low cost numerical procedure is developed to construct a layer-by-layer data structure for 2D triangular unstructured grids. The key point in this procedure is that each layer in this pattern has a quasi-structured data structure presenting ordered element number and node number patterns. The objective of this research is to develop a layer-by-layer ordering and renumbering algorithm. which simplifies the above achievements.In this algorithm, the elements and nodes in the unstructured grid are suitably renumbered to produce a new layer-by-layer data structure very similar to those can be found in structured graids. This algorithm benefits from the ordered data of elements and nodes produced in the preceding layer to construct the current neighboring layer and to order its element and node indices properly. The procedure needs to be started from the first ordered node layer (it is usually the inner boundary), and is extended to next neighboring element and node layers until reaching the outer boundary of the domain. In this method, the achieved overall patterns for the constructed node layers are mostly determined by the primitive chosen node layer. where the procedure is started. If we choose the nodes located at the target object as our node layer, the resulting node layers would schematically take a pattern very similar to lines distributed around the target object in an O-type structured grid. However, if the initial node layer contains both the nodes located at the target object and the grid lines connecting the object to its outer boundary, the overall pattern of the constructed node layers will be schematically very similar to a set of grid lines around the target object in a C-type structured grid. Furthermore, if the target object consists of several components, the first node layer must include, not only the nodes located at all body components but also the nodes located at the grid lines i.e. the lives which connect these sub-bodies to each other. According to our investigation, the current algorithm generates a directional layered data structure very robustly, even in very complex mesh domains. However, in the case of having a complex element connection inside the layers, the method does not guarantee the physical neighborhood condition for some pairs of adjacent elements or nodes in the achieved data structure. These exceptions mostly require negligible additional search inside the constructed layers to find neighboring elements or nodes. Additionally, the current method facilitates the addressing procedure in a data structure, because the search is confined to some neighboring layers instead of the entire grid data. To show the robustness of the method, the new data structure is constructed for an unstructured grid distributed around a submarine. The current evaluations show that the developed algorithm works very successfully, even in domains with complicated geometries and/or complexunstructured mesh distributions.
Keywords
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