Three-dimensional unstructured viscous grids by the advancing-layers method

Abstract

A method is presented for generating three-dimensional viscous unstructured grids on complex configurations. The approach stems from a natural extension of the advancing-layers method (ALM) that has been successfully applied to two-dimensional problems in prior work. High-aspect-ratio tetrahedral cells are constructed in viscous dominated flow regions by the ALM, with the remaining isotropic cells generated by the conventional advancing- front method. Relying on a totally unstructured grid-generation strategy, the method benefits from a high degree of flexibility and automation required for generating grids around complex geometries. Sample three-dimensional grids around complex configurations are presented to show the capability of the method. NSTRUCTURED grid methodology has demonstrated consid- erable success in computational fluid dynamics (CFD) mainly due to its inherent flexibility for discretization of geometrically com- plex domains. The growing number of new techniques and publi- cations imply the importance and increased interest in this class of grids. A thorough survey of the subject is given in Ref. 1. However, despite their remarkable effectiveness in computation of complex inviscid flow fields, unstructured grids have yet to provide for the routine computation of the Navier-Stokes equations in three dimen- sions. The lack of a robust unstructured grid strategy for generating highly stretched cells has been a major obstacle to applying such methodology to complex three-dimensional viscous-flow problems. Among the numerous references on the unstructured grid method- ology in the literature, there are only a few that discuss the problem of three-dimensi onal viscous flow on unstructured grids. Notable among the references that address unstructured viscous grid gener- ation are those cited in Refs. 2-10. Although most of the reported techniques have provided appropriate results for the specific applica- tions shown, many lack the desired generality, flexibility, efficiency, automation, and robustness. Semiunstructured techniques, for example, retain some of the limitations of structured grid-generation methods that impair the re- quired flexibility and robustness of the method to handle arbitrary three-dimensional complex configurations. Prismatic grids are ef- ficient in terms of computer memory requirement and are effec- tive as long as the configuration under consideration is relatively simple. For geometrically complex domains, this class of grid- generation techniques requires sophisticated schemes, to ensure the integrity of generated grids, which makes the method computation- ally intensive.3 Alternatively, prisms have been coupled with more flexible grids (e.g., tetrahedral) to form hybrid grids.5 This type of grid requires a special flow solution strategy to treat different cell types in the field. Furthermore, to form a one-to-one connection between the prismatic and tetrahedral cells, an identical number of prism layers should be maintained globally to obscure the quadri- lateral faces of prisms that obviously do not match with triangular faces of tetrahedral cells. This may limit the extent and flexibility of the prismatic portion of hybrid grids and, thus, reduce the capa- bility of the method for complex problems. Realistic configurations involving sharp edges, integrated components, gaps between close surfaces, etc., are examples of such complexities that require extra careful attention and enhanced capabilities that the existing semi- unstructured techniques may lack.