Method of Tetrahedral Mesh Generation for Regions with Curvilinear Boundaries
Sergey N. Borovikov, Igor A. Kryukov, Igor E. Ivanov · 2006
Abstract. In this paper we briefly discuss our method for tetrahedral meshgeneration for regions with curvilinear boundaries and present some examplesof using generated tetrahedral meshes for solving CFD problems. 1. IntroductionMesh generation is the important auxiliary step in the numeric modeling ofmathematical physics problems. There are two types of meshes: structured andunstructured meshes. Structured meshes are relatively compact and correspond-ing algorithms for manipulating with them are not very complicated. Structuredmeshes are used in both finite-difference and finite-volume numerical schemes.The main drawback of structured meshes is that they can not be generatedfor an arbitrary region, whereas modern problems of computational mathemat-ics require solving in complex three-dimensional regions. Usually, unstructuredmeshes are created for such regions.What is a complex region? It is a region that has a lot of faces with differenttypes of geometries. Usually for creation of such regions computer-aided designsystems are used since many tools have been implemented for the solid modelingin CAD systems. Sometimes it is not possible to construct even multiple blockstructured grids for these regions.In our work we use tetrahedral meshes because only this type of meshescan be constructed for an arbitrary region by direct methods. There are threeprimary methods of generation of tetrahedral meshes: the octree methods, theadvancing front method and the Delaunay approach. We use the Delaunayapproach because the Delaunay triangulations and tetrahedralizations possessmany important geometrical properties.Meshes generated by the algorithm were used to perform some numericalsimulations of CFD problems using the finite volume method. Our methodallows constructing quality meshes even for highly complicated regions. Qualitymesh building is the first and often essential step in numerical simulation. Ahigh-quality numerical solution is not possible without a high-quality initialmesh.295