Non-structural Network Generation Technology And In The Shallow Water Wave Equation Solution

In this thesis, a well-known geometric construction called the Delaunay triangulation is discussed extensively. The problem of planar mesh generation with quality bounds is considered. A good mesh generation algorithm should accept an arbitrary planar straight line graph and output a Delaunay Triangulation of a set of points which conforms to the input and has no small or large angles. Algorithms based upon the Delaunay triangulation are discussed. We also briefly survey some of the previous research on simplicial mesh generation.In this paper, the methods of triangulation in two-dimensional domain are discussed. Based on the analysis and summarization of the current algorithms, several methods and algorithms of mesh generation were investigated. A technique that can generate the initial coarser meshes was discussed. In addition, a method of mesh gradation control by means of point distribution and a method of mesh refinement were also investigated in this paper.Delaunay refinement is a technique for generating unstructured meshes of triangles suitable for use in the finite element method or other numerical methods for solving partial differential equations. Delaunay refinement operates by maintaining a Delaunay triangulation, which is refined by the insertion of additional vertices. The placement of these vertices is chosen to enforce boundary conformity and to improve the quality of the mesh. Ruppert's algorithm for solving this problem are reanalyzed. Using Ruppert's analysis technique, We prove that Ruppert's algorithms can produce triangular meshes that are nicely graded, size-optimal.Several new algorithms are described for adaptivity of Delaunay triangulations. The mesh adaptation is performed by subdividing the cells using information obtained in the previous step of the solution and next rearranging the mesh to be a Delaunay triangulation. The method automatically identifies nodes of the mesh which are candidates for deletion. The mesh refinement procedure sub-divides elements into a number of similar elements in the regions to be refined. For a region to be coarsened, several node deletion processes are described and it is proved that the resulting triangulation is Delaunay. The procedure allows the gradual improvement of the quality of the solution and adjustment of the geometry of the problem.In this dissertation, the finite volume method to solve two-dimensional shallow water equations in unstructured grid system is investigated in detail. Numerical experiments showed that our methods were feasible and efficient...