Automatic Generation Of Finitr Elements Grids In 3-D

Two approaches are derived for the automatic generation of allhexahedral meshes. The first approach adopts the isoparametric concept for the mappmg between a superelement and a cube. The cube is discretized by inserting nodes either regularly or according to a given set of weights in each of the three directions. Then these nodes are mapped back to the superelement. This approach is applicable when the physical domain can be decomposed as a set of superelements. A superelement (topologically equivalent to a cube) consists of six faces and eight edges and is described by 20 nodes allowing curved boundaries.The second approach efficiently meshes solids of revolution. It adopts the transformation between cylindrical and Cartesian coordinates as well as the translation and rotation of coordinates. The applicability of this approach is extended to generate more general solids:1- when the axis of rotation is a curve rather than being a straight line.2- when the radius is a function of the rotational angle rather than being a3- a clustering function is introduced to generate non-uniform meshes.The details of a suggested data structure are presented. It is simple and flexible to provide required data for graphing the mesh and to prepare the input data file for a partial differential equation solver. The proposed algorithms areimpl.emented and the output meshes are plotted for many illustrative solids and surfaces.These approaches for automatic grid generation can be immerged with composite-grid fast solvers and multigrid methods [95] because they efficiently provide structured grids and hence permit the use of the same relaxation routine on different grids and simplify inter-grid transfer operators. Also these automatic generators work well in the field of computational fluid dynamics [43] since they produce orthogonal, boundary fitted grids. The second algorithm is especially applicable for piped shaped domains.For the future work we recommend the following:Due to the current trends in mesh generation [96-101] that seek full automation schemes and to make the combination process of the presented two algorithms easy, a graphical user interface (Gill) is required which may require the following issues:1. Employing Object Oriented programmmg (OOP) techniques usmg C++ language that facilitate automation problem.1. Developments are also directed towards merging (OOP) with the computer aided design (CAD) and computer aided engineering (CAE) technologies to make an interface between them.2. Automatic decomposition of complex domains IS also required for full automation process.3. Introducing parallel processing in the mesh generation process.4. Integrating the proposed algorithms with an adaptive multi grid algorithm to solve more complicated problems in three-dimensional space.