| Grid generation is the pre-processing step of the whole numerical computations process of partial differential equations. It plays a key role in the success of numerical simulations. In practice, quadrilateral mesh is better than triangular one both in efficiency and accuracy of numerical simulations and adaptive mesh is better than non-adaptive one by placing grid elements with different sizes in different zones of problem domains. In this dissertation, three inter-related issues on adaptive surface mesh generation are discussed, i.e. geometry-based adaptive mesh size specification, advancing front triangular surface mesh generation and quadrilateral mesh generation.First, the characteristics of the advancing front technique (AFT) and the general process of surface mesh generation are studied in order to build a generic AFT algorithm framework for surface mesh generation. A series of common algorithms of advancing front surface mesh generation are discussed as well. In this framework, various strategies of geometry modeling, mesh size controlling and mesh generation can be integrated if some programming interfaces are complied with.Secondly, the size control module of the framework is discussed, where a geometry-based adaptive size filed is built with the help of the constrained Delaunay triangulation of the boundary sampling points. A smoothing algorithm of the adaptive size field is detailed to ensure the generated meshes have a proper density distribution and element shapes.At last, the advancing front triangular and quadrilateral surface mesh generation algorithms are presented. The triangular mesher is achieved by recoding a previous version of the meshing algorithm written by Fortran with C language. Some observations about the algorithmic details are discussed in detail. Then the algorithm is extended for quadrilateral surface mesh generation, and some specific techniques involved in the new algorithm are resolved.
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