Preface to the Third Edition

Grid generation codes represent an indispensable tool for solving field problems in applied mathematics, mechanics, physics, and other areas of practical applications. Despite the considerable success achieved in grid generation technologies, development of more efficient and sophisticated algorithms and computer codes for generating grids still remains an important problem. Serious difficulties arise in grid generation in domains with complicated boundary geometries, specifically, with discretely defined boundary segments and in the case when grids have to be adapted to solution singularities, such as boundary and interior layers, shocks, detonation waves, combustion fronts, high-speed jets, and phase transition zones. A promising tool to deal with the numerical problems having such singularities is adaptive grid generation technology. With increasing complexity of the physical problems, there is an increased need for more reliable, robust, and fully automated grid generation codes which enable one to generate suitable meshes in a uniform “black box” mode, without human interaction. The development of such grid systems is a challenging problem in computational physics and applied mathematics. Grid technology still remains a rapidly advancing field of computational and applied mathematics. New achievements are being added by the creation of more sophisticated techniques, modification of the available methods, and implementation of more subtle tools as well as the results of the classical theories of differential equations, calculus of variations, and Riemannian geometry in the formulation of grid models and analysis of grid properties. Therefore, there is a clear need of students, researchers, and practitioners in the field of applied mathematics and industry for the creation of new books and/or updated editions of the available books which will complement the existing ones, providing a description of current developments relating to grid methods, grid codes, and their applications to the solving of actual problems. This third edition of the monograph “Grid Generation Methods” is significantly expanded with new material that discusses recent advances in grid generation technology. It includes a description of updated grid generation methods, which were partly presented in the former monograph of the author, as well as new adaptive approaches for structured and unstructured grids and numerical algorithms