S.A.Ivanenko
Computational Center Russian Academy of Sciences Moscow
A.F.Sidorov
Institute of Mathematics and Mechanics Ural Branch of Russian Academy of Sciences Ekaterinburg
The paper gives the survey of different approaches to the methods of grids generation in complex geometries domains, which have been developed in the USSR and Russia for the last 30 years. Some conclusions are made and the main directions of investigations are described, that were discussed at the 5 th all-union and Russian conferences on the grid generation methods and their applications for the problems of mathematical physics (1987,Sverdlovsk, 1988,Kemerovo, 1990,Sverdlovsk, 1992, Sneshinsk, 1994,Kazan)
The main stress is laid on the methods of block-structured grid generation, directions of generation of grids of non-regular structure are described briefly, the ideology of grid generation is also described, which is widely used in some important research centers: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow; Central Institute of Hydrodynamics, Moscow; Computational Center, Russian Academy of Sciences, Moscow; Russian Federal Nuclear Centers - All-Russia Scientific-Research Institute of Experimental Physics, Arzamas-16, - All-Russia Scientific-Research Institute of Technical Physics, Chelyabinsk-70; Institute of Mathematics and Mechanics, Urals Branch of RAS, Ekaterinburg Institute of Computational Technologies, Siberian Branch of RAS Novosibirsk; Institute of Mathematics, Siberian Branch of RAS, Novosibirsk and so on.
The ways of automation of generation of grids of different types in multy-dimensional domains are presented taking into account different optimility criteria. There are described the method of improvement of aproximate propeties of grids, the ways of reduction of data, the forms and properties of functionals, determining the mapping by means of which curvilinear grids are generated, the main algorithms used to generate grids. The system of tests for comparison of quality of different grids is also considered. Computer codes of grid generation (MOPS-2 by O.B.Khairullina, LADA by O.V.Ushakova, 2DConvex by S.A.Ivanenko) and applications of these grids to the solution of gasdynamics and hydrodynamics problems will be demonstrated.