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Typical individual requirements imposed on grid technologies are as follows [1]: 1. robustness (well-posedness, simplicity, portability, etc); 2. comprehensiveness (realization of all necessary grids); 3. invariance (independence of parametrizations of physical geometries); 4. regularity (orthogonality of grid lines, small deformation of grid cells); 5. grid clustering in the zones of large variations of functions (shock waves, boundary and interior layers); 6. grid clustering in the zones of large or small values of functions (approximation or interpolation errors, depth of a basin); 7. grid line alignment with vector fields (magnetic fields in tokamak-related problems). The grid technology based on the solution of inverted Beltrami equations in monitor metrics provides both individual and balanced requirements. The paper demonstrates recent results of such technology including the formulation of the monitor metrics to realize the grid properties and the development of grid generation codes. Applications to some fluid dynamics and plasma problems are exhibited. The research was made possible in part by Award No 06-01-08009 of the Russian Foundation for Basic Research (RFBR) and by Award No 1.8 of the Integration Project of the Siberian Branch of the Russian Academy of Sciences -- 2006. [1] V.D. Liseikin A Computational Differential Geometry Approach to Grid Generation. 2nd Edition. Berlin: Springer, 2007.
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