Realization of the adaptation criterion in the grid generation technology for constructions bounded by the surfaces of revolution with parallel axes of revolution
O. V. Ushakova1,2
1N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
2Ural Federal University named after the First President of Russia B.N. Yeltsin, Ekaterinburg, Russia
Keywords: adaptation criterion, technology for grid generation, volumes bounded by the surfaces of revolution with parallel axis of revolution
Abstract
A realization of an adaptation criterion in the technology of generation of three-dimensional structured grids designed for the numerical solution of differential equations modeling the vortex processes of multi-component hydrodynamics is described. Earlier the adaptation criterion was realized for volumes of revolution and volumes of revolution deformed by other volumes of revolution. The adaptation criterion is realized within a variational approach for the construction of optimal grids satisfying optimality criteria: closeness of the grid to a uniform and orthogonal one and adaptation to a given function. In the realization of the criterion, the technology is supplemented by a new way of boundary nodes computation and an algorithm for the construction of an admissible set for minimization of a discrete functional formalizing the optimality criteria. Examples of grids adapted to a given function and its first derivatives are given.
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