A morphing algorithm for the generation of structured grids in deformed volumes
N.A. Artyomova1, O.V. Ushakova1,2
1N.N. Krasovsky Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russia
2Ural Federal University named after the First President of Russia B.N. Yeltsin, Yekaterinburg, Russia
Keywords: structured grids, deformed volumes, optimal grids, moving grids
Abstract
A morphing algorithm included in a three-dimensional structured grid generation technology designed for the numerical solution of differential equations modeling vortex processes in multi-component hydrodynamics is described. The algorithm is intended for the generation of structured grids of a special topology in volumes obtained by deformation of volumes of revolution by the bodies formed by surfaces of revolution with parallel axes. The algorithm is developed by using a variational approach for constructing optimal grids and is a non-stationary one: at each iteration the form of a domain and the grid for it are deformed. Then the grid is optimized in accordance with the following optimality criterion: the closeness of the grid to a uniform and orthogonal one. The iterations are continued up to a given degree of deformation. The algorithm allows one to construct grids in domains of very complex geometry, and it is not necessary to describe the boundary of a complex domain, it is sufficient to describe the volume of revolution, the deforming volume, and the parameters of deformation. Examples of grid calculations are given.
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