Non-stationary grid generation algorithm for deformed volumes of revolution

The algorithm is designed for multi-component hydrodynamic simulation and for solving other physical and engineering problems. It is suggested for generating structured grids in the volume of revolution (main body) deformed by another volume of revolution (deforming body). In the deformation process, the deforming body is assumed infinitely stiff and strong (i.e. it does not deform, only the main body deforms). The algorithm is developed within the original variational approach for constructing optimal grids satisfying different requirements. The requirements of closeness of a grid to uniform and orthogonal are considered. The algorithm is performed on the basis of the grid generation technology elaborated earlier within the utilized approach for the volume of revolution. The volume of revolution is obtained by the rotation through 180° around an axis of a plane generatrix curve consisting of segments of straight lines and arcs of circles and ellipses. The technology is fully three-dimensional one and is not reduced to constructing rotational grids obtained by the rotation of two-dimensional grids around the axis. The developed algorithm represents the non-stationary procedure generating three-dimensional structured grids in domains with moving boundaries during which the form of the domain is changing from the volume of revolution to the desired deformed volume. The non-stationary algorithm is an iterative process where, at each stage, the deformation of a grid and then its optimization are carried out. Such algorithm allows to generate grids in very complex geometries. For this there is no need to describe the complex geometry of the deformed domain which is not obvious in the general case. It is necessary to do this only for the volumes of revolutions of the main and deforming bodies by the definition of generatrix curves for them which is essentially easier. It also permits to exclude some other stages of the traditional grid generation for the deformed volume such as generation of an initial grid. The algorithm is realized in the computer code written in C++. Examples of constructed grids are given.