Nonstationary grid generation algorithm for deformed volumes of revolution

The nonstationary grid generation algorithm for deformed volumes of revolution and the corresponding computer code are suggested. The volume of revolution is obtained by the rotation through 180 ◦ around the axis of a planar curve consisting of straight-line segments, arcs of circles, and ellipses. The deformed volume of revolution is obtained as the result of the deformation of the volume of revolution (main body) by pressing on it with the other volume of revolution (additional body).  The algorithm is constructed for numerical modelling of the processes of multicomponent hydrodynamics and developed within the variational approach on the basis of grid generation algorithms for volumes of revolution. The algorithm carries out the generation of structured optimal grids (nondegenerate, closed to uniform and orthogonal ones) composed of hexahedral cells. The computer code is written in C++. The algorithm represents the nonstationary iterative process consisting on each iteration of two stages. On the first stage (deformation), both the main body and grid in it are deformed by pressing on them with the additional body and grid in it. The degree of deformation on each iteration is chosen in such a way that deformed grid does not contain degenerate cells. The second stage (optimization) represents the optimization of a deformed grid by the variational method for construction of optimal grids. On this stage, a special correction of grid nodes to corresponding surface of revolution is applied. The iterative process is applied up to necessary degree of deformation of the main body. Initial grids in main and additional bodies are constructed by grid generation algorithms for volumes of revolution.  Examples of grids in deformed volumes of revolution and results of their testing according to optimality criteria are given.