Variational method for hexahedral grid generation with control metric

A variational method of generating spatial structured (or regular) grids composed of hexahedral cells is considered. In the method it is minimized the functional, whose integrand is a dimensionless ratio of metric invariants. The functional depends on the metric elements of two metrics. One metric is induced by a curvilinear grid generated in the physical domain, while the other control metric given in a special way provides additional control of the cell shape such as condensing the coordinate surfaces and orthogonalizing the coordinate lines of the grid towards the domain boundary. Nondegeneracy conditions for the grid and the hexahedral cell are discussed. The method for redistributing nodes over the domain boundary is considered. Grid generation examples are given.