A variational hexahedral grid generator with control metric

A variational method of constructing a spatial structured grid composed of hexahedral cells is presented. The method executes a minimization of the variational functional. The integrand of the functional is a ratio of the orthogonal invariants. The functional depends on two metrics. One metric is induced by a curvilinear mesh generated in the physical domain and the other control metric, given in the canonical domain, is responsible for an additional cell shape control, for instance, for condensing the coordinate surfaces and orthogonalization of the grid lines towards the domain boundary. Generally, defining the control metric allows to generate an arbitrary given non-folded mesh in the physical domain. For every cell, the functional is discretized on ten tetrahedra forming two dodecahedrons with the same vertices which span the hexahedral cell. The discrete functional possesses an infinite barrier on the boundary of the set of non-folded dodecahedral cells that ensures the construction of the non-folded grid composed of such cells. In the most practical cases the hexahedral grid with the same nodes is non-folded as well. The method of boundary nodes redistribution is considered. Examples of the grid construction are reported.