A variational method of hexahedral mesh generation with control metric

A variational method of constructing a spatial structured grid composed of hexahedral cells is presented. In the method, minimization of the variational functional is executed. The integrand of the functional is a ratio of the metric invariants. The functional depends on metric elements of two metrics. One metric is induced by a curvilinear mesh generated in the physical domain and the other control metric 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. The issues of mesh and cell non-degeneracy are discussed. The method of boundary nodes redistribution is considered. Examples of the grid construction are reported.