An elliptic method for construction of adaptive spatial grids

This paper contains some new results concerning the development of a universal method for the construction of spatial grids. The method is based on numerical solution (a stabilizing correction scheme) of inverted one-, two-, and three-dimensional Beltrami equations and diffusion equations with respect to the control metric. One- and two-dimensional equations are used for the generation of grids on the edges and faces of a domain. Using three-dimensional equations, a grid is constructed inside a domain. Examples of model adaptive spatial hexahedral and prismatic grids and a grid for the calculation of the propagation of a passive impurity in the atmosphere are demonstrated.