Constructing the grid orthogonal and having the given nodal clustering near the boundary of a two-dimensional domain

A problem of constructing a structured countable grid in a two-dimensional domain by mapping a parametric domain with the given quadratic grid onto this two-dimensional domain is considered. The Dirichlet problem is solved for a system of quasi-linear elliptic differential second-order equations to find mapping functions. An additional local mapping that gives the control metric is used to control coordinate lines of the grid. The additional mapping helps obtain the grid with the grid lines of one family orthogonal near the boundary of the domain and having the given clustering of the grid lines of another family towards the boundary of the domain. An example that constructs the grid around the airfoil is given.