On a Dirichlet problem related to the invertibility of mappings arising in 2D grid generation

The present paper deals with the invertibility of mappings that transform simply connected two-dimensional domains into a convex domain. The mapping is de ned by a system of second order elliptic equations. These mappings are used to generate so called structured grids in the physical domain to solve Computational Fluid Dynamics (CFD) problems. These grids are generated by mapping a uniform rectangular mesh from a rectangle onto the physical domain. To enable a consistent discretization of the ow equations, it is necessary that the mesh in the physical domain be nonoverlapping. Hence it is necessary that the mapping be invertible.