  This work concerns with the following problem. Given a two-dimensional domain
whose boundary is a closed polygonal line with internal boundaries defined also
by polygonal lines, it is required to generate a grid consisting only of
quadrilaterals with the following features: (1) conformal, that is, to be a
tessellation of the two-dimensional domain such that the intersection of any
two quadrilaterals is a vertex, an edge or empty (never a portion of one edge),
(2) structured, which means that only four quadrilaterals meet at a single node
and the quadrilaterals that make up the grid need not to be rectangular, and
(3) the mesh generated must be supported on the internal boundaries. The
fundamental technique for generating such grids, is the deformation of an
initial Cartesian grid and the subsequent alignment with the internal
boundaries. This is accomplished through the numerical solution of an elliptic
partial differential equation based on finite differences. The large nonlinear
system of equation arising from this formulation is solved through spectral
gradient techniques. Examples of typical structures corresponding to a
two-dimensional, areal hydrocarbon reservoir are presented.
