In this section we describe the methods we have implemented in
PROMIS for the generation of the mapping function 
, i.e. for the generation of the curvilinear coordinate
system [Wim90].
Curvilinear grid generation is a fairly common method in computational fluid dynamics, whence has come much of the impetus for this technique. An excellent introduction to this field is the textbook of Thompson et al. [Tho85].
An approximate equidistant grid in the computational domain which resolves all geometric contours in detail is mapped onto the physical domain. First, the distribution of the boundary points is determined. From the fixed point locations at the boundary the grid points in the interior of the domain are obtained by algebraic, elliptic, or variational methods.