Conformal grid generation for high aspect ratio simply and doubly connected regions

Conformal co‐ordinate transformations are used to map rectangular computational domains onto arbitrary simply and doubly connected regions with smooth boundaries. The efficient numerical schemes of Wegmann involving the solution of the inverse boundary correspondence function problems associated with the mapping of the unit disc or circular annulus onto simply or doubly connected domains, respectively, are employed. The numerical implementation of these schemes is emphasized. Examples are generated for regions with elliptic inner and outer boundaries. Additional examples are used to demonstrate the accuracy and convergence of the schemes and their practical limitations. The techniques are found to converge well if holomorphic functions are used to describe the boundaries. The use of preconditioning maps is also discussed.