Numerical generation and grid controls of boundary-fitted conformal grids in multiply connected regions

Based on the study of grid generation methods in a simply connected region (Int. J. Numer. Meth. Engng 1997; 40:343), with the aid of a new transformation from a multiply connected region to a simply connected domain, the grid generation in a multiply connected domain is carried out in this paper. 2-D conformal and orthogonal grids are generated in a multiply connected region, mostly involving a multiple-blocks method developed in the present study. To avoid grid distortion on the degenerated boundary caused by physical singularities, controls of grids through specified points are implemented, without losing the conformal properties. Further applications of this gridscontrolling technique for points inside the region, the nested grids, and the multiple-blocks method are introduced and discussed comprehensively. Numerical examples are taken to demonstrate the validity and applicability of the theorems