Two-dimensional orthogonal grid generation with floating boundary points

A least-square formulation of the floating-boundary-point method for two-di mensional orthogonal grid generation is proposed. The functional defined by the deviation from rite Beltrami equation is discretized and minimized via a point-by-point search procedure, Since some internal corner points may b e artificially fixed the present method can preserve boundary geometry desp ite discontinuous slope along a boundary. If there is a sharp internal corn er, the grid takes on characteristics similar to those of polar coordinate systems. Correction based on this fact is employed to preserve monotonic gr id distribution around the corner. Numerical tests show that several cycles of the floating-boundary-point method can produce a smooth grid system wit h approximate grid orthogonality. Two methods with additional iterations ar e examined: one uses a long iteration of the floating boundary method and t he other uses several steps of the floating-boundary-point method followed by a long iteration of the fixed-boundary-point method. Both methods slight ly enhance the mean deviation from orthogonality but deteriorate grid smoot hness and do not guarantee reduction of the maximum deviation from orthogon ality.