The transfinite interpolation formula of grid generation that employs the Hermite interpolation formula is improved by the addition of a grid front marching method embedded with a simple grid smoother. In the test cases, the proposed method preserved approximate grid orthogonality around all the boundaries and eliminates grid nonsmoothness, grid slope discontinuity, and grid overlapping that occurred with the original method. The required CPU time is about 2.2 times more than the CPU time required by the original method and is at least one order of magnitude faster than the elliptic grid solver employed as a grid smoother. The method was also applied to the linear grid system to improve grid smoothness, but its computing time is about 4 times greater than the original method and is of the same order as the elliptic grid smoother. For cases with boundary discontinuity, the grid front marching method is applied to only a few grid levels inward, the remaining grids are generated via the original transfinite interpolation formula, and the required computing time is only slightly longer than that of the original formula. [References: 15]
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