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A new spatial differencing scheme for the transonic full-potential equation in conservative form has been developed. Three consistency conditions for the full-potential equations are derived and are satisifed by the new scheme. This scheme guarantees zero truncation error on any curvilinear mesh for freestream flows in either two- or three-space dimensions. Solutions obtained with this new differencing scheme, away from freestream regions, exhibit greatly improved accuracy, especially for nonsmooth or singular meshes. The computing times associated with the new scheme are approximately the same as the less accurate old scheme when computations are performed on the same mesh.
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Flores et al. (1984) studied this question.
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