On the use of a coordinate transformation for the solution of the Navier-Stokes equations

Abstract The equations of fluid motion have been formulated in a generalized noncartesian, non-orthogonal coordinate system. A particular coordinate transformation, which transforms a domain with an irregular lower boundary into a cube, has been constructed. The transformed system, unlike the original one, has flat boundaries and homogeneous boundary conditions. Where the topography is flat, the original and transformed systems are identical, and extra terms do not appear. A finite difference scheme for solving the transformed equations has been constructed and will be described in a subsequent issue of this journal.

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