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Abstract
The present contribution presents the piecewise parabolic finite analytic scheme (PPFAM3D) for the solution of the three-dimensional (3-D) convection-diffusion equation. The calculation domain is divided into cells, but unlike traditional numerical schemes, the PPFAM3D employs the analytical solution of the linearized convection-diffusion equation in each of them. The piecewise parabolic boundary conditions ensure that the coefficients of the numerical scheme are all positive and that their sum is always equal to 1, thus satisfying the Scarborough criterion. Comparison with other finite analytic schemes shows the PPFAM3D to be superior in accuracy and stability. The scheme is shown to be free form numerical diffusion and to accurately include the diffusion effect, even when in highly skewed convection situations