Abstract
This work presents a Fortran code to solve the advection equation in 1, 2 and 3 dimensions. The scheme is based on a rational interpolation function. Not only the interpolation profile itself but also its first-order spatial derivatives are predicted by the governing equation. Using the Lagrangian invariant solution of the advection to evaluate the gradients makes the method compact. The scheme is indeed constructed over only one mesh cell. The method has third-order accuracy in the smooth region and appears to be able to suppress spurious numerical oscillations near great gradients.
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