The interpolation method in a semi-Lagrangian scheme is decisive to its
performance. Given the number of grid points one is considering to use for the
interpolation, it does not necessarily follow that maximum formal accuracy
should give the best results. For the advection equation, the driving force of
this method is the method of the characteristics, which accounts for the flow
of information in the model equation. This leads naturally to an interpolation
problem since the foot point is not in general located on a grid point. We use
another interpolation scheme that will allow achieving the high order for the
box initial condition.
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