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Centered fourth order advection is formally the most accurate scheme
we have implemented and can be used to great effect in high resolution
simulation where dynamical scales are well resolved. However, the
scheme is noisy like the centered second order method and so must be
used with some finite amount of diffusion. Bi-harmonic is recommended
since it is more scale selective and less likely to diffuse away the
well resolved gradient the fourth order scheme worked so hard to
create.
The centered fourth order fluxes are discretized:
As for the third order scheme, the best discretization near boundaries
is under investigation but currently
on a boundary.
Next: 2.16.4 First order upwind
Up: 2.16 Linear advection schemes
Previous: 2.16.2 Third order upwind
Contents
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