>
> I think we must insist on a monotonic method for remapping so 
> such wiggles are not acceptable. Remember, the new grid is
> arbitrary in principle and if it happened to be very fine in the
> vicinity of the wiggle then the wiggle would be reproduced in the
> remapped field. For a density field this would lead to a locally
> statically unstable situation, etc. It for precisely such reasons
> that the requirement of monotonicity is imposed. It has nothing
> to do with shocks in this case.  Remember Murphy's Law!
>
> Therefore, WENO without limiting is not interesting as a method by
> itself. Have you tried WENO with limiting?



That strictly monotonic version of WENO subroutine is available at 

            http://www.atmos.ucla.edu/~alex/remapping

which is the same directory as before. Just download two files 
"remap2W.F"  and "gmeta_WENO_monotonic" which are the subroutine and
the corresponding plots showing the result (same format as before).


  ==> You may overwrite the older version of file "remap2W.F", since
      if you undefine CPP-switch LIMIT_INTERIOR in the new version,
      it will work exactly as before (the version you already have). 


Strict monotonicity requires downgrade of top and bottom boundary
conditions to the first order of accuracy (just assume that the
field is constant within the top- and botom-most grid boxes),
because this is the only way to guarantee that the side boundary
values (extrapolated within the topmost and botommost grid boxes
toward the boundary) do not exceed corresponding grid-box averages,
thus preventing growth of extremal boundary values.  


Performance:  Slightly more dissipative than the original WENO,
============  but still outperforms PPM.
