<div class="gmail_quote">On Sat, Apr 7, 2012 at 08:35, Matthew Knepley <span dir="ltr"><<a href="mailto:knepley@mcs.anl.gov">knepley@mcs.anl.gov</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div id=":3uk">It will get rid of oscillation and conserve the quantity (looks a little like FCT), but the 0,1 bounds make no sense to me<div>for energy. For concentration (as in the paper), they are natural.</div></div></blockquote>
</div><br><div>FCT is still locally conservative. The superbee limiter has some sharpening ability, but not as much as Lenardic's filter. The filter is more like volume of fluid interface reconstruction, but without the defined normals and precise interface location of a scheme like PLIC.</div>
<div><br></div><div><a href="http://math.uh.edu/~caboussat/Work/Papers/Files/caboussat_arcme.pdf">http://math.uh.edu/~caboussat/Work/Papers/Files/caboussat_arcme.pdf</a></div><div><br></div><div>The closest analogue that would work for temperature is probably clipping with global compensation, but that is very likely to change the dynamics of the system. Also note that this clipping is not random redistribution of mass/energy; depending on the advection scheme, the oscillations can lead, be centered on, or trail the intended discontinuity, leading to systematic mass/energy channels. This may explain why Paul's paper showed such highly different dynamics with and without the filter.</div>
<div><br></div><div>I believe that for energy, you want a locally conservative non-oscillatory method. Clipping is a delicate world to get into. If you have strict max and/or min bounds and want higher than second order accuracy, there are more principled limiting techniques that can preserve the high order accuracy and local conservation (e.g. Zhang and Shu's positivity-preserving limiters; note that these change the definition of max/min to be in terms of the reconstructed initial state instead of the piecewise averages for which a very simple argument shows that any max/min preserving method cannot be more than second order accurate).</div>