<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Hi Matt:<div><br></div><div>As you note, the Lenardic & Kaula filter was designed for the sharp interfaces found in dealing with 2 materials. It's not really suitable for temperature; it wasn't designed for that, and would have the disadvantages noted by Jed. </div><div><br></div><div>Louise</div><div><br></div><div><div><div>On Apr 7, 2012, at 6:35 AM, Matthew Knepley wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite">On Sat, Apr 7, 2012 at 1:41 AM, Jed Brown <span dir="ltr"><<a href="mailto:five9a2@gmail.com">five9a2@gmail.com</a>></span> wrote:<br><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div class="gmail_quote"><div class="im">On Fri, Apr 6, 2012 at 22:20, Matthew Knepley <span dir="ltr"><<a href="mailto:knepley@mcs.anl.gov" target="_blank">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>Can't you also do WENO reconstruction on an FEM solution?</div></blockquote><div><br></div></div><div>It's much less natural and rarely done in practice.</div><div class="im"><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div><div></div></div><div>Okay, that was not how it was explained to me. Is it like a Laplacian filer (which would sharpen edges)? I don't see how this would reduce oscillation,</div><div>although I guess it could result from the solve for the conservation requirement.</div>
</blockquote></div></div><br><div>Look at the algorithm, it is a discrete interface sharpening filter.</div><div><br></div><div><a href="http://www.agu.org/pubs/crossref/1993/92JB02858.shtml" target="_blank">http://www.agu.org/pubs/crossref/1993/92JB02858.shtml</a></div>
<div><br></div><div>It clips values that are greater than 1 or less than 0, tracking the maximum over/undershoot. Values inside the bounds of that over/undershoot are then pressed out to 1 and 0 respectively. Then the remaining conservation error is distributed to all cells that are not identically 0 or 1. I don't see any way that this is sensible for thermodynamics.</div>
</blockquote></div><br>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><br></div><div> Matt<br clear="all"><div><br></div>-- <br>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>
-- Norbert Wiener<br>
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