<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Hi Jed,<div><br></div><div>I'm mainly interested in the parameter limits -- I know how to specify them, but I don't see any explanation of valid values in the code. So for ex20, how large can beta get and still be meaningful? </div><div><br></div><div>For ex29, are you saying that it's always generating a singular linear system, or only for low viscosity and resistivity?</div><div><br></div><div>Thanks!</div><div>Boyana<br><div>
<span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Monaco; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><div><br class="Apple-interchange-newline">--</div><div>Boyana Norris, Ph.D., Computer Scientist, Argonne National Laboratory</div><div><a href="mailto:norris@mcs.anl.gov">norris@mcs.anl.gov</a>, +1.630.252.7908, <a href="http://www.mcs.anl.gov/~norris/">http://www.mcs.anl.gov/~norris/</a></div></span></span>
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<br><div><div>On May 14, 2011, at 1:14 PM, Jed Brown wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div class="gmail_quote">On Sat, May 14, 2011 at 02:53, Barry Smith <span dir="ltr"><<a href="mailto:bsmith@mcs.anl.gov">bsmith@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;">
Do you know what the valid values for the various model parameters in snes ex20 and ex29 are? We are looking for something we can vary similar to how we change the lid velocity and grashof parameters in the driven cavity problems, in order to generate linear systems with different characteristics.</blockquote>
</div><br><div>The options are given in the help strings. Do you want the names of the non-dimensional parameters? Do you want to know how various parameters affect the system?</div><div><br></div><div>In the case of ex20, the exponent beta is the only free parameter. If temperature is always positive, I believe there are no well-posedness issues for any beta. Positive beta becomes degenerate as T -> 0, negative beta becomes singular in that limit. It appears that the method works for all positive beta. When beta is negative, this discretization (or maybe just the line search) is not monotone so it may compute negative temperatures (program crashes). Negative beta is physical for other heat transport problems.</div>
<div><br></div><div>I can't give a similarly detailed explanation of ex29, but low viscosity and low resistivity should tend to make it less diffusive (closer to ideal MHD which is hyperbolic). This discretization seems to produce singular linear systems.</div>
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