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<br><div><div>On Nov 17, 2012, at 8:17 AM, Wolfgang Bangerth wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div><br>John,<br><br><blockquote type="cite">I've attached a plot showing the basal and surface heat flow for a<br></blockquote><blockquote type="cite">spherical shell model I'm currently running. The Ra number is ~ 7.66e5.<br></blockquote><blockquote type="cite"> The model has not completely reached steady state yet, but if the<br></blockquote><blockquote type="cite">trend continues there will be a distinct gap between the surface and<br></blockquote><blockquote type="cite">basal heat flow. The .prm file I used to run the model is also attached.<br></blockquote><br>Can you post a picture of the solution at the time corresponding to the end of the plot you show? If this setup is anything similar to the ones I've made in this geometry then you shouldn't expect to run into any steady-state limit at all. Rather, you get one set of blobs rising at the very beginning and then a long phase where hot material streams up to the surface. The heat flux will then look like in your graph. But it's not a steady state -- it simply moves heat from the bottom into the domain but not out of the top, like in your graph. This takes a long time until the system finally converts to some more chaotic movement. See for example here:<br> <a href="http://www.math.tamu.edu/~bangerth/step-32.2d.convection.gif">http://www.math.tamu.edu/~bangerth/step-32.2d.convection.gif</a><br>So if you're still in the initial phase where nothing happens for a long time, then I wouldn't expect the heat flux at the top and bottom to equal.<br><br><br><blockquote type="cite">In terms of resolution, I did 4 initial global refinement steps, 3<br></blockquote><blockquote type="cite">initial adaptive refinement steps, and the coarsening and refinement<br></blockquote><blockquote type="cite">fractions are, respectively, 0.05 and 0.3.<br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">I'll try increasing the refinement fraction and initial refinements to<br></blockquote><blockquote type="cite">see if this reduces the gap between the global and surface heat fluxes.<br></blockquote><blockquote type="cite">I am bit surprised that the mesh parameters above did not adequately<br></blockquote><blockquote type="cite">resolve the basal boundary layer, if this is also the issue in my models.<br></blockquote><br>Can you post a picture of the mesh as well?<br><br>Best<br> W.<br><br>-- <br>------------------------------------------------------------------------<br>Wolfgang Bangerth email: <a href="mailto:bangerth@math.tamu.edu">bangerth@math.tamu.edu</a><br> www: <a href="http://www.math.tamu.edu/~bangerth/">http://www.math.tamu.edu/~bangerth/</a><br><br></div></blockquote></div><br></div></body></html>