<div>Hi guys,</div><div><br></div><div>I would like to share some figures regarding the advection schemes from my previous practice.</div><div><br></div><div>I've injected a passive tracer (with a minimum value of 1 and a maximum value of 3) into a barotropic</div><div>nondivergent flow (5.5km resolution) and observed its evolution subjected to the advection process</div><div>only (I turned off the explicit lateral diffusion). I selected nine advection schemes:</div><div> code 2: centered 2nd order</div><div> code 3: 3rd order upwind</div><div> code 4: centered 4th order</div><div> code 20: 2nd order DST (Lax-Wendroff)</div><div> code 77: non-linear flux limiter</div><div> code 30: 3rd order DST</div><div> code 33: 3rd order DST with flux limiter</div><div> code 7: 7th order one step method with monotonicity preserving</div><div> code 80: 2nd order Prather scheme</div><div><br></div><div>The tracer is expected to conserve its extrema (min value of 1 and max value of 3) during integration.</div><div>Due to spurious numerical diffusion induced by every discretized advection scheme, this is not the case.</div><div>The temporal evolutions of tracer extrema look like:</div><div><img src="cid:0FE983A2@CB033935.14DE6F5D.png" modifysize="50%" diffpixels="8px" scalingmode="zoom" style="width: 1097px; height: 495px;"></div><div><br></div><div><br></div><div>We can also estimate the spurious domain-averaged numerical diffusivity as:</div><div><img src="cid:37E2920D@B714F46F.14DE6F5D.png" modifysize="75%" diffpixels="16px" style="width: 311px; height: 68px;"></div><div><br></div><div>Results are:</div><div><img src="cid:36170697@F73EF462.14DE6F5D.png" modifysize="50%" diffpixels="8px" scalingmode="zoom" style="width: 1063px; height: 501px;"></div><div><br></div><div>Conclusions:</div><div>1. 2nd and 4th order centered schemes and 2nd DST generate very large spurious extrema</div><div> while keep a very tiny numerical diffusivity;</div><div>2. advection scheme 33 (3rd-order DST with limiter) do not generate spurious extrema but</div><div> has a relatively large numerical diffusivity (up to 25 m^2/s). Limiter prevents false extrema</div><div> but induces larger spurious diffusivity.</div><div>3. 2nd Prather scheme generates very small false extrema while keep a very-low numerical</div><div> diffusivity (~5 m^/2), a very good choice suggested by Hill et al. (2012, OM).</div><div><br></div><div>Hope the figures can be seen correctly and hope this helps.</div><div><sign signid="0"><div style="color:#909090;font-family:Arial Narrow;font-size:12px"><br><br>------------------</div><div style="font-size:14px;font-family:Verdana;color:#000;"><div> <font size="2">Best regards <br> <br>Yu-Kun Qian (Ç®îÚÀ¤) <br>Center for Monsoon and Environment Research</font> </div> <font size="2">Department of Atmospheric Sciences<br>School of Environmental Science and Engineering<font size="2"> <br> </font>Sun Yat-sen University <br>No. 135 Xingang West Road, Haizhu District <br>Guangzhou, 510275, P.R. China <br>Tel; 020-84115227 <br>Email: <a href="mailto:qianyk@mail2.sysu.edu.cn">qianyk@mail3.sysu.edu.cn</a> </font>
<div> <font size="2"> </font> </div></div></sign></div><div> </div><div><tincludetail><div> </div><div> </div><div style="font:Verdana normal 14px;color:#000;"><div style="FONT-SIZE: 12px;FONT-FAMILY: Arial Narrow;padding:2px 0 2px 0;">------------------ Original ------------------</div><div style="FONT-SIZE: 12px;background:#efefef;padding:8px;"><div id="menu_sender"><b>From: </b> "Edward W Doddridge"<ewd@mit.edu>;</div><div><b>Date: </b> Wed, Sep 4, 2019 10:22 PM</div><div><b>To: </b> "mitgcm-support@mitgcm.org"<mitgcm-support@mitgcm.org>; <wbr></div><div></div><div><b>Subject: </b> Re: [MITgcm-support] advection scheme 33</div></div><div> </div><div style="position:relative;"><div id="tmpcontent_res"></div>
Hello Yangxin,
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<div class="">Regarding your first point, there is a section in the manual devoted to advection schemes: <a href="https://mitgcm.readthedocs.io/en/latest/algorithm/adv-schemes.html" class="">https://mitgcm.readthedocs.io/en/latest/algorithm/adv-schemes.html</a></div>
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<div class="">If you found that section insufficient, it would be good to know why. That way we can work towards improving it.</div>
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<div class="">Cheers,</div>
<div class="">Ed</div>
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<div class="">On 3 Sep 2019, at 14:22, Yangxin He <<a href="mailto:y67he@uwaterloo.ca" class="">y67he@uwaterloo.ca</a>> wrote:</div>
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<div style="margin-top: 0px; margin-bottom: 0px;" class="">Hi there,</div>
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<div style="margin-top: 0px; margin-bottom: 0px;" class="">I am running a simple 2d oceanic model with tides sloshing up and down a slope, so internal tides are generated. Part of my data file looks like</div>
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<span style="font-variant-ligatures: no-common-ligatures;" class=""> implicitDiffusion=.TRUE.,</span></div>
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<span style="font-variant-ligatures: no-common-ligatures;" class=""> implicitViscosity=.TRUE.,</span></div>
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<span style="font-variant-ligatures: no-common-ligatures;" class="">#change advection shceme</span></div>
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<span style="font-variant-ligatures: no-common-ligatures;" class=""> tempAdvScheme=33,</span></div>
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<span style="font-variant-ligatures: no-common-ligatures;" class=""> staggerTimeStep=.TRUE.,</span></div>
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<div style="margin-top: 0px; margin-bottom: 0px;" class="">The simulation is fine. Two quick questions, </div>
<div style="margin-top: 0px; margin-bottom: 0px;" class="">1) I am certainly not an expert in coding, but I think it will be a good idea that I can at least have some idea of what I am using. Where can I find out more information about this advection scheme
33? There does not seem much in the manual. </div>
<div style="margin-top: 0px; margin-bottom: 0px;" class="">2) In one of my previous threads here</div>
<div style="margin-top: 0px; margin-bottom: 0px;" class=""><a href="http://mailman.mitgcm.org/pipermail/mitgcm-support/2019-July/012095.html" class="OWAAutoLink" id="LPlnk844452" previewremoved="true">http://mailman.mitgcm.org/pipermail/mitgcm-support/2019-July/012095.html</a><br class="">
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<div style="margin-top: 0px; margin-bottom: 0px;" class="">Jody mentioned adv33 will allow the lateral diffusion set to 0, i.e. diffKhT=0. I tried it, it did work. But why?</div>
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<div style="margin-top: 0px; margin-bottom: 0px;" class="">Thanks</div>
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<div style="margin-top: 0px; margin-bottom: 0px;" class="">Yangxin</div>
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