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<p>For a high Reynolds number simulation I can check the numerical accuracy of the velocity field by checking the Courant numer in the logfile (I use a fixed time step) - how can I check the numerical accurary when simulating low-diffusivity scalars?</p>
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<p>Johan<br>
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<div id="x_divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>From:</b> Nek5000-users <nek5000-users-bounces@lists.mcs.anl.gov> on behalf of nek5000-users@lists.mcs.anl.gov <nek5000-users@lists.mcs.anl.gov><br>
<b>Sent:</b> Friday, June 29, 2018 7:06:22 PM<br>
<b>To:</b> nek5000-users@lists.mcs.anl.gov<br>
<b>Subject:</b> Re: [Nek5000-users] Measure resolution for simulations with low-diffusivity scalars</font>
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<div class="PlainText">What are you looking for? How can I get a bounded scalar solution for a given (low) diffusivity and resolution?<br>
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Stefan<br>
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-----Original message-----<br>
> From:nek5000-users@lists.mcs.anl.gov <nek5000-users@lists.mcs.anl.gov><br>
> Sent: Friday 29th June 2018 17:44<br>
> To: nek5000-users@lists.mcs.anl.gov<br>
> Subject: [Nek5000-users] Measure resolution for simulations with low-diffusivity scalars<br>
> <br>
> Hi,<br>
> <br>
> I want to evolve a scalar field \phi in my simulation with as low diffusivity (conductivity/(rhocp)) as possible.<br>
> I have performed simulations with sequentially reduced diffusivity D:<br>
> <br>
> Simulation 1: D = 1*2.17*10^-5 m^2/s, polynomial order 7<br>
> Simulation 2: D = (1/4)*10^-5 m^2/s, polynomial order 7<br>
> Simulation 3: D = (1/4)*2.17*10^-5 m^2/s, polynomial order 11<br>
> Simulation 4: D = (1/8)*2.17*10^-5 m^2/s, polynomial order 11<br>
> <br>
> Reducing the diffusivity, I keep the ratio D/dt constant, where dt is the time step.<br>
> At t = 0 \phi is bounded to 0 <= \phi <= 1, and it has no sources or sinks.<br>
> Currently, I check the resolution of the simulation after 25 s, by observing the range of \phi.<br>
> I find these values:<br>
> <br>
> Simulation 1: -0.01 < \phi < 0.06<br>
> Simulation 2: -0.23 < \phi < 0.61<br>
> Simulation 3: -0.044 < \phi < 0.16<br>
> Simulation 4: -0.4 < \phi < 0.91<br>
> <br>
> Indeed, the smaller the diffusivity D becomes, the worse resolution of \phi becomes.<br>
> Also, it seems as increasing the polynomial order improves the resolution of \phi.<br>
> However, the Courant numbers in my simulations are (on average):<br>
> <br>
> Simulation 1: C = 0.31<br>
> Simulation 2: C = 0.06<br>
> Simulation 3: C = 0.14<br>
> Simulation 4: C = 0.06<br>
> <br>
> That the Courant number goes down with increasing diffusivity is (I think) just a consequence of reducing the time step (keeping the ratio D/dt constant).<br>
> According to the Courant number, I have really great resolution in Simulation<br>
> 4, but according to the range of \phi I have not. Also, the Helmholtz solver seem to reach the tolerance in fewer iterations for low values of D.<br>
> <br>
> Can somehow Nek output a measure of the resolution of a scalar field? <br>
> How can I improve the resolution at a low D/allow for lower D and keep a good resolution?<br>
> <br>
> Best,<br>
> <br>
> Johan<br>
> <br>
> <br>
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