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<p>Hi,</p>
<p><br>
</p>
<p>I want to evolve a scalar field \phi in my simulation with as low diffusivity (conductivity/(rhocp)) as possible.</p>
<p>I have performed simulations with sequentially reduced diffusivity D:</p>
<p><br>
</p>
<p>Simulation 1: D = <span>1*2.17*10^-5 m^2/s<span>, polynomial order 7</span></span></p>
<p><span>Simulation 2: </span>D = <span>(1/4)*10^-5 m^2/s, polynomial order 7</span></p>
<p><span>Simulation 3: </span>D =<span> (1/4)*</span><span>2.17*10^-5 m^2/s<span>, polynomial order 11</span></span></p>
<p><span>Simulation 4: </span>D = <span>(1/8)*</span><span>2.17*10^-5 m^2/s<span>, polynomial order 11</span></span></p>
<p><span><br>
</span></p>
<p><span>Reducing the diffusivity, I keep the ratio D/dt constant, where dt is the time step.</span></p>
<p><span>At t = 0 \phi is bounded to 0 <= \phi <= 1, and it has no sources or sinks.</span></p>
<p><span>Currently, I check the resolution of the simulation after 25 s, by observing the range of \phi.<br>
</span></p>
<p><span>I find these values:</span></p>
<p><span><br>
</span></p>
<p><span></span></p>
<p>Simulation 1: -0.01 < \phi <span></span>< 0.06</p>
<p><span>Simulation 2: </span><span>-0.23 < \phi <span></span>< 0.61</span><span></span></p>
<p><span>Simulation 3:</span><span><span> </span><span>-0.044 < \phi <span></span>< 0.16</span></span><span></span></p>
<p><span>Simulation 4:</span><span><span> </span><span>-0.4 < \phi <span></span>< 0.91</span></span></p>
<p><br>
</p>
<p>Indeed, the smaller the diffusivity D becomes, the worse resolution of \phi becomes.</p>
<p>Also, it seems as increasing the polynomial order improves the resolution of \phi.</p>
<p>However, the Courant numbers in my simulations are (on average):</p>
<p><br>
</p>
<p></p>
<p>Simulation 1: <span></span><span><span><span>C = 0.31</span></span></span></p>
<p><span>Simulation 2: </span><span><span><span>C = 0.06</span></span></span><span></span></p>
<p><span>Simulation 3:</span><span><span> </span><span>C = 0.14</span></span><span></span></p>
<p><span>Simulation 4:</span><span><span> C = 0.06</span></span></p>
<p><br>
</p>
<p>That the Courant number goes down with increasing diffusivity is (I think) just a consequence of reducing the time step (<span>keeping the ratio D/dt constant</span>)<span></span>.</p>
<p>According to the Courant number, I have really great resolution in <span>Simulation
</span>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.</p>
<p><br>
</p>
<p>Can somehow Nek output a measure of the resolution of a scalar field? <br>
</p>
<p>How can I improve the resolution at a low D/allow for lower D and keep a good resolution?</p>
<p><br>
</p>
<p>Best,</p>
<p><br>
</p>
<p>Johan<br>
<span><span></span><span></span></span></p>
<br>
<span><span></span></span><span></span>
<p></p>
<br>
<p></p>
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