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NACA0012 numerical schemes variation by Michael Alletto - Revision history
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Michael Alletto at 08:53, 6 January 2022
2022-01-06T08:53:51Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 08:53, 6 January 2022</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* '''contact''': <mail address='michael.alletto@gmx.de' description='author'>click here for email address</mail></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* '''contact''': <mail address='michael.alletto@gmx.de' description='author'>click here for email address</mail></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* '''OpenFOAM versions''': <del class="diffchange diffchange-inline">v1912</del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* '''OpenFOAM versions''': <ins class="diffchange diffchange-inline">v2112</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* '''Published under''': CC BY-NC-ND license ([https://creativecommons.org/licenses creative commons licenses])</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* '''Published under''': CC BY-NC-ND license ([https://creativecommons.org/licenses creative commons licenses])</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Files can be downloaded [https://<del class="diffchange diffchange-inline">github</del>.com/<del class="diffchange diffchange-inline">jnmlujnmlu</del>/<del class="diffchange diffchange-inline">OpenFOAMTeaching</del>/<del class="diffchange diffchange-inline">blob</del>/master/<del class="diffchange diffchange-inline">MichaelAlletto/discretizationStudy%20(1).tar.gz </del>here].</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Files can be downloaded [https://<ins class="diffchange diffchange-inline">gitlab</ins>.com/<ins class="diffchange diffchange-inline">mAlletto</ins>/<ins class="diffchange diffchange-inline">openfoamtutorials</ins>/<ins class="diffchange diffchange-inline">-/tree</ins>/master/<ins class="diffchange diffchange-inline">Naca0012transonic </ins>here].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Numerical schemes variation==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Numerical schemes variation==</div></td></tr>
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Michael Alletto
https://wiki.openfoam.com/index.php?title=NACA0012_numerical_schemes_variation_by_Michael_Alletto&diff=3263&oldid=prev
Jozsef Nagy at 06:58, 14 May 2020
2020-05-14T06:58:51Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 06:58, 14 May 2020</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Go back to [https://wiki.openfoam.com/NACA0012_by_Michael_Alletto NACA0012 tutorial page].</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Go back to [https://wiki.openfoam.com/NACA0012_by_Michael_Alletto NACA0012 tutorial page].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>=NACA0012 <del class="diffchange diffchange-inline">grid dependence study</del>=</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>=NACA0012 <ins class="diffchange diffchange-inline">Numerical schemes variation</ins>=</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Files can be downloaded [https://github.com/jnmlujnmlu/OpenFOAMTeaching/blob/master/MichaelAlletto/discretizationStudy%20(1).tar.gz here].</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Files can be downloaded [https://github.com/jnmlujnmlu/OpenFOAMTeaching/blob/master/MichaelAlletto/discretizationStudy%20(1).tar.gz here].</div></td></tr>
</table>
Jozsef Nagy
https://wiki.openfoam.com/index.php?title=NACA0012_numerical_schemes_variation_by_Michael_Alletto&diff=3239&oldid=prev
Jozsef Nagy at 05:51, 14 May 2020
2020-05-14T05:51:10Z
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* '''Published under''': CC BY-NC-ND license ([https://creativecommons.org/licenses creative commons licenses])</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* '''Published under''': CC BY-NC-ND license ([https://creativecommons.org/licenses creative commons licenses])</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Go back to [https://wiki.openfoam.com/NACA0012_by_Michael_Alletto <del class="diffchange diffchange-inline">NAVA0012 </del>tutorial page].</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Go back to [https://wiki.openfoam.com/NACA0012_by_Michael_Alletto <ins class="diffchange diffchange-inline">NACA0012 </ins>tutorial page].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=NACA0012 grid dependence study=</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=NACA0012 grid dependence study=</div></td></tr>
</table>
Jozsef Nagy
https://wiki.openfoam.com/index.php?title=NACA0012_numerical_schemes_variation_by_Michael_Alletto&diff=3238&oldid=prev
Jozsef Nagy: Created page with "* '''contributor''': Michael Alletto * '''affiliation''': WRD MS * '''contact''': <mail address='michael.alletto@gmx.de' description='author'>click here for email address</mai..."
2020-05-14T05:50:41Z
<p>Created page with "* '''contributor''': Michael Alletto * '''affiliation''': WRD MS * '''contact''': <mail address='michael.alletto@gmx.de' description='author'>click here for email address</mai..."</p>
<p><b>New page</b></p><div>* '''contributor''': Michael Alletto<br />
* '''affiliation''': WRD MS<br />
* '''contact''': <mail address='michael.alletto@gmx.de' description='author'>click here for email address</mail><br />
* '''OpenFOAM versions''': v1912<br />
* '''Published under''': CC BY-NC-ND license ([https://creativecommons.org/licenses creative commons licenses])<br />
<br />
Go back to [https://wiki.openfoam.com/NACA0012_by_Michael_Alletto NAVA0012 tutorial page].<br />
<br />
=NACA0012 grid dependence study=<br />
<br />
Files can be downloaded [https://github.com/jnmlujnmlu/OpenFOAMTeaching/blob/master/MichaelAlletto/discretizationStudy%20(1).tar.gz here].<br />
<br />
==Numerical schemes variation==<br />
<br />
This section shows the results of the study of the discretization schemes used for the convective schemes. They are changed in the file system/fvSchemes. The following table shows the schemes which are analysis (note that a very good description of discretization schemes and small listings how they are implemented in OpenFOAM is found in the book ):<br />
<br />
{|<br />
!align="center"| name of scheme<br />
!align="center"| brief description<br />
|-<br />
|align="center"| upwind<br />
|align="center"| first order upwind scheme<br />
|-<br />
|align="center"| Gauss limitedLinear 0<br />
|align="center"| second order linear scheme with limiter switched off<br />
|-<br />
|align="center"| Gauss limitedLinear 0.5<br />
|align="center"| second order linear scheme with limiter partially switched on<br />
|-<br />
|align="center"| Gauss limitedLinear 1<br />
|align="center"| second order linear scheme with limiter switched on<br />
|-<br />
|align="center"| Gauss linearUpwind limited<br />
|align="center"| second order upwind scheme with a limiter<br />
|-<br />
|align="center"| <br />
|align="center"|<br />
<br />
|}<br />
<br />
The next figure shows the influence of the numerical scheme adopted to discretize the divergence of the pressure in the pressure equation (the term fvm::div(phid, p)). It is the term (if it is big enough) which gives the pressure equation a hyperbolic character in case of high Mach numbers (see for the derivation of the pressure equation in case of compressible flows). If the term is small (for incompressible flows) the equation has a elliptic character. In principle this characteristic results in a pressure based flow solver able to treat flows at all speeds . Five different schemes are compared: The first order upwind Gauss labeled as pupwind, three different linear limited schemes with the limiter set to 0, 0.5 and 1 (the are labeled as pLimiteLinear0, pLimiteLinear0.5 and pLimiteLinear1 respectively) and a second order limited upwind scheme (labeled as plinearUpwindLmited).<br />
<br />
[[File:pScheme_alettonaca.png|750px|center|Cp (left), Cf (right)]]<br />
<br />
From the figure below it can be seen that both upwind schemes (the upwind and linear upwind scheme) are too diffusive and smear out the pressure jump originated by the shock wave. The weaker shock results also in a vanishing of the recirculation bubble (see the Cf curve). All three version of the limited linear scheme (0 means the limiter is turned off and 1 means it is fully turned on) give almost identical results. For a discussion on the limiters which are introduced to the standard interpolation schemes in order that they satisfy the total variation diminishing (TVD) principle, see the book of .<br />
<br />
<br />
[[File:OtherScheme_alettonaca.png|750px|center|Cp (left), Cf (right)]]<br />
<br />
<br />
After the analysis of the discretization of the convective terms in the pressure equation, the convective therms in the other equations (energy, momentum and turbulence) are sequantially switched from a second order upstream (the case were all convective terms are discretized with a second order scheme is labeled as all2ndOrder) to a first order upstream. They are labeled as 1stOrdere, 1stOrdereU and 1stOrdereUnuTilda, respectively.<br />
<br />
Regarding the other convective schemes shown in the next figure, the switching from second order to first order upwind leads to a change of the shock strength only when the convective term in the momentum equation is switched to first order.<br />
<br />
Based on the study performed in this section, we can conclude that the initial settings of the tutorial lead to an accurate resolution of the shock wave and do not compromise the robustness (at least for the good quality mesh used in this tutorial).<br />
<br />
<br />
==References==<br />
<br />
[1] Fadl Moukalled, L Mangani, Marwan Darwish, et al. The �finite volume method in computational Fluid dynamics, volume 113. Springer, 2016.</div>
Jozsef Nagy