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V2-f models - Revision history
2024-03-29T00:52:56Z
Revision history for this page on the wiki
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Pete Bachant: /* The \zeta - f equations */
2014-02-07T05:45:26Z
<p><span class="autocomment">The \zeta - f equations</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>where the turbulence time scale <math>T</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>where the turbulence time scale <math>T</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><math>T = \max \left[ min \left( \frac{k}{\varepsilon},\, \frac{0.6}{\sqrt{6} C_{\mu} |S|\zeta} \right), C_T \left( \frac{\nu}{\varepsilon} \right)^{1/2} \right]</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><math>T = \max \left[ <ins class="diffchange diffchange-inline">\</ins>min \left( \frac{k}{\varepsilon},\, \frac{0.6}{\sqrt{6} C_{\mu} |S|\zeta} \right), C_T \left( \frac{\nu}{\varepsilon} \right)^{1/2} \right]</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>and the turbulence length scale <math>L</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>and the turbulence length scale <math>L</math></div></td></tr>
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Pete Bachant
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Pete Bachant: /* The \zeta - f equations */
2014-02-07T05:45:01Z
<p><span class="autocomment">The \zeta - f equations</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>where the turbulence time scale <math>T</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>where the turbulence time scale <math>T</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><math>T = max \left[ min \left( \frac{k}{\varepsilon},\, \frac{0.6}{\sqrt{6} C_{\mu} |S|\zeta} \right), C_T \left( \frac{\nu}{\varepsilon} \right)^{1/2} \right]</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><math>T = <ins class="diffchange diffchange-inline">\</ins>max \left[ min \left( \frac{k}{\varepsilon},\, \frac{0.6}{\sqrt{6} C_{\mu} |S|\zeta} \right), C_T \left( \frac{\nu}{\varepsilon} \right)^{1/2} \right]</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>and the turbulence length scale <math>L</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>and the turbulence length scale <math>L</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><math>L = C_L \, max \left[ min \left( \frac{k^{3/2}}{\varepsilon}, \,</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><math>L = C_L \, <ins class="diffchange diffchange-inline">\</ins>max \left[ <ins class="diffchange diffchange-inline">\</ins>min \left( \frac{k^{3/2}}{\varepsilon}, \,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \frac{k^{1/2}}{\sqrt{6} C_{\mu} |S| \zeta} \right), C_{\eta}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \frac{k^{1/2}}{\sqrt{6} C_{\mu} |S| \zeta} \right), C_{\eta}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \left( \frac{\nu^3}{\varepsilon} \right)^{1/4} \right]</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \left( \frac{\nu^3}{\varepsilon} \right)^{1/4} \right]</math></div></td></tr>
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Pete Bachant
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Svu: /* References */
2012-02-19T19:23:10Z
<p><span class="autocomment">References</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*<b>Durbin, P.</b> Separated flow computations with the <math>k-\epsilon-\overline{v^2} </math>model, AIAA Journal, 33, 659-664, 1995.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*<b>Durbin, P.</b> Separated flow computations with the <math>k-\epsilon-\overline{v^2} </math>model, AIAA Journal, 33, 659-664, 1995.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">*<b>Laurence, D.R., Uribe J.C., Utyuzhnikov, S.V.</b> A Robust Formulation of the v2-f Model, Flow Turbulence and Combustion, 73, 169-185, 2004.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*<b>Popovac, M., Hanjalic, K.</b> Compound Wall Treatment for RANS Computation of Complex Turbulent Flows and Heat Transfer, Flow Turbulence and Combustion, 78, 177-202, 2007.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*<b>Popovac, M., Hanjalic, K.</b> Compound Wall Treatment for RANS Computation of Complex Turbulent Flows and Heat Transfer, Flow Turbulence and Combustion, 78, 177-202, 2007.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Turbulence models]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Turbulence models]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{stub}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{stub}}</div></td></tr>
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Svu
https://cfd-online.com/W/index.php?title=V2-f_models&diff=9906&oldid=prev
Enda.bigarella at 11:20, 4 November 2009
2009-11-04T11:20:42Z
<p></p>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">{{Template:Turbulence modeling}}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Introduction==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Introduction==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The <math>\overline{v^2}-f</math> model is similar to the [[Standard k-epsilon model]]. Additionally, it incorporates also some near-wall turbulence anisotropy as well as non-local pressure-strain effects. It is a general turbulence model for low [[Reynolds number|Reynolds-numbers]], that does not need to make use of wall functions because it is valid upto solid walls.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The <math>\overline{v^2}-f</math> model is similar to the [[Standard k-epsilon model]]. Additionally, it incorporates also some near-wall turbulence anisotropy as well as non-local pressure-strain effects. It is a general turbulence model for low [[Reynolds number|Reynolds-numbers]], that does not need to make use of wall functions because it is valid upto solid walls.</div></td></tr>
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Enda.bigarella
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Peter: Reverted edits by TacaoRdomr (Talk) to last version by Jola
2008-12-18T11:38:31Z
<p>Reverted edits by <a href="/Wiki/Special:Contributions/TacaoRdomr" title="Special:Contributions/TacaoRdomr">TacaoRdomr</a> (<a href="/W/index.php?title=User_talk:TacaoRdomr&action=edit&redlink=1" class="new" title="User talk:TacaoRdomr (page does not exist)">Talk</a>) to last version by <a href="/Wiki/User:Jola" title="User:Jola">Jola</a></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">relc4tz</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Introduction==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Introduction==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The <math>\overline{v^2}-f</math> model is similar to the [[Standard k-epsilon model]]. Additionally, it incorporates also some near-wall turbulence anisotropy as well as non-local pressure-strain effects. It is a general turbulence model for low [[Reynolds number|Reynolds-numbers]], that does not need to make use of wall functions because it is valid upto solid walls.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The <math>\overline{v^2}-f</math> model is similar to the [[Standard k-epsilon model]]. Additionally, it incorporates also some near-wall turbulence anisotropy as well as non-local pressure-strain effects. It is a general turbulence model for low [[Reynolds number|Reynolds-numbers]], that does not need to make use of wall functions because it is valid upto solid walls.</div></td></tr>
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Peter
https://cfd-online.com/W/index.php?title=V2-f_models&diff=9483&oldid=prev
TacaoRdomr: trocvi
2008-12-18T11:03:10Z
<p>trocvi</p>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">relc4tz</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Introduction==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Introduction==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The <math>\overline{v^2}-f</math> model is similar to the [[Standard k-epsilon model]]. Additionally, it incorporates also some near-wall turbulence anisotropy as well as non-local pressure-strain effects. It is a general turbulence model for low [[Reynolds number|Reynolds-numbers]], that does not need to make use of wall functions because it is valid upto solid walls.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The <math>\overline{v^2}-f</math> model is similar to the [[Standard k-epsilon model]]. Additionally, it incorporates also some near-wall turbulence anisotropy as well as non-local pressure-strain effects. It is a general turbulence model for low [[Reynolds number|Reynolds-numbers]], that does not need to make use of wall functions because it is valid upto solid walls.</div></td></tr>
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TacaoRdomr
https://cfd-online.com/W/index.php?title=V2-f_models&diff=7711&oldid=prev
Jola at 10:00, 12 June 2007
2007-06-12T10:00:41Z
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*<b>Popovac, M., Hanjalic, K.</b> Compound Wall Treatment for RANS Computation of Complex Turbulent Flows and Heat Transfer, Flow Turbulence and Combustion, 78, 177-202, 2007.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*<b>Popovac, M., Hanjalic, K.</b> Compound Wall Treatment for RANS Computation of Complex Turbulent Flows and Heat Transfer, Flow Turbulence and Combustion, 78, 177-202, 2007.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">[[Category:Turbulence models]]</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{stub}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{stub}}</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">[[Category:Turbulence models]]</del></div></td><td colspan="2"> </td></tr>
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Jola
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Mirzapopovac: /* References */
2007-03-16T18:02:06Z
<p><span class="autocomment">References</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*<b>Durbin, P.</b> Separated flow computations with the <math>k-\epsilon-\overline{v^2} </math>model, AIAA Journal, 33, 659-664, 1995.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*<b>Durbin, P.</b> Separated flow computations with the <math>k-\epsilon-\overline{v^2} </math>model, AIAA Journal, 33, 659-664, 1995.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>*<b>Popovac, M., Hanjalic, K.</b> Compound Wall Treatment for RANS Computation of Complex Turbulent Flows and Heat Transfer, Flow<del class="diffchange diffchange-inline">, </del>Turbulence and Combustion, 78, 177-202, 2007.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>*<b>Popovac, M., Hanjalic, K.</b> Compound Wall Treatment for RANS Computation of Complex Turbulent Flows and Heat Transfer, Flow Turbulence and Combustion, 78, 177-202, 2007.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{stub}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{stub}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Turbulence models]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Turbulence models]]</div></td></tr>
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Mirzapopovac
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Mirzapopovac: /* References */
2007-03-16T18:01:24Z
<p><span class="autocomment">References</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*<b>Durbin, P.</b> Separated flow computations with the <math>k-\epsilon-\overline{v^2} </math>model, AIAA Journal, 33, 659-664, 1995.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*<b>Durbin, P.</b> Separated flow computations with the <math>k-\epsilon-\overline{v^2} </math>model, AIAA Journal, 33, 659-664, 1995.</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>*<b>Popovac, M., Hanjalic, K.</b> Compound Wall Treatment for RANS Computation of Complex Turbulent Flows and Heat Transfer, Flow, Turbulence and Combustion, <del class="diffchange diffchange-inline">DOI 10.1007/s10494</del>-<del class="diffchange diffchange-inline">006-9067-x</del>, 2007.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>*<b>Popovac, M., Hanjalic, K.</b> Compound Wall Treatment for RANS Computation of Complex Turbulent Flows and Heat Transfer, Flow, Turbulence and Combustion, <ins class="diffchange diffchange-inline">78, 177</ins>-<ins class="diffchange diffchange-inline">202</ins>, 2007.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Turbulence models]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Turbulence models]]</div></td></tr>
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Mirzapopovac
https://cfd-online.com/W/index.php?title=V2-f_models&diff=7109&oldid=prev
Mirzapopovac: /* The <math>\zeta - f</math> equations */
2007-01-26T10:24:28Z
<p><span class="autocomment">The <math>\zeta - f</math> equations</span></p>
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<td colspan='2' style="background-color: white; color:black;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black;">Revision as of 10:24, 26 January 2007</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>and the turbulent quantities are obtained from another set of equations. When the change of variables is done, the obtained transport equation for <math>\zeta</math> reads</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>and the turbulent quantities are obtained from another set of equations. When the change of variables is done, the obtained transport equation for <math>\zeta</math> reads</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><math>\frac{\partial \zeta}{\partial t} + U_j \frac{\partial \zeta}{\partial x_j} = f - \frac{\zeta}{k} P_k + \frac{\partial}{\partial <del class="diffchange diffchange-inline">x_k</del>} \left[ \left( \nu + \frac{\nu_t}{\sigma_{\zeta}} \right) \frac{\partial \zeta}{\partial <del class="diffchange diffchange-inline">x_k</del>} \right]</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><math>\frac{\partial \zeta}{\partial t} + U_j \frac{\partial \zeta}{\partial x_j} = f - \frac{\zeta}{k} P_k + \frac{\partial}{\partial <ins class="diffchange diffchange-inline">x_j</ins>} \left[ \left( \nu + \frac{\nu_t}{\sigma_{\zeta}} \right) \frac{\partial \zeta}{\partial <ins class="diffchange diffchange-inline">x_j</ins>} \right]</math></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>and, in conjunction with the quasi-linear SSG pressure-strain model, the elliptic equation for the relaxation function <math>f</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>and, in conjunction with the quasi-linear SSG pressure-strain model, the elliptic equation for the relaxation function <math>f</math></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>where the turbulence time scale <math>T</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>where the turbulence time scale <math>T</math></div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><math>T = max \left[ min \left( \frac{k}{\varepsilon},\, \frac{0.6}{\sqrt{6} C_{\mu} |S|\zeta} \right), C_T \left( \frac{\nu<del class="diffchange diffchange-inline">^3</del>}{\varepsilon} \right)^{1/2} \right]</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><math>T = max \left[ min \left( \frac{k}{\varepsilon},\, \frac{0.6}{\sqrt{6} C_{\mu} |S|\zeta} \right), C_T \left( \frac{\nu}{\varepsilon} \right)^{1/2} \right]</math></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>and the turbulence length scale <math>L</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>and the turbulence length scale <math>L</math></div></td></tr>
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