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Gcowles: /* 2D External Mode */
2011-11-14T14:58:12Z
<p><span class="autocomment">2D External Mode</span></p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 14:58, 14 November 2011</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></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>where <math>\bar{v}_n</math> is the velocity component normal to the sides of the triangle and ''s''' is the closed trajectory comprised of the three sides. <del class="diffchange diffchange-inline">Eq. (3.3) </del>is integrated numerically using <del class="diffchange diffchange-inline">the </del>modified fourth-order Runge-Kutta time-stepping scheme. This is a multi-stage time-stepping approach with second-order temporal accuracy. The detailed procedure for this method is described as follows:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>where <math>\bar{v}_n</math> is the velocity component normal to the sides of the triangle and ''s''' <ins class="diffchange diffchange-inline"> </ins>is the closed trajectory comprised of the three sides. <ins class="diffchange diffchange-inline">This equation </ins>is integrated numerically using <ins class="diffchange diffchange-inline">a </ins>modified fourth-order Runge-Kutta time-stepping scheme. This is a multi-stage time-stepping approach with second-order temporal accuracy. The detailed procedure for this method is described as follows:</div></td></tr>
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Gcowles
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Gcowles: /* 2D External Mode */
2011-11-14T14:57:05Z
<p><span class="autocomment">2D External Mode</span></p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 14:57, 14 November 2011</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===2D External Mode===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===2D External Mode===</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;">Let us consider the continuity equation first. Integrating Eq. (2.30) over a given triangle area yields:</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><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\iint \limits_{\Omega} \frac{\partial \zeta}{\partial t} \mathrm{d}x\mathrm{d}y = - \iint \limits_{\Omega}\left[\frac{\partial(\bar{u}D)}{\partial x} + \frac{\partial(\bar{v}D)}{\partial y} \right] \mathrm{d}x\mathrm{d}y = - \oint \limits_{s'} \bar{v}_n D \mathrm{d}s'</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\iint \limits_{\Omega} \frac{\partial \zeta}{\partial t} \mathrm{d}x\mathrm{d}y = - \iint \limits_{\Omega}\left[\frac{\partial(\bar{u}D)}{\partial x} + \frac{\partial(\bar{v}D)}{\partial y} \right] \mathrm{d}x\mathrm{d}y = - \oint \limits_{s'} \bar{v}_n D \mathrm{d}s'</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></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><del class="diffchange diffchange-inline"><!-- </del><math><del class="diffchange diffchange-inline">\int\int\frac{\partial \zeta}{\partial t} = - \iint\left[\frac{\partial(\bar{u}D}\partial x} +\frac{\partial(</del>\bar{v}<del class="diffchange diffchange-inline">D}\partial y} \right] dx dy </del></math>--<del class="diffchange diffchange-inline">></del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">where </ins><math>\bar{v}<ins class="diffchange diffchange-inline">_n</ins></math> <ins class="diffchange diffchange-inline"> is the velocity component normal to the sides of the triangle and ''s''' is the closed trajectory comprised of the three sides. Eq. (3.3) is integrated numerically using the modified fourth</ins>-<ins class="diffchange diffchange-inline">order Runge</ins>-<ins class="diffchange diffchange-inline">Kutta time-stepping scheme. This is a multi-stage time-stepping approach with second-order temporal accuracy. The detailed procedure for this method is described as follows:</ins></div></td></tr>
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Gcowles
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Gcowles: /* 2D External Mode */
2011-11-14T14:56:00Z
<p><span class="autocomment">2D External Mode</span></p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 14:56, 14 November 2011</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===2D External Mode===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===2D External Mode===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\iint \limits_{\Omega} \frac{\partial \zeta}{\partial t} \mathrm{d}x\mathrm{d}y = - \iint \limits_{\Omega}\left[\frac{\partial(\bar{u}D)}{\partial x} + \frac{\partial(\bar{v}D)}{\partial y} \right] \mathrm{d}x\mathrm{d}y = </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\iint \limits_{\Omega} \frac{\partial \zeta}{\partial t} \mathrm{d}x\mathrm{d}y = - \iint \limits_{\Omega}\left[\frac{\partial(\bar{u}D)}{\partial x} + \frac{\partial(\bar{v}D)}{\partial y} \right] \mathrm{d}x\mathrm{d}y = <ins class="diffchange diffchange-inline">- \oint \limits_{s'} \bar{v}_n D \mathrm{d}s'</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></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><!-- <math>\int\int\frac{\partial \zeta}{\partial t} = - \iint\left[\frac{\partial(\bar{u}D}\partial x} +\frac{\partial(\bar{v}D}\partial y} \right] dx dy </math>--></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><!-- <math>\int\int\frac{\partial \zeta}{\partial t} = - \iint\left[\frac{\partial(\bar{u}D}\partial x} +\frac{\partial(\bar{v}D}\partial y} \right] dx dy </math>--></div></td></tr>
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Gcowles
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Gcowles: /* 2D External Mode */
2011-11-14T14:54:46Z
<p><span class="autocomment">2D External Mode</span></p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 14:54, 14 November 2011</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===2D External Mode===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===2D External Mode===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\iint \limits_{\Omega} \frac{\partial \zeta}{\partial t} \mathrm{d}x\mathrm{d}y = - \iint \limits_{\Omega}\left[\frac{\partial(\bar{u}D)}{\partial x} + \frac{\partial(\bar{v}D)}{\partial y} \right]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\iint \limits_{\Omega} \frac{\partial \zeta}{\partial t} \mathrm{d}x\mathrm{d}y = - \iint \limits_{\Omega}\left[\frac{\partial(\bar{u}D)}{\partial x} + \frac{\partial(\bar{v}D)}{\partial y} \right] <ins class="diffchange diffchange-inline">\mathrm{d}x\mathrm{d}y = </ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></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><!-- <math>\int\int\frac{\partial \zeta}{\partial t} = - \iint\left[\frac{\partial(\bar{u}D}\partial x} +\frac{\partial(\bar{v}D}\partial y} \right] dx dy </math>--></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><!-- <math>\int\int\frac{\partial \zeta}{\partial t} = - \iint\left[\frac{\partial(\bar{u}D}\partial x} +\frac{\partial(\bar{v}D}\partial y} \right] dx dy </math>--></div></td></tr>
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Gcowles
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Gcowles: /* 2D External Mode */
2011-11-14T14:54:32Z
<p><span class="autocomment">2D External Mode</span></p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 14:54, 14 November 2011</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===2D External Mode===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===2D External Mode===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\iint \limits_{\Omega} \frac{\partial \zeta}{\partial t} = - \iint \limits_{\Omega}\left[\frac{\partial(\bar{u}D)}{\partial x} + \frac{\partial(\bar{v}D)}{\partial y} \right]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\iint \limits_{\Omega} \frac{\partial \zeta}{\partial t} <ins class="diffchange diffchange-inline">\mathrm{d}x\mathrm{d}y </ins>= - \iint \limits_{\Omega}\left[\frac{\partial(\bar{u}D)}{\partial x} + \frac{\partial(\bar{v}D)}{\partial y} \right]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></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><!-- <math>\int\int\frac{\partial \zeta}{\partial t} = - \iint\left[\frac{\partial(\bar{u}D}\partial x} +\frac{\partial(\bar{v}D}\partial y} \right] dx dy </math>--></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><!-- <math>\int\int\frac{\partial \zeta}{\partial t} = - \iint\left[\frac{\partial(\bar{u}D}\partial x} +\frac{\partial(\bar{v}D}\partial y} \right] dx dy </math>--></div></td></tr>
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Gcowles
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Gcowles: /* 2D External Mode */
2011-11-14T14:54:10Z
<p><span class="autocomment">2D External Mode</span></p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 14:54, 14 November 2011</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===2D External Mode===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===2D External Mode===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\iint \limits_{\Omega} \frac{\partial \zeta}{\partial t} = - \iint \left[\frac{\partial(\bar{u}D)}{\partial x} + \frac{\partial(\bar{v}D)}{\partial y} \right]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\iint \limits_{\Omega} \frac{\partial \zeta}{\partial t} = - \iint <ins class="diffchange diffchange-inline">\limits_{\Omega}</ins>\left[\frac{\partial(\bar{u}D)}{\partial x} + \frac{\partial(\bar{v}D)}{\partial y} \right]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></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><!-- <math>\int\int\frac{\partial \zeta}{\partial t} = - \iint\left[\frac{\partial(\bar{u}D}\partial x} +\frac{\partial(\bar{v}D}\partial y} \right] dx dy </math>--></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><!-- <math>\int\int\frac{\partial \zeta}{\partial t} = - \iint\left[\frac{\partial(\bar{u}D}\partial x} +\frac{\partial(\bar{v}D}\partial y} \right] dx dy </math>--></div></td></tr>
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Gcowles
http://fvcom.smast.umassd.edu/wiki/index.php?title=Discretization&diff=194&oldid=prev
Gcowles at 14:53, 14 November 2011
2011-11-14T14:53:54Z
<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===2D External Mode===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===2D External Mode===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\<del class="diffchange diffchange-inline">iint_</del>{\Omega} \frac{\partial \zeta}{\partial t} = - \iint \left[\frac{\partial(\bar{u}D)}{\partial x} + \frac{\partial(\bar{v}D)}{\partial y} \right]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\<ins class="diffchange diffchange-inline">iint \limits_</ins>{\Omega} \frac{\partial \zeta}{\partial t} = - \iint \left[\frac{\partial(\bar{u}D)}{\partial x} + \frac{\partial(\bar{v}D)}{\partial y} \right]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></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><!-- <math>\int\int\frac{\partial \zeta}{\partial t} = - \iint\left[\frac{\partial(\bar{u}D}\partial x} +\frac{\partial(\bar{v}D}\partial y} \right] dx dy </math>--></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><!-- <math>\int\int\frac{\partial \zeta}{\partial t} = - \iint\left[\frac{\partial(\bar{u}D}\partial x} +\frac{\partial(\bar{v}D}\partial y} \right] dx dy </math>--></div></td></tr>
</table>
Gcowles
http://fvcom.smast.umassd.edu/wiki/index.php?title=Discretization&diff=193&oldid=prev
Gcowles: /* 2D External Mode */
2011-11-14T14:53:15Z
<p><span class="autocomment">2D External Mode</span></p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 14:53, 14 November 2011</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===2D External Mode===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===2D External Mode===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\<del class="diffchange diffchange-inline">iint </del>\frac{\partial \zeta}{\partial t} = - \iint \left[\frac{\partial(\bar{u}D)}{\partial x} + \frac{\partial(\bar{v}D)}{\partial y} \right]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\<ins class="diffchange diffchange-inline">iint_{\Omega} </ins>\frac{\partial \zeta}{\partial t} = - \iint \left[\frac{\partial(\bar{u}D)}{\partial x} + \frac{\partial(\bar{v}D)}{\partial y} \right]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></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><!-- <math>\int\int\frac{\partial \zeta}{\partial t} = - \iint\left[\frac{\partial(\bar{u}D}\partial x} +\frac{\partial(\bar{v}D}\partial y} \right] dx dy </math>--></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><!-- <math>\int\int\frac{\partial \zeta}{\partial t} = - \iint\left[\frac{\partial(\bar{u}D}\partial x} +\frac{\partial(\bar{v}D}\partial y} \right] dx dy </math>--></div></td></tr>
</table>
Gcowles
http://fvcom.smast.umassd.edu/wiki/index.php?title=Discretization&diff=192&oldid=prev
Gcowles at 14:52, 14 November 2011
2011-11-14T14:52:39Z
<p></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 14:52, 14 November 2011</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===2D External Mode===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===2D External Mode===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\iint \frac{\partial \zeta}{\partial t} = - \iint \left[\frac{\partial(\bar{u}D)}{\partial x} <del class="diffchange diffchange-inline"> </del>\right]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\iint \frac{\partial \zeta}{\partial t} = - \iint \left[\frac{\partial(\bar{u}D)}{\partial x} <ins class="diffchange diffchange-inline"> + \frac{\partial(\bar{v}D)}{\partial y} </ins>\right]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></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><!-- <math>\int\int\frac{\partial \zeta}{\partial t} = - \iint\left[\frac{\partial(\bar{u}D}\partial x} +\frac{\partial(\bar{v}D}\partial y} \right] dx dy </math>--></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><!-- <math>\int\int\frac{\partial \zeta}{\partial t} = - \iint\left[\frac{\partial(\bar{u}D}\partial x} +\frac{\partial(\bar{v}D}\partial y} \right] dx dy </math>--></div></td></tr>
</table>
Gcowles
http://fvcom.smast.umassd.edu/wiki/index.php?title=Discretization&diff=191&oldid=prev
Gcowles: /* 2D External Mode */
2011-11-14T14:52:17Z
<p><span class="autocomment">2D External Mode</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 14:52, 14 November 2011</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===2D External Mode===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===2D External Mode===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\iint \frac{\partial \zeta}{\partial t} = - \iint \left[\frac{\partial(\bar{u}D)}{\partial x}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\iint \frac{\partial \zeta}{\partial t} = - \iint \left[\frac{\partial(\bar{u}D)}{\partial x} <ins class="diffchange diffchange-inline"> \right]</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></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><!-- <math>\int\int\frac{\partial \zeta}{\partial t} = - \iint\left[\frac{\partial(\bar{u}D}\partial x} +\frac{\partial(\bar{v}D}\partial y} \right] dx dy </math>--></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><!-- <math>\int\int\frac{\partial \zeta}{\partial t} = - \iint\left[\frac{\partial(\bar{u}D}\partial x} +\frac{\partial(\bar{v}D}\partial y} \right] dx dy </math>--></div></td></tr>
</table>
Gcowles