https://www.cfd-online.com/W/index.php?title=Special:Contributions/Gazaix&feed=atom&limit=50&target=Gazaix&year=&month=CFD-Wiki - User contributions [en]2024-03-19T06:44:27ZFrom CFD-WikiMediaWiki 1.16.5https://www.cfd-online.com/Wiki/2-D_vortex_in_isentropic_flow2-D vortex in isentropic flow2012-01-06T14:35:29Z<p>Gazaix: Correct bug</p>
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<div>The test case involves [[convection]] of an [[isentropic]] [[vortex]] in [[inviscid flow]].<br />
The [[free-stream conditions]] are <br />
<br />
:<math><br />
\begin{matrix}<br />
\rho &=& 1 \\<br />
u &=& 0.5\\<br />
v &=& 0\\<br />
p &=& 1/\gamma<br />
\end{matrix}<br />
</math><br />
<br />
Perturbations are added to the [[free-stream]] in such a way that there is no<br />
[[entropy]] gradient in the [[flow-field]]. The perturbations are given by<br />
<br />
:<math><br />
\begin{matrix}<br />
(\delta u, \delta v) &=& \frac{\beta}{2\pi} \exp\left( \frac{1-r^2}{2}<br />
\right) [ -(y-y_o), (x-x_o) ] \\<br />
\rho &=& \left[ 1 - \frac{ (\gamma-1)\beta^2}{8\gamma\pi^2} \exp\left(<br />
1-r^2\right) \right]^{\frac{1}{\gamma-1}} \\<br />
p &=& \frac{ \rho^\gamma }{\gamma}<br />
\end{matrix}<br />
</math><br />
<br />
where <br />
<br />
:<math><br />
r = [ (x-x_o)^2 + (y-y_o)^2 ]^{1/2}<br />
</math><br />
<br />
is distance from the [[vortex]] center <math>(x_o, y_o)</math>. <br />
<br />
One choice for the domain and parameters is: <br />
<br />
:<math><br />
\Omega = [0,10] \times [-5,5], \quad<br />
(x_o, y_o) = (5,0), \quad<br />
\beta = 5<br />
</math><br />
<br />
As a result of [[isentropy]], the exact solution corresponds to a pure [[advection]]<br />
of the [[vortex]] at the [[free-stream velocity]]. Further details can be found in Yee et al. (1999).<br />
<br />
==References==<br />
<br />
*{{reference-paper | author=Yee, H-C., Sandham, N. and Djomehri, M., | year=1999 | title=Low dissipative high order shock-capturing methods using characteristic-based filters| rest=JCP, Vol. 150}}<br />
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{{stub}}</div>Gazaix