2-D vortex in isentropic flow
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- | The test case involves convection of an isentropic vortex in inviscid flow. | + | The test case involves [[convection]] of an [[isentropic]] [[vortex]] in [[inviscid flow]]. |
- | The free-stream conditions are | + | The [[free-stream conditions]] are |
:<math> | :<math> | ||
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</math> | </math> | ||
- | Perturbations are added to the free-stream in such a way that there is no | + | Perturbations are added to the [[free-stream]] in such a way that there is no |
- | entropy gradient in the flow-field. The perturbations are given by | + | [[entropy]] gradient in the [[flow-field]]. The perturbations are given by |
:<math> | :<math> | ||
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(\delta u, \delta v) &=& \frac{\beta}{2\pi} \exp\left( \frac{1-r^2}{2} | (\delta u, \delta v) &=& \frac{\beta}{2\pi} \exp\left( \frac{1-r^2}{2} | ||
\right) [ -(y-y_o), (x-x_o) ] \\ | \right) [ -(y-y_o), (x-x_o) ] \\ | ||
- | \rho &=& \left[ 1 - \frac{ (\gamma-1)\beta^2}{8\gamma\pi} \exp\left( | + | \rho &=& \left[ 1 - \frac{ (\gamma-1)\beta^2}{8\gamma\pi^2} \exp\left( |
1-r^2\right) \right]^{\frac{1}{\gamma-1}} \\ | 1-r^2\right) \right]^{\frac{1}{\gamma-1}} \\ | ||
p &=& \frac{ \rho^\gamma }{\gamma} | p &=& \frac{ \rho^\gamma }{\gamma} | ||
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</math> | </math> | ||
- | is distance from the vortex center <math>(x_o, y_o)</math>. One choice for the domain | + | is distance from the [[vortex]] center <math>(x_o, y_o)</math>. |
- | and parameters | + | |
+ | One choice for the domain and parameters is: | ||
:<math> | :<math> | ||
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</math> | </math> | ||
- | As a result of isentropy, the exact solution corresponds to a pure advection | + | As a result of [[isentropy]], the exact solution corresponds to a pure [[advection]] |
- | of the vortex at the free-stream velocity. Further details can be found in Yee et al. (1999). | + | of the [[vortex]] at the [[free-stream velocity]]. Further details can be found in Yee et al. (1999). |
==References== | ==References== | ||
*{{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}} | *{{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}} | ||
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Revision as of 14:35, 6 January 2012
The test case involves convection of an isentropic vortex in inviscid flow. The free-stream conditions are
Perturbations are added to the free-stream in such a way that there is no entropy gradient in the flow-field. The perturbations are given by
where
is distance from the vortex center .
One choice for the domain and parameters is:
As a result of isentropy, the exact solution corresponds to a pure advection of the vortex at the free-stream velocity. Further details can be found in Yee et al. (1999).
References
- Yee, H-C., Sandham, N. and Djomehri, M., (1999), "Low dissipative high order shock-capturing methods using characteristic-based filters", JCP, Vol. 150.