# 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> | ||

Line 11: | Line 11: | ||

</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> | ||

Line 30: | Line 30: | ||

</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>. One choice for the domain |

and parameters are | and parameters are | ||

Line 39: | Line 39: | ||

</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}} |

## Revision as of 18:42, 13 August 2007

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 are

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.