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Roe States (average) in curvilinear coordinates?
Hi,
I wonder if anyone can help me with this problem. I haven't found anything on this in the open litterature yet and have struggled unsuccesfully with the derivation. For a perfect gas in orthogonal coordinates and in any dimension, the Roe average between the left and right states can be found easily to achieve A(Q_R-Q_L)=F_R-F_L where the flux jacobian A is found from the Roe averaged properties. However, when F and Q are expressed in curvilinear coordinates (conformal mapping), the average cannot be found easily. I managed to obtain such an average for a 1D problem, but am stuck in 2D and 3D. Does anyone know anything about this? -bernard |

Re: Roe States (average) in curvilinear coordinates?
Hi:
You may want to look the text by Tannehill, anderson and pletecher, second edition, 1997. section 6.6. About a few monthses, if I finish my phd; God willing, in my thesis I have tried to simply explain all the things about roe in generalized coordinates. You can also find some info about roe scheme implemenation in gen. coord. in the manual of CFL3D code of Nasa Langely. If you could find any other informative report in this regards i wonder you can share it with me. Regrads Mohammad |

Re: Roe States (average) in curvilinear coordinates?
Hi,
I wonder if you could linearize the equations first using Roe-averages, and then transform them. Isn't it possible? Regards, Nishikawa |

Re: Roe States (average) in curvilinear coordinates?
Hi dear Nishikawa:
According to Roe scheme, as it is an approximate solver of Rimm. problem, I have started with the linearized equations. Then at each cell face of the control volume, I have found the "L" and "R" conditions, then using Roe avarging I have determined the conditions at the cell face. Then the numerical flux. There is no big difference between finite volume-in which you solve totally in physical domain and finite volume-finite difference approach, in which the equations are solved in computational domain. In both of the appraches, we need the unit vectors normal to the cell face. I hope this help. Regards. Mohammad |

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