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-   -   Riemann invariants....Any physical interpretation? (http://www.cfd-online.com/Forums/main/120632-riemann-invariants-any-physical-interpretation.html)

 Farouk July 11, 2013 05:51

Riemann invariants....Any physical interpretation?

Hi there,
I am really new to the CFD simulation, and started some simple algorithms recently. I then got introduced to the Riemann Invariants. Can any one provide some physical interpretation?
Also, why is it the case, that when we have an open tube, and the flow is entering with a subsonic speed, then at this point, only one characteristic exist dx/dt=u+a ?

 FMDenaro July 11, 2013 06:17

Quote:
 Originally Posted by Farouk (Post 439137) Hi there, I am really new to the CFD simulation, and started some simple algorithms recently. I then got introduced to the Riemann Invariants. Can any one provide some physical interpretation? Also, why is it the case, that when we have an open tube, and the flow is entering with a subsonic speed, then at this point, only one characteristic exist dx/dt=u+a ? Thank you in advance.
Riemann invariants are a combination of convective and sound velocity (multiplied by a gas-dependent constant) that remains constant along particular curves of the space-time domain. Therefore, you have a physical global quantity that propagates with the same initial value in some directions and at some velocity. I dont think that some further physical meaning exist...

Furthermore at subsonic speed you have u<a, thus

dx/dt = u+a= a*(M+1) >0 for C+
dx/dt = u-a= a*(M-1) <0 for C-

You can see that for subsonic flows two characteristic curves exist but having opposite direction

 Farouk July 11, 2013 07:39

Quote:
 Originally Posted by FMDenaro (Post 439140) Riemann invariants are a combination of convective and sound velocity (multiplied by a gas-dependent constant) that remains constant along particular curves of the space-time domain. Therefore, you have a physical global quantity that propagates with the same initial value in some directions and at some velocity. I dont think that some further physical meaning exist... Furthermore at subsonic speed you have u0 for C+ dx/dt = u-a= a*(M-1) <0 for C- You can see that for subsonic flows two characteristic curves exist but having opposite direction
Hi FMDenaro and thanks for the quick reply. Actually, I see that there are most of the times three characteristics, two which you already mentioned, and the third one, for dx/dt=u.

I see that for subsonic case, with subsonic flow exiting the tube, the two characteristics which exist are dx/dt=u+a and dx/dt=u. The question now is why is it so? what did cancel the third characteristic C-?