CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Main CFD Forum

Riemann invariants....Any physical interpretation?

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Display Modes
Old   July 11, 2013, 05:51
Default Riemann invariants....Any physical interpretation?
  #1
New Member
 
CFDLearner
Join Date: Jul 2013
Posts: 16
Rep Power: 4
Farouk is on a distinguished road
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.
Farouk is offline   Reply With Quote

Old   July 11, 2013, 06:17
Default
  #2
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,662
Rep Power: 23
FMDenaro will become famous soon enough
Quote:
Originally Posted by Farouk View Post
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
FMDenaro is online now   Reply With Quote

Old   July 11, 2013, 07:39
Default
  #3
New Member
 
CFDLearner
Join Date: Jul 2013
Posts: 16
Rep Power: 4
Farouk is on a distinguished road
Quote:
Originally Posted by FMDenaro View Post
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
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-?

Thank you for your help.
Farouk is offline   Reply With Quote

Old   July 11, 2013, 07:58
Default
  #4
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,662
Rep Power: 23
FMDenaro will become famous soon enough
For homoentropic flows, the entropy is constant everywhere in the domain and the characteristic C0, that is dx/dt = u (trajectory) is not relevant to define an invariant property.

The third characteristic becomes relevant for isoentropic flows where s is constant only along the trajectory dx/dt=u. However, Riemann invariants do not exist for such case.

In a subsonic flow, at inlet you have two characteristic curves (u, u+a) entering in the domain and one leaving (u-a) while at an outlet you have two characteristics leaving (u, u+a) and one entering (u-a) from outlet.

This fact must be respected in prescribing the correct BCs.
FMDenaro is online now   Reply With Quote

Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Superlinear speedup in OpenFOAM 13 msrinath80 OpenFOAM Running, Solving & CFD 18 March 3, 2015 06:36
Riemann Invariants for the 2-Dimensional Euler Equations Cthames21 Main CFD Forum 1 April 3, 2013 11:31
Riemann invariants of adjoint equations of shallow water equations zqb0929 Main CFD Forum 0 March 15, 2012 01:54
Riemann Invariants Tush Main CFD Forum 3 July 7, 2009 13:49
Riemann Invariants Mikhail CFX 0 September 22, 2005 14:39


All times are GMT -4. The time now is 08:00.