CFD Online Logo CFD Online URL
Home > Forums > Main CFD Forum

Riemann Invariants

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

LinkBack Thread Tools Display Modes
Old   June 20, 2008, 10:29
Default Riemann Invariants
Posts: n/a
Can some one please give me insight about the Riemann Invariants in 2D Inviscid flows...???Any literature will be welcome. Also I need to know the 4 formulae, if possible in non-dim. form.Explain if possible.Thank u in adv...

Tushar, IIT Guwhatai, India.

  Reply With Quote

Old   June 20, 2008, 12:11
Default Re: Riemann Invariants
Posts: n/a
The Riemann invariants are defined only for one-dimensional flows, in two-dimensional flows they are called the Charactersitics of the flow and are the analogs to the 1D Riemann invariants. The Riemann invariants are really about what and how is propagated through the flow? Any information can propagates in the flow at 3 different velocities. If v is the velocity of the fluid, c is the sound velocity there, then any information can propagates at the speeds:




these are the characteristics speeds of the propagation of the information. What propagates are called (Riemann) invariants and so you have in the present case 3 of them. say R1, R2 and R3. In a subsonic regime v<c .

R1 propagates at speed v with the flow (down stream)

R2 propagates at supersonic speed v+c with the flow (down stream)

R3 propagates at subsonic speed v-c against the flow (up stream).

THese 3 quantitties (R1, R2, R3) are the solution of an algebraic equations, they are the eigen vectors of that system of equations with eigen values v, v+c, and v-c.

When one consider a boundary and wants to know what flows through that boundary, one needs to consider the flow normal (perpendicular) to that boundary and negelct any space derivative in the dimension parallel (tangent) to that boundary, as only the component of the velocity normal to that boundary contributes to the passing of flow and information through that boundary. Then one writes the flow equations at that boundary (neglecting parallel derivatives) and one solves for the linearized equations and obtains the Riemann Invariants R1, R2, R3 or characteristics of the flow.

For a complete treatment see e.g. Landau Lifshitz.

  Reply With Quote

Old   June 21, 2008, 12:11
Default Re: Riemann Invariants
Posts: n/a
Thank you so much...
  Reply With Quote

Old   July 7, 2009, 13:49
Nishant Kumar
Join Date: Jun 2009
Posts: 32
Rep Power: 8
Nishu is on a distinguished road
Hey Patrick,

Do you know from where I can get the code for 1D Riemann compressible flows?

Nishu is offline   Reply With Quote


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
Riemann problem prapanj Main CFD Forum 3 February 1, 2013 23:04
Riemann invariants shallow water RicardoGoncalves Main CFD Forum 0 May 30, 2011 09:52
Question abt. the Riemann analytic solver jinwon Main CFD Forum 0 July 16, 2007 14:11
Is there any two-phase riemann analytic solution? jinwon Main CFD Forum 3 June 17, 2007 01:52
Riemann Invariants Mikhail CFX 0 September 22, 2005 14:39

All times are GMT -4. The time now is 04:47.