Talk:Rankine–Hugoniot conditions

message: I find this article very difficult to understand. It seems to have much assumed knowledge, and many of the symbols are undefined. It would benefit greatly from practical examples and applications, and full definitions of symbols. (Not to mention reputable references) Sholto Maud 02:38, 31 May 2006 (UTC)
replies: text: I have expanded this article with the intention of making it clearer and to provide some additional references. However, unfortunately, this subject does require some familiarity with thermodynamics and a reasonable level of mathematics. I hope this helps. Griffgruff (talk) 23:18, 6 July 2009 (UTC)
replies: text:  I also added some introductory remarks to guide non-expert readers towards the central idea of treating the jumps as discontinuities, which wasn't previously explained. For the moment these remarks need some hyperlinks and citations. I will put these in when I have a bit more time; folks should also feel free to pitch in and edit as they see fit. Rtfisher (talk) 08:28, 15 October 2023 (UTC)
thread_title: Greater explanation needed

message: The last equation (energy flux) contains a unit mismatch, that is to say, different units are added.
The first component (e- Internal energy) is [Cv x T] (Cv- specific heat in constant volume, T- temperature) the unit is [J/mol]
The two other added parts are [P/roh] and [1/2 x u^2] both of which have the same unit [(m/sec)^2] yet different from the first (e).
I don't see how you can add the three [ e+P/roh+(1/2 x u^2) ].
... unless the equation is per unit mass...
Is it?
: Yes. Lowercase e and ρ indicate that the quantities are specific (meaning, that they are per unit mass). Titoxd(?!? - cool stuff) 20:56, 1 March 2008 (UTC)
thread_title:  Problem on the energy flux equation 

message: A shcok is always a dissipative phenomenon, requiring viscosity.  The Rankine-Hugoniot relations only assume that the fluid is non-viscous outside the shock.  — Preceding unsigned comment added by Mkovari (talk • contribs) 10:37, 16 November 2012 (UTC)
thread_title:  Inviscid 

message: Correct me if I am mistaken, but I believe that equation number 2 i.e. 1-D euler momentum equation has a mistke in it : on the right hand side, shouldn't the convective term be :
\frac{\partial}{\partial x} \frac{\rho u^2}{2}
instead of :
\frac{\partial}{\partial x} \rho u^2
--GLorieul (talk) 19:20, 4 March 2014 (UTC)
replies: text: No, the momentum equation does not have a factor of 1/2 missing.  To see why you can take a look at the derivation of these equations @ .Bbanerje (talk) 21:11, 5 March 2014 (UTC)
thread_title:  Error in 1D Euler equation - momentum equation 

message: Note that jump conditions (for discontinuous functions) could not be obtained from differential equations in principle, so the derivation oj jump conditions in section “The jump condition” is erroneous. Re-casting of differential equations in another form would result, for this approach, in another (incorrect) “conservation law”. For example, the equation
::\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}=0
can be rewritten in two equivalent forms (for smooth solutions):
::\frac{\partial u}{\partial t}+\frac{\partial u^2/2}{\partial x}=0
and 
::\frac{\partial u^2/2}{\partial t}+\frac{\partial u^3/3}{\partial x}=0,
so this way of reasoning would give two (contradictory) jump conditions. Albina-belenkaya (talk) 20:36, 9 January 2015 (UTC)
replies: text: For physical reasons behind jump conditions in nonlinear hyperbolic PDEs see  PDE Notes by J. Shatah. Bbanerje (talk) 04:55, 12 January 2015 (UTC)
replies: text:  The Rankine -- Hugoniot conditions are not, of course, incorrect. What I mean is that the way of reasoning (i.e., derivation of jump conditions by integrating PDEs) is wrong. The right way is postulating the integral relations for hyperbolic system (or derivation of jump conditions from a more complicated system for viscous heat-conducting gas; in this case the shock wave is a narrow zone with large gradients). In present version of the article this point is not clearly stated. Albina-belenkaya (talk) 18:42, 12 January 2015 (UTC)
replies: text:  I agree that a more rigorous approach would be better.  You could add a section below the textbook derivation to explain the problems with this approach and what the solution is. Bbanerje (talk) 00:20, 13 January 2015 (UTC)
thread_title:  Derivation of Rankine-Hugoniot jump condition from PDE is wrong 

message: The article states that "In a coordinate system that is moving with the shock, the Rankine–Hugoniot conditions can be expressed as:" but the equations given are in the frame of the pre-shock medium, no? --129.11.68.6 (talk) 14:04, 8 October 2015 (UTC)
thread_title:  Equations not in frame of shock 

message: The jump conditions are incorrect. This is a major mistake. Should be fixed. Here are the correct equations:
   \frac{\rho_2}{\rho_1} = \frac{v_1}{v_2}=\frac{\gamma+1}{\gamma-1+2M_1^{-2}}
   \frac{p_2}{p_1}&=&\frac{2\gamma M_1^2 - (\gamma-1)}{\gamma+1}
                    
where M_1=\frac{v_1}{c_{s,1}} is the Mach number of the upstream flow.  The pressure behind a strong shock depends on the upstream ram pressure, not on the upstream pressure. That's why the Mach number appears on the right hand side. On the other hand, the density jump has an upper limit. There is no symmetry as shown in the article.
See for example section 7.2 in http://www.astronomy.ohio-state.edu/~dhw/A825/notes7.pdf
— Preceding unsigned comment added by 141.213.169.21 (talk) 01:20, 14 March 2018 (UTC)
thread_title:  Incorrect jump conditions 

message: The article attributes the "Michelson-Rayleigh" line to Albert Michelson. I do not believe this is the correct Michelson. Landau & Lifschitz's text on Fluid Mechanics (section 129, 1987 edition) cites "V. A. Mikhel'son, 1890." While Albert Michelson was alive at that time, the earliest papers in the archive at the University of Chicago only date back to 1891. https://www.lib.uchicago.edu/e/scrc/findingaids/view.php?eadid=ICU.SPCL.MICHELSON#:~:text=,Palomar%20Observatories%2C%20reprints%20of. I have also found the citation to the original paper and will include it and correct the misattribution.
Rtfisher (talk) 07:47, 15 October 2023 (UTC)
thread_title:  Misattribution to Albert Michelson