Re: Solving compressible 1-D Euler equations

[John B. Thoo]

On Jun 17, 2005, at 8:01 PM, Joe Koski wrote:

> on 6/17/05 8:38 PM, John B. Thoo at address@hidden wrote:
>
> > Hi.  Is there something already available for solving the compressible
> > 1-D Euler equations?  I'm interested in something where I can simply
> > state the initial conditions, e.g., and then let it run.
> >
> > I looked in <http://octave.sourceforge.net/>, but didn't see anything.
> > (Perhaps I didn't look in the right places.)
> >
> > TIA.
> > ---John.
> John,
>
> It has been a while (40 years) since I had compressible fluid 
> dynamics, but
> I remember, from several math courses, that there were many unrelated 
> Euler
> equations. The one for fluid flow was a linear, first order PDE, if I 
> recall
> correctly.
>
> There are many ODE and PDE solvers related to Octave. Perhaps a bit 
> more
> definition will trigger some suggestions about how to solve the 
> particular
> equation that you have in mind.
>
> Joe

Hi, Joe.  I'm sorry for not having provided more.  I'm not very well 
versed with this (or with numerics), so I wasn't aware that there are 
many unrelated Euler equations.  The ones I'm interested in are for gas 
dynamics (ideal gas).  Here is one way I know them to be.

    [  \rho  ]        [    \rho v    ]
    [ \rho v ]    +   [ \rho v^2 + p ]    =  0
    [    E   ]_t      [   v (E + p)  ]_x

where  \rho  is the density,  v  is the velocity,  p  is the pressure, 
and

            p        1
  E = ------------ + - \rho v^2
       \gamma - 1    2

is the total energy with  \gamma  the ratio of specific heats.

[R. J. LeVeque, _Numerical Methods for Conservation Laws_, Birkhauser 
(1992), pp.52--54.]

I don't know if this is what you were asking for.

TIA.
---John.



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