Re: Solving compressible 1-D Euler equations

[Shai Ayal]

Hi John,

This is a 1D+time partial differential equation -- not so trivial to solve. 
 As with Joe, I too am struggling with  memories of my graduate years to 
try and remember if it simple or not. I think it is not so simple. I would 
try to look it up with google. It is probably not too hard to code up 
something in Octave. But beware -- unless you find some clever way of using 
octave's matrix (perhaps sparse) operations, you will end up with something 
very slow. If this is the case, you can try this nifty tool:

http://www.xmds.org/

Shai

John B. Thoo wrote:
> 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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--
Shai Ayal, Ph.D.
Head of Research
BioControl Medical BCM
3 Geron St.
Yehud 56100
ISRAEL
Tel:  + 972 3 6322 126 ext 223
Fax:  + 972 3 6322 125
email: address@hidden



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