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Re: Solving compressible 1-D Euler equations
From: |
John B. Thoo |
Subject: |
Re: Solving compressible 1-D Euler equations |
Date: |
Fri, 17 Jun 2005 21:09:45 -0700 |
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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