Subject: itensor, ic_convert for continuity equation
From: Valery Pipin
Date: Tue, 12 Jan 2010 22:23:26 +0800
The right code is
derivabbrev:true$
load(itensor)$
load(ctensor)$
ct_coordsys(cartesian3d)$
cmetric()$
christof(all)$
depends([rho,p,q,T],[ct_coords, t])$
imetric: g$
eq:ishow( s = covdiff((rho([],[]) * q([],[a])),a))$
ic_convert(eq);
s: [0,0,0]$
%th(2), ev;
Look at itensor8.dem
I belive that there should be a demo for the Navie-Stokes equations aswell
> Dear all,
> I am trying to get the Navier Stokes equation into MAXIMA using the
> tensorial packages.
> I am starting by writing the continuity eq
>
> d rho / d t + (rho v^ i )_{ ,j } = 0
>
> or in latex
> \frac{\partial \rho}{\partial t} + (\rho v^i)_{,j} (
> http://tinyurl.com/ydxd6pc )
>
> The idea is to start with "itensor" and then convert it to "ctensor"
> defining the metrics in order to arrive to a final equation in a
> defined coordinate system.
>
> derivabbrev:true$
> load(itensor)$
> load(ctensor)$
> ct_coordsys(cartesian3d)$
> cmetric()$
> christof(mcs)$
> depends([rho,p,q,T],[ct_coords, t])$
> imetric: g$
> eq: ishow( s([a],[]) = covdiff((rho([],[]) * q([a],[])),b))$
> ic_convert(eq);
> s: [0,0,0]$
> %th(2), ev;
>
> I get::
> "Improper indices in - rho([], []) q([%3], []) ichr2([a, b], [%3])
> + rho([], []) q([a], [], b) + rho([], [], b) q([a],
> []) -- an error. To debug this try debugmode(true);"
>
> I use the same indices both in LHS and RHS and "s" is a dummy var to
> give value zero to the LHS. it is basically the same thing done in
> "Maxima Digest, Vol 41, Issue 37" message 5 by Viktor T. Toth.
> Do you know where I am wrong?
>
> Regards
>
> Fabio
>
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