Subject: itensor, ic_convert for continuity equation
From: Fabio
Date: Tue, 12 Jan 2010 14:36:36 +0100
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