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Re: NDSolve: PDE's with more than 2 indep. variables.

• To: mathgroup at smc.vnet.net
• Subject: [mg85333] Re: NDSolve: PDE's with more than 2 indep. variables.
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 6 Feb 2008 05:42:16 -0500 (EST)
• Organization: Uni Leipzig
• References: <fob009$hs0$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de

Hi,

the larger problem is, that for fluid dynamics, you need
a time integration that is not dissipative and I would expect
that NDSolve[] has no TVD method implemented and the finite
difference approximations it compute are not of ENO type.

And you may run into serious memory problems when you need
to construct a 4d (space+time) interpolation function.

But it is easy to implement you own solver.

Regards
   Jens
LMZ wrote:
> Hi folks:
> 
> Is there any way at all to use NDSolve to solve PDE's with more than 2
> independent variables. This is actually very important, because if the
> answer is no, then it makes impossible the use of Mathematica in a
> huge field: Fluid Dynamics, in which we'd like to numerically model
> the evolution in time of the velocity or vorticity field. Depending on
> whether there are 2 or 3-D, this could involve 3 or four indep
> variables. Is there ANY package or version of Mathematica that allows
> this to be done? None of the NDSolve examples in Help have more than 2
> variables (x,t). I have version 3.0. When I try to NDSolve with limits
> on 3 variables, it complains that it was expecting Options at position
> four in NDSolve, not another variable.
> 
> got from here http://forums.wolfram.com/student-support/topics/3194
> 
> maybe from 99 something changed...
>