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

• To: mathgroup at smc.vnet.net
• Subject: [mg85336] Re: NDSolve: PDE's with more than 2 indep. variables.
• From: Oliver Ruebenkoenig <ruebenko at uni-freiburg.de>
• Date: Wed, 6 Feb 2008 05:43:49 -0500 (EST)
• Organization: InterNetNews at News.BelWue.DE (Stuttgart, Germany)
• References: <fob009\$hs0\$1@smc.vnet.net>

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Hi there,

if you do not mind using something different than NDSolve, have a look at
the IMTEK Mathematica Supplement (IMS) There you will find several general
navier-stokes solvers using the FEM/FDM method.

IMS should work with Mathematica Version 5.0 or higher.

1) FDM Solver:
http://www.imtek.uni-freiburg.de/simulation/mathematica/IMSweb/imsTOC/Differential%20Equation%20Systems/Discretization/FDMNavierStokesDocu.html

2) FEM Solver where i used special elements:
http://www.imtek.uni-freiburg.de/simulation/mathematica/IMSweb/imsTOC/Application%20Examples/Finite%20Element%20Method/FlowAroundCylinderDocu.html

3) a _much_ more general FEM Solver:
http://www.imtek.uni-freiburg.de/simulation/mathematica/IMSweb/imsTOC/Application%20Examples/Finite%20Element%20Method/NavierStokes2DDocu.html

also you find a navier-stokes solver coupled to a level-set to model free
surface flow.

http://www.imtek.uni-freiburg.de/simulation/mathematica/IMSweb/imsTOC/Application%20Examples/Finite%20Element%20Method/FreeSurfaceFlow2DDocu.html

This example shows the ejection of ink from an ink-jet print head. There
are several other examples included. Here we have 4 variables (2D) u and v
velocity, p pressure, and phi for the implicit function.

HTH,
Oliver

On Wed, 6 Feb 2008, 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...
>
>

Oliver Ruebenkoenig, <ruebenko AT uni-freiburg.de>

```

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