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: <email@example.com>
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>