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Re: heat equation through different media/problem with constant flux

  • To: mathgroup at smc.vnet.net
  • Subject: [mg87803] Re: heat equation through different media/problem with constant flux
  • From: Oliver Ruebenkoenig <ruebenko at uni-freiburg.de>
  • Date: Thu, 17 Apr 2008 06:58:22 -0400 (EDT)
  • References: <fu6mi8$nnm$1@smc.vnet.net>

Luigi,

On Thu, 17 Apr 2008, Luigi B wrote:

> Dear All,
> I am trying to solve the heat conduction problem in a sequence of
> three media with different properties. For that I am using NDSolve
> with my own grid. The code (without the 'tedious' definition of the
> time dependent boundary conditions) is:
>
> \!\(NDSolve[{=A2=DF\_t u[x,
>    t] == alfa[x]*=A2=DF\_{x, 2}u[x, t], u[
>        x, 0] == TavSInt[0] + \(TavRInt[0] - TavSInt[0]\)\/L*
>      x, u[0, t] == TavSInt[
>        t], \([L, t]\) == TavRInt[
>          t]}, u, {x, 0, L}, {t, 0, tmax}, MaxSteps -> 50000, Method -
>> \
> {"\<MethodOfLines\>", \ "\<SpatialDiscretization\>" -> {\ \
> "\<TensorProductGrid\>", "\<Coordinates\>" -> {mygrid}}}]\)
>
>
> However, i still do not get a satisfactory result. Probably because I
> am not including the condition that at the interface between two media
> the heat flux is constant. How can I do this?

The thing is here, that you have a jump condition between the two
materials. A crude workaround would be to refine the mesh at the
interface. Another option would be to smooth out the interface.

Jose LLuis G=C3=B3mez-Mu=C3=B1osome time a ago did a finite element version of a
similar problem. You can find it as part of the IMTEK Mathematica
Supplement.

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

There is also a 3D version of it.

http://www.imtek.uni-freiburg.de/simulation/mathematica/IMSweb/imsTOC/Application%20Examples/Finite%20Element%20Method/CompositeMaterials3DDocu.html

hth,

Oliver

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


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