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Thread Subject:
PDE multilayer diffusion

Subject: PDE multilayer diffusion

From: cabeludo

Date: 30 Jan, 2012 19:57:10

Message: 1 of 8

Hi, I am working right now on diffusion of molecules through a layer of hydrogel. I am using pdepe function to do so. Works fine.

Now I want to add a layer, my construct through which the molecules have to diffuse is thus a two layer complex, with two different diffusion coefficients and length.

how can I implement this problem? Is the function pdepe useful?

thanks for the help

Subject: PDE multilayer diffusion

From: Torsten

Date: 31 Jan, 2012 07:42:18

Message: 2 of 8

On 30 Jan., 20:57, "cabeludo " <kormi...@hotmail.com> wrote:
> Hi, I am working right now on diffusion of molecules through a layer of hydrogel. I am using pdepe function to do so. Works fine.
>
> Now I want to add a layer, my construct through which the molecules have to diffuse is thus a two layer complex, with two different diffusion coefficients and length.
>
> how can I implement this problem? Is the function pdepe useful?
>
> thanks for the help

PDEPE does not support internal boundary conditions which have to be
set in multilayer
problems.
You will have to discretize your equations in space by yourself using
the method-of-lines
and solve the resulting system of ordinary differential equations by
ODE15S, e.g.

Best wishes
Torsten.

Subject: PDE multilayer diffusion

From: Bill Greene

Date: 31 Jan, 2012 15:52:10

Message: 3 of 8

Without seeing your PDE it is impossible to say for certain, but I believe
PDE Toolbox could solve your 2-layer diffusion problem.

Regards,

Bill

Subject: PDE multilayer diffusion

From: cabeludo

Date: 31 Jan, 2012 18:52:09

Message: 4 of 8

Torsten <Torsten.Hennig@umsicht.fraunhofer.de> wrote in message <a09dce6e-9659-42d8-a910-08c2907d1898@do4g2000vbb.googlegroups.com>...
> On 30 Jan., 20:57, "cabeludo " <kormi...@hotmail.com> wrote:
> > Hi, I am working right now on diffusion of molecules through a layer of hydrogel. I am using pdepe function to do so. Works fine.
> >
> > Now I want to add a layer, my construct through which the molecules have to diffuse is thus a two layer complex, with two different diffusion coefficients and length.
> >
> > how can I implement this problem? Is the function pdepe useful?
> >
> > thanks for the help
>
> PDEPE does not support internal boundary conditions which have to be
> set in multilayer
> problems.
> You will have to discretize your equations in space by yourself using
> the method-of-lines
> and solve the resulting system of ordinary differential equations by
> ODE15S, e.g.
>
> Best wishes
> Torsten.



Hmmm, not sure if I got it.
What is the method-of-lines, and ODE15S?

Subject: PDE multilayer diffusion

From: Torsten

Date: 1 Feb, 2012 07:41:54

Message: 5 of 8

On 31 Jan., 19:52, "cabeludo " <kormi...@hotmail.com> wrote:
> Torsten <Torsten.Hen...@umsicht.fraunhofer.de> wrote in message <a09dce6e-9659-42d8-a910-08c2907d1...@do4g2000vbb.googlegroups.com>...
> > On 30 Jan., 20:57, "cabeludo " <kormi...@hotmail.com> wrote:
> > > Hi, I am working right now on diffusion of molecules through a layer of hydrogel. I am using pdepe function to do so. Works fine.
>
> > > Now I want to add a layer, my construct through which the molecules have to diffuse is thus a two layer complex, with two different diffusion coefficients and length.
>
> > > how can I implement this problem? Is the function pdepe useful?
>
> > > thanks for the help
>
> > PDEPE does not support internal boundary conditions which have to be
> > set in multilayer
> > problems.
> > You will have to discretize your equations in space by yourself using
> > the method-of-lines
> > and solve the resulting system of ordinary differential equations by
> > ODE15S, e.g.
>
> > Best wishes
> > Torsten.
>
> Hmmm, not sure if I got it.
> What is the method-of-lines, and ODE15S?- Zitierten Text ausblenden -
>
> - Zitierten Text anzeigen -

http://en.wikipedia.org/wiki/Method_of_lines
http://www.mathworks.de/help/techdoc/ref/ode23.html

Best wishes
Torsten.

Subject: PDE multilayer diffusion

From: Torsten

Date: 1 Feb, 2012 07:43:50

Message: 6 of 8

On 31 Jan., 16:52, "Bill Greene" <w.h.gre...@gmail.com> wrote:
> Without seeing your PDE it is impossible to say for certain, but I believe
> PDE Toolbox could solve your 2-layer diffusion problem.
>
> Regards,
>
> Bill

Could you give a link to an example where internal boundary are
treated,
e.g. continuity of concentration and mass flux at the interface of the
two layers ?

Best wishes
Torsten.

Subject: PDE multilayer diffusion

From: Bill Greene

Date: 1 Feb, 2012 13:39:10

Message: 7 of 8


> Could you give a link to an example where internal boundary are
> treated,
> e.g. continuity of concentration and mass flux at the interface of the
> two layers ?
>
> Best wishes
> Torsten.

My understanding of the problem definition is that
this user is trying to solve the diffusion equation
in a model with two layers, each with it's own material
properties. When using the weak formulation of the
equations, which the FE method in PDE Toolbox is based
on, no special treatment is needed at places in the model
where material properties change. In PDE Toolbox each
layer (material region) is modeled as an individual
"subdomain" with its own material properties.

The two-pole, DC motor example in the PDE Toolbox User's
Guide is one example of a model like this.

Regards,

Bill

Subject: PDE multilayer diffusion

From: cabeludo

Date: 1 Feb, 2012 20:00:09

Message: 8 of 8

"Bill Greene" wrote in message <jgbf9u$52n$1@newscl01ah.mathworks.com>...
>
> > Could you give a link to an example where internal boundary are
> > treated,
> > e.g. continuity of concentration and mass flux at the interface of the
> > two layers ?
> >
> > Best wishes
> > Torsten.
>
> My understanding of the problem definition is that
> this user is trying to solve the diffusion equation
> in a model with two layers, each with it's own material
> properties. When using the weak formulation of the
> equations, which the FE method in PDE Toolbox is based
> on, no special treatment is needed at places in the model
> where material properties change. In PDE Toolbox each
> layer (material region) is modeled as an individual
> "subdomain" with its own material properties.
>
> The two-pole, DC motor example in the PDE Toolbox User's
> Guide is one example of a model like this.
>
> Regards,
>
> Bill

Seems incredible, but I didn't know the existence of this toolbox. I coded all by myself and created my own GUI. But now that I know, I'll work on it!

I'll post news here as soon as I get some!

thanks a lot

Y.

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