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Thread Subject:
PDE Toolbox for diffusion and advection-diffusion problem?

Subject: PDE Toolbox for diffusion and advection-diffusion problem?

From: JC

Date: 17 Nov, 2009 21:46:02

Message: 1 of 6

It looks like PDE Toolbox is not able to solve for the advection-diffusion problem?

Also, for the diffusion problem, it is not able to define the 'Q' (volume source) as a function of 'c' (concentration)?

Subject: PDE Toolbox for diffusion and advection-diffusion problem?

From: JC

Date: 19 Nov, 2009 05:07:28

Message: 2 of 6

Anyone? Please help. Thanks.

Subject: PDE Toolbox for diffusion and advection-diffusion problem?

From: JC

Date: 19 Nov, 2009 05:09:03

Message: 3 of 6

"JC " <hanjc83@hotmail.com> wrote in message <hdv5iq$o1s$1@fred.mathworks.com>...
> It looks like PDE Toolbox is not able to solve for the advection-diffusion problem?
>
> Also, for the diffusion problem, it is not able to define the 'Q' (volume source) as a function of 'c' (concentration)?

Anyone? Please help. Thanks.

Subject: PDE Toolbox for diffusion and advection-diffusion problem?

From: Knut Schnute

Date: 8 Sep, 2012 21:28:08

Message: 4 of 6

Hey JC,

I am having the same problem that you had a coupe of years ago. Have you been able to find an answer yet?

Best,
Knut

Subject: PDE Toolbox for diffusion and advection-diffusion problem?

From: Bill Greene

Date: 12 Sep, 2012 13:35:08

Message: 5 of 6

You didn’t specify but I assume you are interested in solving the time-dependent advection-diffusion equation.

Version R2012b of PDE Toolbox, which has just been released, has a new capability to allow the coefficients in the parabolic (and hyperbolic) equation to be functions of the solution. So having a source term that is a function of concentration is now straightforward.

It is also possible to use this capability to obtain a solution to the advection-diffusion equation if the diffusion coefficient is not extremely small relative to the advection coefficient (i.e. the Peclet number is not very large). The trick is to include the advection term in the source term by making it a function of the concentration gradient. For example, it could be set to something like ‘Q – c1*ux – c2*uy’ where
Q is the actual source term, c1 and c2 are the advection coefficients in the x and y directions, and ux and uy are the partial derivatives of the concentration. But, since this version of PDE Toolbox doesn’t include any algorithms for stabilizing high-Peclet number flows, you should proceed carefully.

Bill

Subject: PDE Toolbox for diffusion and advection-diffusion problem?

From: Thorsten Bartels-Rausch

Date: 5 Nov, 2012 10:30:08

Message: 6 of 6

Hi Matlab-users

May I add a question about solving the time-dependent advection-diffusion equation. Maybe you are aware of a publication of book dealing with this issue. That would be of great help.

I have been using matlab for years to simulate a chromatographic systems. So far, these were 1-dimensional systems taking into account the transport in the carrier gas (advection) and reversible adsorption/desorption and the ODE solvers worked fine for this.
Now, I would like to add diffusion in the gas-phase to the system. The diffusion along the chromatographic column is not important (advection is dominating); but diffusion perpendicular to the gas-flow is of interest. So we have active transport along the x-axis and diffusion along the y-axis, both are time dependent.

Would you have a step-by-step description of how to use the PDE Toolbox to solve this? Using the PDE toolbox sounds very interesting. Or can this be done by the pdepe solver?

thanks for any help,
thorsten

"Bill Greene" wrote in message <k2q32c$al3$1@newscl01ah.mathworks.com>...
> You didn’t specify but I assume you are interested in solving the time-dependent advection-diffusion equation.
>
> Version R2012b of PDE Toolbox, which has just been released, has a new capability to allow the coefficients in the parabolic (and hyperbolic) equation to be functions of the solution. So having a source term that is a function of concentration is now straightforward.
>
> It is also possible to use this capability to obtain a solution to the advection-diffusion equation if the diffusion coefficient is not extremely small relative to the advection coefficient (i.e. the Peclet number is not very large). The trick is to include the advection term in the source term by making it a function of the concentration gradient. For example, it could be set to something like ‘Q – c1*ux – c2*uy’ where
> Q is the actual source term, c1 and c2 are the advection coefficients in the x and y directions, and ux and uy are the partial derivatives of the concentration. But, since this version of PDE Toolbox doesn’t include any algorithms for stabilizing high-Peclet number flows, you should proceed carefully.
>
> Bill

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