Hi Matlabusers
May I add a question about solving the timedependent advectiondiffusion 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 1dimensional 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 gasphase to the system. The diffusion along the chromatographic column is not important (advection is dominating); but diffusion perpendicular to the gasflow is of interest. So we have active transport along the xaxis and diffusion along the yaxis, both are time dependent.
Would you have a stepbystep 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 timedependent advectiondiffusion 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 advectiondiffusion 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 highPeclet number flows, you should proceed carefully.
>
> Bill
