Solving a non linear set of pdes with multiple dependent variables.

I'm currently working on a student project to design a pressure swing adsorption system. To do this, I need to solve a set of 5 coupled non-linear PDEs with multiple dependent variables. I was wondering if anyone has ever tackled a similar problem with MATLAB before, and whether it would be possible using the PDE Toolbox. Any pointers for the direction I should be heading in would be appreciated.

[Torsten]

We will have to see the equations to answer your question.

Best wishes

Torsten.

[PSA]

Hi Torsten, thanks for replying. The equations are outlined in the two files I've attached, initial conditions are zero for all variables at t = 0 for all z.

[Gizem Kusoglu]

Hi PSA, did you solve your problem? Could you please share your way for solution, if you find solution with matlab?

Answer 1

[Torsten]

There is no ready-to-use MATLAB tool available to solve the equations you posted. The problem is that you have a system of ordinary together with partial differential equations.

You'll have to discretize the equations in space and solve the resulting system of ordinary differential equations using ODE15S, e.g.. Look up "method-of-lines" for more details.

Best wishes

Torsten.

[santi]

Hello Torsten, I have same problem to solve and i'm facing problem in discreatizing boundary conditions.

Answer 2

[PSA]

Ah yes I'd considered that, unfortunately the authors of the paper from which those equations came noted that doing so would lead to stiffness problems and was therefore not feasible. Consequently I'll proceed by applying a Crank-Nicolson discretisation in space and time, I'm also trying to use COMSOL to solve them but that is a different matter altogether.

Thanks for the input.

Chris

[Torsten]

The stiffness argument does not apply because you can use a stiff solver, namely ODE15S. I strongly recommend using the method-of-line approach because you only have to do the spatial discretization, but don't have to care about the time integration.

Best wishes

Torsten.

[PSA]

Ah I had no idea, thanks for clarifying that. MOL should be much simpler, thanks!

Answer 3

[ahmad]

Hi, if it still matters to you, I do not see any problem solving the set of posted equations using the pdepe MATLAB solver. However, of course you can always use MOL, but that would be a bit more work to do.

Best, Ahmad

Answer 4

[santi]

Ahmad, can you please tell me how can i solve these set of equations by using pdepe.