Multi-domain PDE system with pdepe

Hello everyone,

I am trying to create a 1-D transient model of an electrochemical cell that has 5 different layers (domains). I structured the whole problem using pdepe but unfortunately I noticed how it is not possible to handle variable boundaries internally to the domains (so as to handle jumps and possible missing of some equations in the domains). Therefore I step in here by asking some questions:

1.Considering that the model is now completely set up according to the logic of pdepe, does it make sense to spend time trying to modify the source code of pdepe allowing the inclusion of internal BCs to handle jumps in the solution due to the absence of the variable in that domain?

2. In case there is no solution in using pdepe, what is the best tool to deal with this problem in matlab?

Thank you in advance for your response.

[Torsten]

What do you mean by

inclusion of internal BCs to handle jumps in the solution due to the absence of the variable in that domain

How can internal BCs compensate for the absence of variables ?

[Francesco]

I apologize for formulating the question wrongly, my problem is as follows:

1. For some variables, there is no continuity of flow between one domain and another and therefore discontinuities occur (some variables are zero in these domains).

2. At the interface between some internal domains, I would like to set a boundaries other than flow continuity, which from what I understand pdepe allows only at the extremes of the domain.

I wanted to know if There is a way that pdpe can handle these needs of mine, because the model is almost all built according to the logic of pdepe but unfortunately reading later some discussions on the forum I understand that it is not able to. [ref: https://it.mathworks.com/matlabcentral/answers/1906680-adding-more-boundary-conditions-to-pdepe].

If there is no solution, what is the best matlab tool to be able to deal with such a problem?

Thank you for responding quickly.

[Torsten]

There is no solution possible with "pdepe".

COMSOL can handle such user-defined transmission conditions. If you don't have access to COMSOL, you will have to discretize your equations in space including boundary and transmission conditions and solve the resulting system of differential-algebraic equations in time using ODE15S, e.g.

Look up "method-of-lines" for more details.