## Coupling between two PDEs

Discussion about coding and new developments

### Coupling between two PDEs

Hi all,

I would like to solve two PDE's with two variables (Mdot, T). However, the dTdt term presents on both PDEs.

How I could solve them in one/separate solver using high-level language?
I started by modifying "ModelPDE" solver, however, "ModelPDE" case only solve one variable.

MasterYodha

Posts: 7
Joined: 05 Jul 2013, 14:20

### Re: Coupling between two PDEs

HI there,

from my experience with elmer you have to possibilities:
1) If the domain for the two PDES is the same:
Use one solver with a variable that has 2 DOFS
Each DOF can be treated as a variable. That way you can have fully implicit solutions (up to linearisation) of the equations.

2)Use two separate solvers for each variable. The dTdt term can be calculated from the solver for T ("Calculate Velocity =Logical True" in sif file). Then u have a Variable "T Velocity" available for the other solvver that can be implimentet there explicitly.

I always prefer number one because it is the more stable one in my opinion, however if the cross effects are not to big between the variables, way number 2 might even improve your calculation speed because of the smaller linear systems.
I think way number 2 is also the one that suits the whole ELMER design a bit better.

best regards
Franz
Franz Pichler

Posts: 196
Joined: 29 Sep 2011, 12:25

### Re: Coupling between two PDEs

Hi Franz,

Yes, I agree with you. I chose number 1 by modifying the ThermoElectricSolver.src which has two variables (potential, temperature) in one solver. It is also written in high-level language.

Regarding the dTdt term, I just know that we could export first-derivative term out of a solver. Its really inspiring me.
Do you know what is the keyword to export dTdx and d2Tdx2 also?

Best regards, Yodha
MasterYodha

Posts: 7
Joined: 05 Jul 2013, 14:20

### Re: Coupling between two PDEs

For the dTdx stuff you should check out the flux solver and search in the forum for "calculate flow" and similar keywords. This is an often discussed matter with many possible approaches,
but with the Flux solver its actually quite simple,

regarding d^2Tdx^2 i have not much eperience. I guess you can work a way out where you just save the components of dTdx in variables and the again use the flux solver. This might be possible without any effort by applying the flux solver to "T Flux 1" for example. I am guessing here though,

best regards
Franz
Franz Pichler

Posts: 196
Joined: 29 Sep 2011, 12:25