Solving advection equation on domain split in two

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1

Hello,

I am trying to solve the advection equation (with advective velocity b=(0,-1)) on a domain that has been split in two subdomains. To split the domain, I’m using the code previously made available by Guosheng, see:

What I would like to do, is solve the advection equation on the whole domain. As initial test case I use as initial condition that u=1 and the inflow condition is 1 so that the solution must be 1 for the whole simulation. This is not happening. Instead, on half the domain the solution is equal to 1 and on the other half the solution eventually tends to u=0.5. I think this has to do with the call to u.Other() on the interface between the two subdomains. I attach my code. Do you have any suggestions how to fix this issue?

Thanks!
Sander

Attachment: transport.py

2

Hi Sander,

for the explicit part it is working like this:

If there is a neighbouring volume element, the .Other refers to that. Thus, internal interfaces are ignored. You can use a GridFunction from a FacetFESpace to add source terms on internal edges (see attached file).

for the implicit part - I don’t know. Use HDG !!!

best, Joachim

Attachment: transport.py

3

Hi Joachim,

Thanks for the suggestion. HDG indeed does the job. Attached the code using HDG.

Thanks,
Sander

Attachment: hdg-transport.py