Interface continuity conditions in heat transfer problems

General
1

Hello everyone, as shown in the figure, for heat transfer problems involving multiple regions, how can I use FEniCS to implement the continuity conditions of temperature and heat flux density at the interface? Your help is appreciated. Thank you!

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(The red line represents the interface)

2

Your question is very vague, and thus it is difficult to give any precise guidance. Please see Read before posting: How do I get my question answered?

Apart from that, general suggestions would be:

  • if you want to write a weak formulation on the entire domain, then those conditions at the interface would come for free, at least if you are using Lagrange finite elements (i.e., continuous). Then the question I guess you are asking is how to define subdomains: see e.g. Defining subdomains for different materials — FEniCSx tutorial
  • if instead you want to write a weak formulation on subdomain I and another on subdomain II, then consider reading this multiphenicsx tutorial tutorial_lagrange_multipliers_interface
2 Likes
4

Dear leader, I understand the posting guidelines. Here I just want to get a simple example. The interface continuity condition comes from a heat transfer textbook. The Dirichlet boundary condition and Neumann condition are both explained in the FEniCS official tutorial, but the interface continuity condition required for multi-region heat transfer problems is not covered. The issue I am facing is that the two regions cannot be written as a unified weak form of the Fourier equation, so I cannot use your first suggestion. However, this is a general problem, and interface continuity conditions need to be satisfied for any heat transfer between multiple regions, which is not addressed in the FEniCS tutorial.

5

then user the second suggestion.

6

Alright, thank you for your response.