Integration over an immersed, non-matching interface/surface

Question

Hello,

I am solving a problem in which I have two different, non-matching meshes (say M1 and M2). I solve Navier Stokes in mesh M1, and now want to calculate stress integrals etc on the boundary of mesh M2. I have no simplified example yet, but if needed, I can make one up.
I was wondering whether I can get some tips on performing this integration. How should I approach this? Should I interpolate the solution from M1, to M2 using a projection, and then integrate along the facetnormals (boundary) of M2?

Any help will be appreciated, since I am kinda stuck on this problem.

Thanks

Comments

I, too am working on figuring out how to handle a similar issue for an electrodynamics problem. My current thinking is that I have to reference the nodal values calculated along the interface in the first subdomain and interpolate that vector with the test functions from second subdomain. Have you figured out how to get this submesh-to-submesh boundary referencing to work? If you have what did you do?