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I need a little help and advice with a project I want to do: the idea is to "couple" (I don't know whether I can call it like this) a conservative Navier-Stokes Solver (Fractional-step, 2nd order FDM) with itself. Roughtly speaking, I would like to split the domain in halves so to be able to solve one fluid on one side and another fluid on the other side. The interface is supposed to be fixed at all times, and for the moment I don't need to have different discretizations for each domain. The problem is that one of the fluids is around 1000 times lighter that the other fluid, so (I think) the transmission conditions for the stresses are not going to be as straightforward. Anyhoo, I would like someone to point me in the right track (state-of-the-art literature, jargon, "big names",etc) and shoot some ideas if you like. Ciao & grazie

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    $\begingroup$ The transmission conditions are actually quite simple: the traction forces need to be equal. If you keep the interface fixed, then only the tangential traction forces are equal from both sides, and the normal velocity is zero from both sides. $\endgroup$ – Wolfgang Bangerth Mar 1 '15 at 17:14
  • $\begingroup$ Ok, Thanks Wolfgang. Now, lets say I want to have different discretization on both sides now, Is there any literature I can follow to do such an implementation? I mean, I have been collecting a lot of literature (Domain decomposition, Operator Splitting, etc) that seems to be more applicable in FEM than to FDM. I haven't been able to find anything regarding FDM and coupling of simple interfaces (maybe because I am using the "wrong" words in order to search). EDIT 1: I am kind of new to this subject, I really ask for your patience. $\endgroup$ – Kbzon Mar 2 '15 at 8:07
  • $\begingroup$ @SantiagoLópezCastaño when you say the literature appears to be more applicable to finite element methods, are you differentiating these from finite volume methods? $\endgroup$ – aeroNotAuto Mar 6 '15 at 14:18
  • $\begingroup$ No, what I tried to say is that most of the literature I've found in heterogeneous domain decomposition is related to weak (energy) formulations in Hilbert spaces, which is suitable for FEM. In short, I would like to bridge the non-overlapping domain decomposition concept to the FDM realm to be able to work with two different structured grids. NO FVM IS INVOLVED. $\endgroup$ – Kbzon Mar 6 '15 at 14:32
  • $\begingroup$ You may want to try the preCICE coupling library. It is general-purpose so, as long as you have the two domains with their solvers, you can easily couple them. If they are well-known solvers, an adapter may already exist. Otherwise, it is quite easy to make an adapter for your own solver. See precice.org . You can also find it on GitHub, with some tutorials: github.com/precice/precice/wiki . $\endgroup$ – MakisH Dec 12 '17 at 23:56

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