A How to simulate a membrane in a (2D) fluid?

[Xezlec]

I wasn't sure whether to post this in here or in computer programming, since it touches on both.

I have a personal project that is based on a 2-dimensional finite-element fluid simulation (which already works just fine) but needs to be able to simulate an elastic membrane stretched across a pipe as well, which would block the flow of the fluid and stretch out according to pressure as you would expect. Most importantly, it needs to be able to be placed at a T-junction in the pipe such that it can bulge out and block the flow through the other pipe, and that bulge needs to be properly asymmetrical if the pressures on the two sides of the cross pipe are different.

It does not have to be perfect, and does not need to model any really dynamic behavior like waves or anything, but it has to "look about right" when bulging out asymmetrically.

I've spent well over a year, off and on, trying to get this to work (and it's a step in a broader project I've been working on for over 5 years). I've tried things based on the Young-Laplace equation in various ways, and things based on Hooke's Law, treating the membrane as a set of balls and springs. Everything seems to fail one way or another. It's hard to prevent the membrane from crossing itself, hard to couple the pressure and velocity of the fluid to the membrane in a way that doesn't screw up, hard to neatly handle the walls, hard to handle the fact that the membrane can stretch arbitrarily along its length, and hard to get it all to be stable. I can solve most of these problems, but never all of them at once.

I am desperate. I need some kind of idea that will actually work. This is a long shot, but does anybody have any ideas or good references on the subject?

Thanks!

 

[hilbert2]

That kind of thing usually requires an "immersed boundary method", as the finite element mesh can't stay same when the immersed solid object moves from one place to another. It's not an easy problem, unless you can calculate the shape of the bulging membrane in a static situation as a function of pressure and then assume that it immediately assumes that shape when you put a pressure difference between the two sides. If you take a look at some articles about the modeling of blood flow through human heart valves, you'll see that quite difficult mathematics is involved when there's combined elastic solid and liquid phase motion.

 

[Xezlec]

I was afraid of that.