I would like to get started solving Fluid-Structure interaction problems.

I already have some experience with Finite Elements, including my own MATLAB and Julia software packages for developing Finite Element programs, i.e., I can confidently approximate the solution to some basic 1D and 2D initial-boundary-value-problems using my code.

I am looking for resources (books or articles, or blog-posts, or any published material in general) that address issues related to the development of software for solving Fluid-Structure interaction problems. Can you make any suggestions?

  • $\begingroup$ A possible next step would be to implement a Navier-Stokes solver $\endgroup$ – user21 Jun 15 '17 at 16:57
  • $\begingroup$ That is something that I will probably do in the near future. I already have a solver for a (stationary) Stokes-flow in a lid-driven cavity boundary value problem ($\nu \Delta \textbf{u} + \frac{1}{\rho} \nabla p =\textbf{f}, \quad\nabla \cdot \textbf{u} = 0$). I also have a solver for a (dynamic) 1D dynamic Euler-Bernoulli beam ($EI \frac{\partial^4 w}{\partial x^4} = - \mu \frac{\partial^2 w}{\partial t^2} + f(x,t)$). I was thinking I could come up with a problem and solve it with a "partitioned approach" at first, since I already have these solvers. $\endgroup$ – amarney Jun 15 '17 at 17:12
  • $\begingroup$ Particulate Stokes flow problems can be fun, and certainly have a wealth of literature backing them up; everything from theory to practice. $\endgroup$ – Spencer Bryngelson Jun 16 '17 at 1:39

You may like this tutorial for simulating the flow in a deformable artery.

In this 1D example you can actually see how the fluid and the solid solver work and how preCICE couples them. Both a serial and a parallel version of the solvers are available.

As soon as you get some understanding of the basics, you can start building more complex simulations, using existing solvers. See this tutorial for example: FSI with SU2 and CalculiX.

If you have your own solvers, you can actually create your own adapter. As preCICE is free software, you can even modify preCICE itself to fit your needs.

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