GridapFSI

This is an application repository with a collection of drivers for the simulation of Fluid-Structure Interaction (FSI) problems. It is based on Gridap, a package for grid-based approximation of PDEs with Finite Element, and GridapODEs, a package that provides time integration tools for Gridap.

Installation

This is a Julia package that can be easily installed using the Pkg manager. Open the Julia REPL, type ] to enter into the package mode, and install as follows

pkg> add https://github.com/gridapapps/GridapFSI.jl

Usage

First, include the main GridapFSI module:

using GridapFSI

Then, execute the main() function especifying the driver name and the optional arguments. By default the elasticFlag driver is called, with the default parameters corresponding to the FSI2 test case. Other drivers can be called with the following sintax:

main(problemName="<driverName>",kwargs...)

Currently the following drivers are implemented:

• problemName="analytical": A monolithic FSI simulation using a manufactured analytical solution.
• problemName="elasticFlag": A monolighic FSI simulation of the elastic flag behind a cylinder benchmark.

Examples

Elastic flag after a cylinder: FSI-1

The FSI-1 test case for the elastic flag benchmark proposed by S. Turek and J. Horn can be run with the following command:

output = main(
  Um=0.2,
  Re=20,
  rho_s=1.0e-3,
  strategy="biharmonic",
  alpha_m=1.0e-6,
  alpha_m_weight="volume",
  model="models/elasticFlagFine.json",
  dt=1.0,
  tf=25.0,
  theta=0.6
  )

This call will run the FSI1 test case using a θ-method with a time step size of dt=1.0, using the Biharmonic mesh motion strategy with a cell volume weighted constant, and a discrete model defined in models/elasticFlagFine.json. In this test the displacement, velocity and pressure fields are outputed to .vtu files located in the automatically generated folder fsi-results. The result output consists on a tuple with the values of time, drag and lift forces. For this specific case we have the following values at the final time:

# elements	# DOFs	x-displ of A	y-displ of A	Drag force	Lift force
7342	152,745	2.257e-5	8.728e-4	14.215	0.6803
Reference		2.27e-5	8.209e-4	14.295	0.7638

Elastic flag after a cylinder: FSI-2

The FSI-2 test case for the elastic flag benchmark proposed by S. Turek and J. Horn can be run with the following command:

output = main(
  strategy="biharmonic",
  alpha_m=1.0e-6,
  alpha_m_weight="volume",
  model="models/elasticFlagFine.json",
  dt=0.01,
  tf=10.0,
  theta=0.6
  )

The output is the same as the FSI-1 case. In this case, the solution results in a periodic oscillation of the flag as seen in the following movie.

Flow around a cylinder with forced cross-flow oscillations

🚧🚧🚧 work in progress 🚧🚧🚧

In this example we analyse the flow around a cylinder that moves in the cross-flow direction with a forced oscillation. To run this test, execute the following command:

output = main(problemName="oscillator",dt=0.025,tf=10.0)

The main feature of this example is that we first solve a wake oscillator model with nonlinear coupling for the vortex-induced vibration of a rigid cylinder constrained to vibrate in the cross-flow direction. This is done by solving a nonlinear ODE using the DifferentialEquations.jl package. The solution obtained from the wake model is then used as a boundary condition for the displacement and velocity of the cylinder subject to forced motion.

Contributing

Contributions with the definition of new drivers and additional FSI formulations are welcome. The repository is organized as follows:

• GridapFSI.jl: module with the main function and inclusion of submodules.
• FSIDrivers.jl: module with a list of user-defined drivers. Each driver must implement the execute function with the corresponding problem name (<driverName>).

  function execute(problem::Problem{:<driverName>}; kwargs...)
    # user-defined driver
  end

• WeakForms.jl: module with the definition of the weak forms for all required residuals and Jacobians appearing in the FSI formulation.

Please, follow the Gridap contributing guides when developing new features in the repository.

How to cite

If you have used these drivers in a scientific publication, please cite Gridap library and the stabilization method as follows:

@software{gridap_project,
  author       = {Francesc Verdugo and
                  Santiago Badia and
                  Víctor Sande and
                  Alberto F. Martin and
                  Oriol Colomés and
                  Jesús Bonilla},
  title        = {Gridap.jl},
  year         = 2020,
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.3934468},
  url          = {https://doi.org/10.5281/zenodo.3934468}
}