If you like to setup your own FSI simulation using the provided dealiiadapter, this section should help you to configure the source code and the parameter file.
In order to change your geometry and set appropriate boundary conditions, you need to modify the source file. The parameter file (e.g. parameters.prm
) is used to set certain properties: material properties, numerical properties or preCICErelated properties.
DEAL_II_NUM_THREADS
. By default, all available cores on the respective machine are utilized.
Parameter file
This section gives additional information about the parameter files. Here is an example:
subsection Time
# End time
set End time = 10
# Time step size
set Time step size = 0.05
# Write results every x timesteps
set Output interval = 10
# Output folder
set Output folder = dealiioutput
end
The first subsection deals with specifications for timerelated settings. The output interval specifies when simulation results are written to an output file. In this example, the program will store the results every 10 time steps. Using a time step size of 0.05 seconds, a result file is written every 0.5 seconds.
subsection Discretization
# Polynomial degree of the FE system
set Polynomial degree = 3
# Time integration scheme
# 0 = forward, 1 = backward
set theta = 0.5
# Newmark beta
beta = 0.25
# Newmark gamma
gamma = 0.5
end
This subsection configures the numerical discretization: The polynomial degree is associated to the degree of the applied shape functions. Theta is related to the time integration scheme of the linear solver, which is a onesteptheta method. Accordingly, its value can be chosen between 0 and 1, where 0 denotes an explicit forward Euler method and 1 denotes an implicit backward Euler method with each having first order accuracy. It is recommended to use theta to 0.5, which results in a second order accurate and energyconserving CrankNicolson scheme. If you prefer dissipative behavior, you need to choose theta greater than 0.5. Have a look in the Solver details for more information. The nonlinear solver uses, however, an implicit Newmark scheme, which allows a configuration using the parameters beta and gamma.
subsection System properties
# Poisson's ratio
set Poisson's ratio = 0.4
# Shear modulus
set mu = 0.5e6
# density
set density = 1000
# Body forces x,y,z
set body forces = 0.0,0.0,0.0
end
This section defines the material properties and allows the definition of body forces. Possion’s ratio and lambda define the material properties. For an overview of all available parameters and conversion formulas have a look at the conversion table at the bottom of the elastic moduli wikipedia article: Body forces are usually gravitational forces and defined directionwise (x,y,z).
subsection Solver
# Structural model to be used: linear or neoHookean
set Model = linear
# Linear solver: CG or Direct
set Solver type = Direct
# Max CG solver iterations (multiples of the system matrix size)
# In 2D, this value is best set at 2. In 3D, a value of 1 works fine.
set Max iteration multiplier = 1
# Absolute CG solver residual (multiplied by residual norm, ignored if Model == linear)
set Residual = 1e6
# Number of NewtonRaphson iterations allowed (ignored if Model == linear)
set Max iterations NewtonRaphson = 10
# Relative displacement error tolerance for nonlinear iteration (ignored if Model == linear)
set Tolerance displacement = 1.0e6
# Relative force residual tolerance for nonlinear iteration (ignored if Model == linear)
set Tolerance force = 1.0e9
end
This subsection defines parameters for the applied solver. First of all, the underlying model needs to specified: you can either choose a linear elastic model or employ a hyperelastic nonlinear neoHookean solid. The nonlinear solvers applies an iterative NewtonRaphson scheme to solve the system iteratively. The following selections determine the properties of the linear and nonlinear solver. Depending on your configuration, some parameters might not be relevant. The residual of the linear solver is only relevant for the nonlinear model, since the residual is adjusted between individual Newton iterations. For the linear model, this value is hardcoded.
UMFPACK
in order to use the direct solver, which is enabled by default.
subsection precice configuration
# Cases: FSI3 or PF for perpendicular flap
set Scenario = FSI3
# PF xlocation
set Flap location = 0.0
# Name of the precice configuration file
set precice configfile = preciceconfig.xml
# Name of the participant in the preciceconfig.xml file
set Participant name = Solid
# Name of the coupling mesh in the preciceconfig.xml file
set Mesh name = SolidMesh
# Name of the read data in the preciceconfig.xml file
set Read data name = Stress
# Name of the write data in the preciceconfig.xml file
set Write data name = Displacement
end
This section defines preCICErelated settings. The scenario and flaplocation parameters can be deleted for your own project since they are just needed for the configuration of our tutorial cases. The other parameters are related to the preciceconfig.xml
file. Have a look at the respective entry in the preCICE configuration section for details. Make sure the names are the same as in the preciceconfig.xml
.
Source code file
Grid generation
Similar to the deal.II tutorial cases, the grid is generated in a function called make_grid()
, which is called in the beginning of the run()
function. There are a bunch of options to construct the mesh inside this function, which are extensively described in the deal.II documentation: If your geometry is rather simple (e.g. a shell or a sphere), have a look at the GridGenerator class in the documentation. If you have complex geometries, you might want to create your mesh with external software and load the geometry file in the source code file. In this case, have a look at the GridIn class. The documentation also provides a list of supported mesh file formats.
In our case, we configured the source code file for two tutorial cases. Hence, there is additionally an if
condition in the make_grid()
function, which asks for the chosen tutorial case. Since both cases have a rectangular grid, we generate our mesh by using the subdivided_hyper_rectangle()
function. Moreover, the deal.II tutorial programs provide various examples for the grid generation.
Boundary conditions
Boundary conditions are applied to specific mesh regions via boundary IDs. We need to distinguish three mesh regions:

Dirichlet boundaries, where a constant zero displacement is prescribed

Neumann boundaries, where a prescribed traction acts on the surface. This is solely the coupling interface in our case

Boundaries without a specified condition (strictly speaking zero traction)
Hence, the first task is the assignment of mesh IDs to the desired mesh region. This is done in the make_grid()
function. In our case, we used the colorized = true
option during the grid generation, which automatically assigns each side of our rectangle an individual boundary ID. But you could also iterate over all cells and ask for your own condition (e.g. geometric conditions) and set the boundary ID accordingly. Make sure you only have one boundary ID for the interface mesh in the end. If you have more than one, sum them up in a single ID in a second step as done at the end of the make_grid()
function. The interface mesh ID is a global variable and needed by the Adapter
constructor.
The interface mesh is assumed to be the only Neumann boundary. If you have other loads acting on the surface, you need to add it manually during assembly. Constant volume loads (gravity) can be used and are switched off by default, since the tutorial cases don’t need them.
Similar to the collection of the interface mesh ID in a single boundary ID, you could sum up your Dirichlet boundaries in one ID. In this case, you could use the clamped_mesh_id
as in the tutorial cases. If you want to set more specific Dirichlet boundaries e.g. in a specific direction, have a look at the bottom of the assemble_rhs()
/ the make_constraints()
function. You need to modify the interpolate_boundary_values()
function by e.g. choosing a different direction in the fe.component_mask()
. The tutorials give an example for doing this in the outofplane direction. A detailed documentation is given in the deal.II documentation.