FSI Tutorial 2D

Introduction

We consider a 2d driven cavity example as sketched in Fig. 1.1. For further details and references we refer the reader to [Wall99]

The driven cavity example in 2d

The driven cavity example in 2d

You can find the complete journal in tests/tutorials/tutorial_fsi.jou.

Within Cubit, open the Journal-Editor (Tools\(\to\)Journal Editor), paste the text from the journal file and press play.

Export the created geometry and mesh to an EXODUS file via File\(\to\)Export…. During export, set the dimension explicitly to 2D.

The FSI problem with a partitioned solver

Here, we create the 4C input file for the FSI problem, that is solved using a partitioned scheme, which means that the fluid and the solid problem are solved sequentially. For a monolithic scheme, see the section below.

Geometry description

The geometry is described in the file tutorial_fsi_2d.e we created before. It contains two element blocks for the fluid and the structure domain, respectively. We reference this file in the input file and assign the correct element types and material properties to the blocks:

STRUCTURE GEOMETRY:
  FILE: tutorial_fsi_2d.e
  ELEMENT_BLOCKS:
  - ID: 1
    ELEMENT_NAME: WALL
    ELEMENT_DATA: MAT 2 KINEM nonlinear EAS none THICK 1.0 STRESS_STRAIN plane_strain
      GP 2 2
FLUID GEOMETRY:
  FILE: tutorial_fsi_2d.e
  ELEMENT_BLOCKS:
  - ID: 2
    ELEMENT_NAME: FLUID
    ELEMENT_DATA: MAT 1 NA ALE
MATERIALS:
- MAT: 1
  MAT_fluid:
    DYNVISCOSITY: 0.01
    DENSITY: 1
- MAT: 2
  MAT_ElastHyper:
    NUMMAT: 1
    MATIDS:
    - 3
    DENS: 500
- MAT: 3
  ELAST_CoupNeoHooke:
    YOUNG: 250
- MAT: 4
  MAT_Struct_StVenantKirchhoff:
    YOUNG: 1
    NUE: 0
    DENS: 1

General parameters

We set the following parameters in the input file:

PROBLEM TYPE:
  PROBLEMTYPE: Fluid_Structure_Interaction
ALE DYNAMIC:
  ALE_TYPE: springs_spatial
  MAXITER: 4
  TOLRES: 0.0001
  TOLDISP: 0.0001
  RESULTSEVERY: 1
  LINEAR_SOLVER: 1
FLUID DYNAMIC:
  LINEAR_SOLVER: 2
  TIMEINTEGR: Np_Gen_Alpha
  GRIDVEL: BDF2
  ADAPTCONV: true
  ITEMAX: 50
STRUCTURAL DYNAMIC:
  INT_STRATEGY: Standard
  M_DAMP: 0.5
  K_DAMP: 0.5
  TOLDISP: 1e-12
  TOLRES: 1e-12
  TOLPRE: 1e-10
  TOLINCO: 1e-10
  PREDICT: ConstDisVelAcc
  LINEAR_SOLVER: 3
FSI DYNAMIC:
  MAXTIME: 3
  NUMSTEP: 3
  SECONDORDER: true
SOLVER 1:
  SOLVER: UMFPACK
  AZSUB: 300
  NAME: ALE solver
SOLVER 2:
  SOLVER: Belos
  AZTOL: 1e-12
  AZSUB: 300
  NAME: Fluid solver
SOLVER 3:
  SOLVER: UMFPACK
  AZSUB: 300
  NAME: Structure solver

We define the domain of the ALE problem as a clone of the fluid domain and assign a material:

CLONING MATERIAL MAP:
- SRC_FIELD: fluid
  SRC_MAT: 1
  TAR_FIELD: ale
  TAR_MAT: 4

  • FUNCT 1

    insert SYMBOLIC_FUNCTION_OF_SPACE_TIME (1-cos(2*t*pi/5)) defining time-dependent inflow and lid movement

  • FUNCT 2

    insert SYMBOLIC_FUNCTION_OF_SPACE_TIME 10*(y-1)*(1-cos(2*t*pi/5)) representing the spatial inflow distribution

Safe the file under a different name, e.g. ’dc2d_fsi.head’.

Boundary conditions

The boundary conditions are set as follows:

  • Dirichlet boundary conditions for structure, fluid and ALE:

DESIGN LINE DIRICH CONDITIONS:
- E: 1
  ENTITY_TYPE: node_set_id
  NUMDOF: 2
  ONOFF:
  - 1
  - 1
  VAL:
  - 0
  - 0
  FUNCT:
  - 0
  - 0
- E: 5
  ENTITY_TYPE: node_set_id
  NUMDOF: 3
  ONOFF:
  - 1
  - 1
  - 0
  VAL:
  - 0
  - 0
  - 0
  FUNCT:
  - 0
  - 0
  - 0
- E: 6
  ENTITY_TYPE: node_set_id
  NUMDOF: 3
  ONOFF:
  - 1
  - 1
  - 0
  VAL:
  - 1
  - 0
  - 0
  FUNCT:
  - 1
  - 0
  - 0
- E: 7
  ENTITY_TYPE: node_set_id
  NUMDOF: 3
  ONOFF:
  - 1
  - 1
  - 0
  VAL:
  - 1
  - 0
  - 0
  FUNCT:
  - 2
  - 0
  - 0
DESIGN POINT DIRICH CONDITIONS:
- E: 3
  ENTITY_TYPE: node_set_id
  NUMDOF: 2
  ONOFF:
  - 1
  - 1
  VAL:
  - 0
  - 0
  FUNCT:
  - 0
  - 0
- E: 4
  ENTITY_TYPE: node_set_id
  NUMDOF: 2
  ONOFF:
  - 1
  - 1
  VAL:
  - 0
  - 0
  FUNCT:
  - 0
  - 0
- E: 10
  ENTITY_TYPE: node_set_id
  NUMDOF: 3
  ONOFF:
  - 1
  - 1
  - 0
  VAL:
  - 1
  - 0
  - 0
  FUNCT:
  - 1
  - 0
  - 0
- E: 11
  ENTITY_TYPE: node_set_id
  NUMDOF: 3
  ONOFF:
  - 1
  - 1
  - 0
  VAL:
  - 0
  - 0
  - 0
  FUNCT:
  - 0
  - 0
  - 0
- E: 12
  ENTITY_TYPE: node_set_id
  NUMDOF: 3
  ONOFF:
  - 1
  - 1
  - 0
  VAL:
  - 0
  - 0
  - 0
  FUNCT:
  - 0
  - 0
  - 0
DESIGN LINE ALE DIRICH CONDITIONS:
- E: 6
  ENTITY_TYPE: node_set_id
  NUMDOF: 2
  ONOFF:
  - 1
  - 1
  VAL:
  - 0
  - 0
  FUNCT:
  - 0
  - 0
- E: 8
  ENTITY_TYPE: node_set_id
  NUMDOF: 2
  ONOFF:
  - 1
  - 1
  VAL:
  - 0
  - 0
  FUNCT:
  - 0
  - 0
DESIGN POINT ALE DIRICH CONDITIONS:
- E: 13
  ENTITY_TYPE: node_set_id
  NUMDOF: 2
  ONOFF:
  - 1
  - 1
  VAL:
  - 0
  - 0
  FUNCT:
  - 0
  - 0

  • FSI coupling conditions:

DESIGN FSI COUPLING LINE CONDITIONS:
- E: 2
  ENTITY_TYPE: node_set_id
  coupling_id: 1
- E: 9
  ENTITY_TYPE: node_set_id
  coupling_id: 1

Running the Simulation

Run in a shell

./4C <input_file_name> <output_directory>/output_prefix

Postprocessing

Warning

The procedure described here is likely outdated and needs to be update by the output taskforce!

You can postprocess your results with any visualization software you like. In this tutorial, we choose Paraview.

Before you can open the results, you have to generate a filter again. Call make post_drt_ensight in the 4C-directory. Filter your results in the output directory with the call

./post_drt_ensight --file=[outputdirectory]/outputprefix

After this open paraview, go to

  • File:math:`to`Open Data and select the filtered *.case file.

  • Only for older versions of Paraview:

    • Select the time step in the Select Time Value window on the left and

    • shift Byte order to little endian

  • Click on accept (or apply) to activate the display.

  • In the Display tab (section Color) you can choose now between Point pressure and Point velocity, whatever you want to display.

  • Use a warp vector to visualize the simulation results on the deformed domain.

  • For the scale, activate the Scalar bar button in the View section.

The FSI problem with a monolithic solver

There are two possibilities for monolithic schemes:

  • fluid-split: the fluid field is chosen as slave field, the structure field is chosen as master field.

  • structure-split: the structure field is chosen as slave field, the fluid field is chosen as master field.

In order to use a monolithic solver, change the coupling algorithm COUPALGO in the FSI DYNAMIC section in the *.head-file. Additionally, special care has to be taken of the interface degrees of freedom, that are subject to Dirichlet boundary conditions. The interface is always governed by the master field. The slave interface degrees of freedom do not occur in the global system of equations and, thus, are not allowed to carry Dirichlet boundary conditions.

Tolerances for the nonlinear convergence check in monolithic FSI are set with the following parameters in the FSI DYNAMIC section:

TOL_DIS_INC_INF
TOL_DIS_INC_L2
TOL_DIS_RES_INF
TOL_DIS_RES_L2
TOL_FSI_INC_INF
TOL_FSI_INC_L2
TOL_FSI_RES_INF
TOL_FSI_RES_L2
TOL_PRE_INC_INF
TOL_PRE_INC_L2
TOL_PRE_RES_INF
TOL_RPE_RES_L2
TOL_VEL_INC_INF
TOL_VEL_INC_L2
TOL_VEL_RES_INF
TOL_VEL_RES_L2

Fluid split

  • Choose iter_monolithicfluidsplit as COUPALGO in the FSI DYNAMIC section.

  • Remove the Dirichlet condition on node set 12 in order to remove the Dirichlet boundary conditions from the fluid (=slave) interface degrees of freedom.

Create the input file as described above. Start 4C as usual.

Structure split

  • Choose iter_monolithicstructuresplit as COUPALGO in the FSI DYNAMIC section.

  • Remove the Dirichlet condition on node set 4 in order to remove the Dirichlet boundary conditions from the structure (=slave) interface degrees of freedom.

Start 4C as usual.