FSI Tutorial 2d with pre_exodus and Cubit

Introduction

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

You can find the complete journal file within your 4C distribution. It is located in <4C-sourcedir>/tests/framework-test/tutorial_fsi.jou.

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

Export now the created geometry and mesh to an exodus-file (filename: dc2d.exo) via File\(\to\)Export…. During export, set the dimension explicitly to 2d.

General Procedure of Creating a Valid 4C Input File

With a given mesh including some nodal clouds to apply conditions to you need another text-file (bc-file) where you specify, what you would like to do with it. It contains for example the specific element declaration (fluid, structure, parameters, etc.) and the particular boundary condition such as Dirichlet or Neumann. Finally, a header-file consists of general parameters such as solvers, algorithmic parameters, etc. Those three files are merged by pre_exodus into an input file for 4C. This file is then automatically validated using all available 4C validation and is therefore likely to run.

Sure, you usually do not have already a proper header-file and matching bc-file. By typing

./pre_exodus --exo=yourmesh.e

you get two preliminary files ’default.head’ and ’default.bc’. The first contains the currently valid header parameters with default values and commented options which you can edit to adapt it to your means. Similarly, ’default.bc’ consists of all your mesh entities and a list of all currently valid conditions. See next section for details how to work with it and how to get valid input files.

Running a Simulation with 4C

To start the solver use the call

./4C [inputdirectory]/your_example.dat [outputdirectory]/outputprefix

(in the 4C-directory; of course, you may choose a different directory as well, if you take care for the path names). The results are then written to the result directory with the prefix you chose.

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.

After running the 4C executable without boundary condition and header information, we have created the ’default.head’ and ’default.bc’ file` that we are now supposed to edit.

header-file

Find the following sections in ’default.head’ and edit as given:

ALE DYNAMIC

LINEAR_SOLVER 1
FLUID DYNAMIC

CONVTOL              1e-08

GRIDVEL              BDF2

ITEMAX               50

LINEAR_SOLVER        2

TIMEINTEGR           Np_Gen_Alpha
FSI DYNAMIC

MAXTIME              3

NUMSTEP              30

SECONDORDER          yes

SHAPEDERIVATIVES     yes

TIMESTEP             0.1
SOLVER 1

NAME ALE solver

SOLVER UMFPACK
SOLVER 2

NAME Fluid solver

SOLVER Aztec_MSR
SOLVER 3

NAME Structure solver

SOLVER UMFPACK
STRUCTURAL DYNAMIC

LINEAR_SOLVER 3

TOLRES 1e-10
MATERIALS

insert MAT 1 MAT_fluid DYNVISCOSITY 0.01 DENSITY 1.0 for definition of fluid material

insert MAT 2 MAT_ElastHyper NUMMAT 1 MATIDS 3 DENS 500 to define a hyperelastic structural material

insert MAT 3 ELAST_CoupNeoHooke YOUNG 250.0 NUE 0.0 to specify the structural material as Neo-Hooke material

insert MAT 4 MAT_Struct_StVenantKirchhoff YOUNG 1.0 NUE 0.0 DENS 1.0 to define an ALE material
CLONING MATERIAL MAP

insert SRC_FIELD fluid SRC_MAT 1 TAR_FIELD ale TAR_MAT 4 to specify the ALE material that is used for the fluid field
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’.

bc-file

The main section of the default.bc file contains the element set and boundary condition information:

--------------------------BCSPECS

Element Block, named:
of Shape: HEX8
has <xxx> Elements
*eb1="ELEMENT"
sectionname=""
description=""
elementname=""

[further element sections]

Node Set, named: <bc_name>
Property Name: none
has <xx> Nodes
*ns1="CONDITION"
sectionname=""
description=""

[further node set definitions to be used for conditions]

Edit the ’default.bc’ file as follows:

For the element definitions, which are consecutively enumerated as eb<number>:

*eb1="ELEMENT" the structure elements with their material

sectionname="STRUCTURE"
description="MAT 2 KINEM nonlinear EAS none THICK 1.0 STRESS_STRAIN plane_strain GP 2 2"
elementname="WALL"

*eb2="ELEMENT" the fluid elements with ALE and the fluid material

sectionname="FLUID"
description="MAT 1 NA ALE"
elementname="FLUID"

For Dirichlet boundary conditions for structure, fluid and ALE, which are defined by a node set number, ns<number>, but also by its name:

*ns1="CONDITION" Fixing the structure at left and right side

sectionname="DESIGN LINE DIRICH CONDITIONS"
description="NUMDOF 2 ONOFF 1 1 VAL 0.0 0.0 CURVE none none FUNCT 0 0"

*ns2="CONDITION"

sectionname="DESIGN FSI COUPLING LINE CONDITIONS"
description="coupling_id 1"

*ns3="CONDITION"

sectionname="DESIGN POINT DIRICH CONDITIONS"
description="NUMDOF 2 ONOFF 1 1 VAL 0.0 0.0 CURVE none none FUNCT 0 0"

*ns4="CONDITION"

sectionname="DESIGN POINT DIRICH CONDITIONS"
description="NUMDOF 2 ONOFF 1 1 VAL 0.0 0.0 CURVE none none FUNCT 0 0"

*ns5="CONDITION"

sectionname="DESIGN LINE DIRICH CONDITIONS"
description="NUMDOF 3 ONOFF 1 1 0 VAL 0.0 0.0 0.0 CURVE none none none FUNCT 0 0 0"

*ns6="CONDITION"

sectionname="DESIGN LINE DIRICH CONDITIONS"
description="NUMDOF 3 ONOFF 1 1 0 VAL 1.0 0.0 0.0 CURVE 1 none none FUNCT 0 0 0"

*ns7="CONDITION"

sectionname="DESIGN LINE DIRICH CONDITIONS"
description="NUMDOF 3 ONOFF 1 1 0 VAL 1.0 0.0 0.0 CURVE 1 none none FUNCT 1 0 0"

*ns8="CONDITION"

sectionname="DESIGN LINE ALE DIRICH CONDITIONS"
description="NUMDOF 2 ONOFF 1 1 VAL 0.0 0.0 CURVE none none FUNCT 0 0"

*ns9="CONDITION"

sectionname="DESIGN FSI COUPLING LINE CONDITIONS"
description="coupling_id 1"

*ns10="CONDITION"

sectionname="DESIGN POINT DIRICH CONDITIONS"
description="NUMDOF 3 ONOFF 1 1 0 VAL 1.0 0.0 0.0 CURVE 1 none none FUNCT 0 0 0"

*ns11="CONDITION"

sectionname="DESIGN POINT DIRICH CONDITIONS"
description="NUMDOF 3 ONOFF 1 1 0 VAL 0.0 0.0 0.0 CURVE none none none FUNCT 0 0 0"

*ns12="CONDITION"

sectionname="DESIGN POINT DIRICH CONDITIONS"
description="NUMDOF 3 ONOFF 1 1 0 VAL 0.0 0.0 0.0 CURVE none none none FUNCT 0 0 0"

*ns13="CONDITION"

sectionname="DESIGN POINT ALE DIRICH CONDITIONS"
description="NUMDOF 2 ONOFF 1 1 VAL 0.0 0.0 CURVE none none FUNCT 0 0"

Copy the following condition and parametrize it as given below to further prescibe Dirichlet boundary conditions on the ALE field:

*ns6="CONDITION"

sectionname="DESIGN LINE ALE DIRICH CONDITIONS"
description="NUMDOF 2 ONOFF 1 1 VAL 0.0 0.0 CURVE none none FUNCT 0 0"

As any of these conditions matches an already defined NodeSet it will also match the corresponding ’E-id’ in the later 4C input file. Finally save the file under a different name, e.g. ’dc2d_fsi.bc’.

Creating 4C Input File and Running the Simulation

Run in a shell

 ./pre_exodus --exo=dc2d.e --head=dc2d_fsi.head
--bc=dc2d_fsi.bc --dat=dc2d_fsi.dat

where the filenames might have to be replaced accordingly. This will result in the specified dat-file which is already validated to be accepted by 4C. However, if the file is meaningful cannot be assured. Hint: When you have an already existing input file, you can always validate it by simply executing ./pre_exodus --dat=inputfile.dat, before(!) you start a parallel 4C computation on a cluster, for example.

Run the simulation by providing the created dat-file and an output file to 4C and postprocess the results.

Postprocessing

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.
Modify Dirichlet condition *ns12="CONDITION" to
```
sectionname="DESIGN POINT DIRICH CONDITIONS"
description="NUMDOF 3 ONOFF 0 0 0 VAL 0.0 0.0 0.0 CURVE none none none FUNCT 0 0 0"
```
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.
Modify Dirichlet condition *ns4="CONDITION" to
```
sectionname="DESIGN POINT DIRICH CONDITIONS"
description="NUMDOF 2 ONOFF 0 0 VAL 0.0 0.0 CURVE none none FUNCT 0 0"
```
in order to remove the Dirichlet boundary conditions from the structure (=slave) interface degrees of freedom.

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