Fluid Tutorial

Introduction

In this tutorial we want to simulate the incompressible flow past a circular cylinder. For further details and references we refer the reader to: [Wall99]

Problem definition and geometrical setup (with friendly permission ;-))

Preprocessing

Creating the Geometry with Cubit

We will use Cubit for creating the geometry and the mesh. Within Cubit, open the Journal-Editor (Tools \(\to\) Journal Editor), paste the text below and press play. After successful geometry and mesh creation, export everything to an EXODUS file of your choice via File \(\to\)Export… and set the dimension explicitly to 2D.

$***********************
$ preliminaries
$***********************
reset
set geometry engine acis
$***********************
$ create geometry
$***********************

$ define geometric parameters
$ in cm
# {fluid_length = 4.0} $ x-direction
# {fluid_width = 2.0} $ y-direction
# {cyl_radius = 0.08}
# {cyl_offset = 1.0}
$ create domain
create vertex {-cyl_offset} {fluid_width/2.0} 0
create vertex {-cyl_offset} {-fluid_width/2.0} 0
create vertex {fluid_length-cyl_offset} {fluid_width/2.0} 0
create vertex {fluid_length-cyl_offset} {-fluid_width/2.0} 0
create vertex 0 0 0
create vertex {cyl_offset} {fluid_width/2.0} 0
create vertex {cyl_offset} {-fluid_width/2.0} 0
create curve vertex 1 vertex 5
create curve vertex 5 vertex 6
create curve vertex 6 vertex 1
create curve vertex 10 vertex 2
create curve vertex 2 vertex 8
create curve vertex 12 vertex 7
create curve vertex 7 vertex 13
create curve vertex 15 vertex 9
create curve vertex 18 vertex 3
create curve vertex 3 vertex 4
create curve vertex 4 vertex 17
create surface curve 3 1 2
create  surface curve 1 4 5
create  surface curve 5 6 7
create  surface curve 7 8 2
create  surface curve 8 9 10 11
create vertex 0 0 0
create vertex 0 {cyl_radius} 0
create vertex {cyl_radius} 0 0
create curve arc center vertex 24 25 26 {cyl_radius} full
create surface curve 17
delete vertex 24 25 26
subtract volume 6 from volume 1 2 3 4
imprint volume all
merge volume all

$***********************
$ create mesh
$***********************

# {numele_past_x = 37}
# {numele_past_y = 34}
# {numele_cyl_x = 30}
# {numele_inflow = 22}
# {numele_radial = 50}
group "radial" add curve 19 20 23 26
curve  9 scheme equal interval {numele_past_x}
curve  10 scheme equal interval {numele_past_y}
curve  in group radial scheme equal interval {numele_radial}
curve  3 6 scheme equal interval {numele_cyl_x}
curve  4 scheme equal interval {numele_inflow}
$ apply bias for better mesh
curve 19 scheme bias factor 0.9 start vertex 1 interval {numele_radial}
propagate curve bias volume all
curve 20 scheme bias factor 0.9 start vertex 6 interval {numele_radial}
propagate curve bias volume all
curve 23 scheme bias factor 0.9 start vertex 2 interval {numele_radial}
propagate curve bias volume all
curve 26 scheme bias factor 0.9 start vertex 7 interval {numele_radial}
propagate curve bias volume all
mesh surface all

$***********************
$ boundary conditions
$***********************
reset block
block 1 surface all
nodeset 1 curve 4
nodeset 1 name "inflow"
nodeset 2 curve 3 9
nodeset 2 name "top"
nodeset 3 curve 6 11
nodeset 3 name "bottom"
nodeset 4 curve 18 21 24 27
nodeset 4 name "cylinder"
nodeset 5 vertex 1 2
nodeset 5 name "corners"

$***********************
$ export mesh
$***********************
export mesh "tutorial_fluid.e" dimension 2 block all overwrite

The generated mesh should look like this:

Mesh for a flow past a circular cylinder.

Working with 4C

General Procedure of Creating a Valid 4C Input File

The execution of 4C is controlled by an input file. Let us create a file tutorial_fluid.4C.yaml and enter the essential parameters:

PROBLEM TYPE:
  PROBLEMTYPE: Fluid
FLUID DYNAMIC:
  LINEAR_SOLVER: 1
  PREDICTOR: explicit_second_order_midpoint
  NUMSTEP: 10
  RESTARTEVERY: 1
SOLVER 1:
  SOLVER: UMFPACK
MATERIALS:
- MAT: 1
  MAT_fluid:
    DYNVISCOSITY: 0.004
    DENSITY: 1
FUNCT1:
- SYMBOLIC_FUNCTION_OF_SPACE_TIME: 0.5*(sin((t*pi/0.1)-(pi/2)))+0.5

The mesh is read from the EXODUS file created in the previous step. We can read the mesh as follows:

FLUID GEOMETRY:
  FILE: tutorial_fluid.e
  ELEMENT_BLOCKS:
  - ID: 1
    ELEMENT_NAME: FLUID
    ELEMENT_DATA: MAT 1 NA Euler

This tells 4C to read the mesh as the fluid geometry and assign corresponding elements.

Setting the boundary conditions

The boundary conditions are set as follows:

DESIGN LINE DIRICH CONDITIONS:
- E: 1
  ENTITY_TYPE: node_set_id
  NUMDOF: 3
  ONOFF:
  - 1
  - 1
  - 0
  VAL:
  - 1.0
  - 0.0
  - 0.0
  FUNCT:
  - 1
  - null
  - null
- E: 2
  ENTITY_TYPE: node_set_id
  NUMDOF: 3
  ONOFF:
  - 0
  - 1
  - 0
  VAL:
  - 0.0
  - 0.0
  - 0.0
  FUNCT:
  - null
  - null
  - null
- E: 3
  ENTITY_TYPE: node_set_id
  NUMDOF: 3
  ONOFF:
  - 0
  - 1
  - 0
  VAL:
  - 0.0
  - 0.0
  - 0.0
  FUNCT:
  - null
  - null
  - null
- E: 4
  ENTITY_TYPE: node_set_id
  NUMDOF: 3
  ONOFF:
  - 1
  - 1
  - 0
  VAL:
  - 0.0
  - 0.0
  - 0.0
  FUNCT:
  - null
  - null
  - null
DESIGN POINT DIRICH CONDITIONS:
- E: 5
  ENTITY_TYPE: node_set_id
  NUMDOF: 3
  ONOFF:
  - 1
  - 1
  - 0
  VAL:
  - 1.0
  - 0.0
  - 0.0
  FUNCT:
  - null
  - null
  - null

Running a Simulation with 4C

Execute 4C as usual:

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

The prefix that you choose will be applied to all output files that 4C generates.

Postprocessing

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

Filtering result data

Before you can admire your results, you have to generate a filter which converts the generic binary 4C output to the desired format. Starting from the build-release directory, execute make post_drt_ensight.
The filter should now be available in the build-release folder. Filter your results with the following call inside the build-release folder:

./post_drt_ensight - -file=<outputdirectory>/outputprefix
Further options of the filter program are made visible by the command ./post_drt_ensight –help

Visualize your results in Paraview

After the filtering process is finished open paraview by typing

paraview &

File :math:`to` Open and select the filtered *\*.case* file: outputprefix_fluid.case
Press Apply to activate the display.
Set the time step in the top menu bar to \(19\) (\(=0.2\)).
In the Color section you can now choose between pressure and velocity. Select velocity and pick the \(X\)-component from the adjacent drop-down menu. Then press the Rescale button and the Show button. You receive a visualization of the \(X\)-velocity field, which should look similar to this figure:

X-velocity for a flow past a circular cylinder — \(X\)-velocity for a flow past a circular cylinder