Example 9822: Solution of Navier-Stokes equations (including gravity) through a simple, symmetric pulmonary arterial network

This example models blood flow in a simple, symmetric pulmonary arterial network by solving the Navier-Stokes flow equations, including the effects of gravity. The main arterial trunk vessels are read in and 4 generations of symmetric branching are created from these end points. The reduced Navier-Stokes equations are solved using a Lax-Wendroff numerical technique, the solution procedure used is detailed in Smith (2002) .

Created by Kelly Burrowes, 08/2004.

Orthogonal views of the solution, pressure solution (kPa) shown on the left; velocity solution (mm/s) shown on the right. Spectrums extend from minimum values (dark blue) to maximum values (red).

To create an image in order to visualise the results of the simulation, use CMGUI with the file draw.com.

The comfile run by this example is as follows:

# Example 9822

# If the example path is not set, default to current directory
if (! defined $example) {
    $example = "./";
}
# Drop off the trailing / in the example path
$chopped = chop $example;
if ($chopped ne "/") {
    $example .= $chopped;
}

fem define param;r;$example/flow;

fem define coord;r;$example/flow;
fem define base;r;$example/flow;

fem de node;r;$example/trunk as parent;
fem de elem;r;$example/trunk as parent;

#evaluate ordering of parent vessels before creating symmetric mesh
fem evaluate order; 
#Now set up a symmetric mesh 
fem de mesh;c lung symmetric num_generation 4 branch_angle 40 elem parent;

fem define mesh;c lung field only_radius; 
#only sets up radius field

fem evaluate order;
#fem update mesh geometry radius_field 1 anatomical Arteries;

fem update mesh geometry radius_field 1 element 1 constant 12;
fem update mesh geometry radius_field 1 Rd_strahler ratio_diameter 1.5997;

fem de elem;w;test;
fem de elem;r;test; #sets up NLL - element length array

#adds two more fields to store the pressure and velocity fields, adds 0 as default value
fem define;add field;d;$example/arteries field_variables 2;
#fem define field;w;test;
fem define element;d;$example/arteries field;

fem define grid;r;$example/flow coronary;
# Defines grid points with coronary option to discretise the spatial computational domain. 
fem update grid geometry;
fem define equation;r;$example/flow;       # Defines equations                          
fem define material;r;$example/flow;       # Reads in physical & mechanical properties
fem update material field material 4 no_field 1;
fem define time;r;$example/step;        
fem define initial;r;$example/flow;        # Defines initial conditions
fem define solve;r;$example/flow;          # Defines solution parameters

$time_initial=0.00;                       # Sets the initial time
$time_final=1.5;                         # Sets the final time
$time_step=0.001;                        # Sets the time step time
$write_out_period=0.1;                 # Sets the results write out period

fem export points;$time_initial grid as vessel offset 0;   
fem export grid;vessel as vessel offset_node 0 elastic_tube; 

# Results output loop

for ($time=$time_initial;$time<$time_final;$time=$time+$write_out_period)
{
fem solve restart to $write_out_period delta_t $time_step;
fem export points;$time+$write_out_period grid as vessel offset 0
}                                                                           

Additional testing commands:

fem list nodes

Files used by this example are:

Name              Modified     Size

example_9822.com  22-Jan-2007  2.4k
draw.com          26-Aug-2004  1.4k
flow.ipbase       26-Aug-2004  893 
flow.ipcoor       26-Aug-2004  572 
flow.ipequa       22-Nov-2005  1.3k
flow.ipgrid       26-Aug-2004  216 
flow.ipinit       01-Dec-2005  907 
flow.ipmate       26-Aug-2004  6.7k
flow.ippara       23-Jun-2005  5.9k
flow.ipsolv       26-Aug-2004  759 
step.iptime       26-Aug-2004  1.5k
test.com          22-Jan-2007  2.5k
test.ipelem       26-Aug-2004   40k
test_output.com   26-Aug-2004   15 
trunk.ipelem      26-Aug-2004  2.8k
trunk.ipnode      26-Aug-2004  2.4k
vessel.exelem     26-Aug-2004   62k

Download the entire example:

Name                           Modified     Size

examples_9_98_982_9822.tar.gz  23-Jan-2007   59k

Testing status by version:

Testing status by file:

• signal
  

  i686-linux
  SIGABRT	cm-debug:	exit due to SIGABRT signal.
  x86_64-linux
  SIGABRT	cm-debug:	exit due to SIGABRT signal.

  
  
• cmiss_test.log
  

  i686-linux
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.
  mips-irix
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.
  Success	cm-debug-clear-malloc:	cmiss_test.log.retain.
  Success	cm-debug-clear-malloc7:	cmiss_test.log.retain.
  Success	cm64:	cmiss_test.log.retain.
  Success	cm64-debug:	cmiss_test.log.retain.
  rs6000-aix
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.
  Success	cm64:	cmiss_test.log.retain.
  Success	cm64-debug:	cmiss_test.log.retain.
  x86_64-linux
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.

  
  
• cmiss_test.out
  

  i686-linux
  Failure	cm:	ndiff test: significant differences with generic answer.
  Missing	cm-debug:	output file not generated for ndiff; generic answer.
  mips-irix
  Success	cm:	ndiff test: no significant differences with generic answer.
  Success	cm-debug:	ndiff test: no significant differences with generic answer.
  Success	cm-debug-clear-malloc:	ndiff test: no significant differences with generic answer.
  Success	cm-debug-clear-malloc7:	ndiff test: no significant differences with generic answer.
  Success	cm64:	ndiff test: no significant differences with generic answer.
  Success	cm64-debug:	ndiff test: no significant differences with generic answer.
  rs6000-aix
  Success	cm:	ndiff test: no significant differences with generic answer.
  Success	cm-debug:	ndiff test: no significant differences with generic answer.
  Success	cm64:	ndiff test: no significant differences with generic answer.
  Success	cm64-debug:	ndiff test: no significant differences with generic answer.
  x86_64-linux
  Failure	cm:	ndiff test: significant differences with generic answer.
  Missing	cm-debug:	output file not generated for ndiff; generic answer.

  
  

Html last generated: Sun Mar 6 05:50:36 2016

Input last modified: Mon Jan 22 13:53:33 2007