05-Jun-2023 14:30:05

mesh2d_test():
  MATLAB/Octave version 5.2.0
  Test mesh2d().

airfoil_exterior_test():
  Demonstrate mesh2d() on an airfoil

  Airfoil, max element size is 0.50.
  Graphics saved as "airfoil_exterior_vertices.png"
WARNING: 1 duplicate node(s) removed
  106 boundary vertices input, 640 nodes and 1020 triangles created

  Wrote nodes to file "airfoil_exterior_nodes.txt"
  Wrote elements to file "airfoil_exterior_elements.txt"

airfoil_exterior_test():
  Normal end of execution.

airfoil_interior_test():
  Demonstrate mesh2d() on an airfoil

  Airfoil, max element size is 0.50.
  Graphics saved as "airfoil_interior_vertices.png"
WARNING: 1 duplicate node(s) removed
  102 boundary vertices input, 246 nodes and 369 triangles created

  Wrote nodes to file "airfoil_interior_nodes.txt"
  Wrote elements to file "airfoil_interior_elements.txt"

airfoil_interior_test():
  Normal end of execution.

baffle_test():
  MATLAB/Octave version 5.2.0
  Demonstrate mesh2d() on a channel with circular baffles.

  Channel, max element size is 0.50, baffles inserted.
  82 boundary vertices input, 510 nodes and 870 triangles created

baffle_test():
  Normal end of execution.

circle_test():
  MATLAB version
  Demonstrate mesh2d() on a circle.

  Circle.
  16 boundary vertices input, 249 nodes and 432 triangles created

  Wrote FEM node file "circle_nodes.txt"
  Wrote FEM element file "circle_elements.txt"
  Wrote XML file "circle.xml"

circle_test():
  Normal end of execution.

circles_test():
  Demonstrate mesh2d() on a channel with an off-center hole.

  Circle with a hole, max element size is 0.50.
  32 boundary vertices input, 250 nodes and 404 triangles created

circles_test():
  Normal end of executions.

ell_test:
  ell() demonstrates mesh2d() on the L-shaped region.

  EXAMPLE 1:
  Minimal Input
  Use 6 vertices on the boundary.
  6 boundary vertices input
  21 nodes and 24 triangles created

  EXAMPLE 2:
  Set a few small boundary segments.
  Use 8 vertices on the boundary.
  8 boundary vertices input
  43 nodes and 57 triangles created

  EXAMPLE 3:
  Set maximum element size HDATA.HMAX = 0.1
  6 boundary vertices input
  225 nodes and 384 triangles created

  EXAMPLE 4:
  Specify small elements near reentrant corner using a size function.
  6 boundary vertices input
  979 nodes and 1850 triangles created

  EXAMPLE 5:
  Repeat example #1, then call refine ( ).
  6 boundary vertices input
  21 nodes and 24 triangles created
  Graphics saved as "ell_mesh5.png"
  6 boundary vertices input
  65 nodes and 96 triangles created

  EXAMPLE 6:
  Repeat example #2, then call smoothmesh ( ).
  8 boundary vertices input
  43 nodes and 57 triangles created
  8 boundary vertices input
  43 nodes and 57 triangles created

ell_test():
  Normal end of execution.

face_test():
  Test meshfaces() on a variety of geometries.

mesh_test():
  This is a demo function for mesh2d
  Several example meshes are shown, 
  starting with some simple examples and progressing to 
  the CFD-like applications for which the function was designed.

  The following is a simple mesh in a circle.
The element size function is generated automatically to try to adequately resolve the geometry. 

This means that the mesh size is related to the length of the line segments used to define the 
geometry. The following example is the same as the last, but with more lines used to represent the 
circle.
It is often necessary to specify the element size in some locations
Mesh2d can now deal with very fine "sliver" geometry features 

The following is a mesh used to simulate the flow past a cylinder. 

This example also shows how user specified and automatic size functions are combined
The following is a mesh used to simulate the flow past an airfoil/flap configuration. 

The following is a mesh of Lake Superior and is a standard test of mesh algorithms. 

This example uses the automatic size function only
The following shows the influence of gradient limiting on the size function. 
The value dhmax is reduced to 0.1 
The following example shows how the element size can be controlled using the  
various settings in HDATA. 
The following example shows how an existing mesh can be refined using the  
REFINE function. This avoids doing expensive retriangulation. 

mesh_test
  Normal end of execution.

mesh_oops_test:
  MATLAB/Octave version 5.2.0
  Demonstrate mesh2d() for creating meshes.

  EXAMPLE 1: The Circle
  We start with 24 points on the circumference.
  The element size function is generated automatically to try
  to adequately resolve the geometry.

  This means that the mesh size is related to the length of 
  the line segments used to define the geometry.


  24 boundary vertices input, 57 nodes and 88 triangles created
The following example is the same as the last, 
but with more lines used to represent the circle.
  150 boundary vertices input, 572 nodes and 992 triangles created
It is often necessary to specify the element size in some locations.
  4 boundary vertices input, 759 nodes and 1434 triangles created
Mesh2d can now deal with very fine "sliver" geometry features.
  8 boundary vertices input, 1083 nodes and 1840 triangles created
The following is a mesh used to simulate the flow past a cylinder. 
  204 boundary vertices input, 6631 nodes and 12966 triangles created
The following is a mesh used to simulate the flow past an airfoil/flap configuration. 
  126 boundary vertices input, 3501 nodes and 5987 triangles created
The following is a mesh of Lake Superior and is a standard test of mesh algorithms. 
  303 boundary vertices input, 1879 nodes and 2899 triangles created
The following shows the influence of gradient limiting on the size function. 
The following example shows how the element size can be controlled.
  4 boundary vertices input, 183 nodes and 300 triangles created
The following example shows how an existing mesh can be refined.
  4 boundary vertices input, 81 nodes and 128 triangles created
  4 boundary vertices input, 129 nodes and 224 triangles created
  4 boundary vertices input, 129 nodes and 224 triangles created

mesh_oops_test:
  Normal end of execution.

obstacle_test():
  Demonstrate mesh2d() on the channel with a square obstacle.

  EXAMPLE 1:
  Channel, no obstacle.
  4 boundary vertices input, 25 nodes and 28 triangles created

  EXAMPLE 2:
  Channel, max element size is 0.25.
  4 boundary vertices input, 295 nodes and 508 triangles created

  EXAMPLE 3:
  Channel, max element size is 0.25, obstacle inserted.
  8 boundary vertices input, 281 nodes and 466 triangles created

obstacle_test
  Normal end of execution.

rectangle_minus_circle_test():
  Demonstrate mesh2d() on a rectangle minus a circle.

  Rectangle (4 nodes) minus circle (12 nodes).
n_circle =  12
v =

  -1.00000  -1.00000
   1.00000  -1.00000
   1.00000   1.00000
  -1.00000   1.00000
   0.75000   0.50000
   0.71651   0.62500
   0.62500   0.71651
   0.50000   0.75000
   0.37500   0.71651
   0.28349   0.62500
   0.25000   0.50000
   0.28349   0.37500
   0.37500   0.28349
   0.50000   0.25000
   0.62500   0.28349
   0.71651   0.37500

e =

    1    2
    2    3
    3    4
    4    1
    5    6
    6    7
    7    8
    8    9
    9   10
   10   11
   11   12
   12   13
   13   14
   14   15
   15   16
   16    5

  16 boundary vertices input, 280 nodes and 484 triangles created

  Wrote FEM node file "rectangle_minus_circle_nodes.txt"
  Wrote FEM element file "rectangle_minus_circle_elements.txt"
  Wrote XML file "rectangle_minus_circle.xml"

rectangle_minus_circle_test():
  Normal end of execution.

refine_test():
  Demonstrate mesh2d() refinement option on the L-shaped region.
  1) Create a default mesh.
  2) Use the default refinement option.
  3) Use the refinement option with a mask vector.

  EXAMPLE 1:
  Minimal Input
  Use 6 vertices on the boundary.
  Graphics saved as "refine_demo1.png"
  6 boundary vertices input, 21 nodes and 24 triangles created

  EXAMPLE 2:
  Refine all triangles with centroid above y=1/2.
  Graphics saved as "refine_demo2.png"
  6 boundary vertices input, 52 nodes and 76 triangles created

  EXAMPLE 3:
  Refine all triangles with centroid x < 1.
  Graphics saved as "refine_demo3.png"
  6 boundary vertices input, 101 nodes and 164 triangles created

refine_test():
  Normal end of execution.

square_border_test():
  Demonstrate meshfaces() on an square in a square.
  We want to mesh two adjacent regions in such a way
  that the meshes use common nodes on their interface.

  Instead of using MESH2D, we need to used MESHFACES.

square_border_test:
  Normal end of execution.

two_foci_demo():
  Demonstrate mesh2d() on the two foci problem.

two_foci_demo():
  Normal end of execution.

mesh2d_test():
  Normal end of execution.

05-Jun-2023 14:43:50