Cross section 2

Let’s consider a cross section (See examples/matrix/cross_section_2)

_images/cross_section_2_draft.png

Cross section

We can use Matrix class to create this type of geometry. First we need to decompose geometry into blocks and then modify each of them according to the dimensions.

Decomposition

Geometry could be decomposed into 4 blocks: BOTTOM, TOP1, TOP2 and TOP3, where TOP3 part is required for a small surface with \(F\), \(u_v\) boundary condition at the end of the upper part of the geometry. Without the boundary condition, 3 blocks would be enough. Each of these blocks will be described by Matrix class.

_images/cross_section_2_decomposition.png

Decomposition of geometry

Geometry

Let’s define that X-axis is directed to the right, Y - in the depth and Z - upward, i.e cross section is symmetric along Y-axis.

First we should create a separate file for each of the blocks:

  • top_1.yaml

1 data:
2   class: block.Matrix
3   matrix: [ [ 0, 0.250 ], [ 0, 1 ], [ 0, 0.250 ] ]

  • top_2.yaml

1  data:
2    class: block.Matrix
3    matrix: [ [ 0, 0.220 ], [ 0, 1 ], [ 0, 0.250 ] ]

  • top_3.yaml

1 data:
2   class: block.Matrix
3   matrix: [ [ 0, 0.030 ], [ 0, 1 ], [ 0, 0.250 ] ]

  • bottom.yaml

1 data:
2   class: block.Matrix
3   matrix: [ [ 0, 0.250 ], [ 0, 1 ], [ 0, 0.250 ] ]

Each of the files consists of one high level field data whose has 2 fields: 1. class - name of the class of the block 2. matrix - lists of point coordinates by axes

For example Matrix has 2 points by X-axis with coordinates 0 and 0.250.

Matrix also has 2 points by Y-axis with 0 and 1 coordinates and 2 points by Z-axis with 0 and 0.250. Thus Matrix is a box with dimensions: 0.250, 1 and 0.250 by X, Y and Z axis respectively and origin at point (0, 0, 0).

We could generate geometry of bottom.yaml into bottom.geo_unrolled file:

python -m gmsh_scripts bottom.yaml
_images/cross_section_2_geometry_bottom.png

Geometry of the the BOTTOM block

Now we should create main file main.yaml with all blocks:

 1 data:
 2   class: block.Block
 3   do_register: 0
 4   children: [
 5     /bottom.yaml,
 6     /top_1.yaml,
 7     /top_2.yaml,
 8     /top_3.yaml
 9   ]
10   children_transforms: [
11     [ ],
12     [ [ 0, 0, 0.250 ] ],
13     [ [ 0.250, 0, 0.250 ] ],
14     [ [ 0.470, 0, 0.250 ] ]
15   ]

File also has one high level field data with 4 sub-fields:

  1. class - name of the class of the block

  2. do_register - create this block? (set 0 because we don’t need this block itself, i.e. it’s only a container for other blocks)

  3. children - references to other block files (should start with / character)

  4. children_transforms - transforms of other blocks

Field children_transforms is a list of Transform for each children. In this tutorial we only need simple Translate that are given by 3 numbers - offset along X, Y ans Z axes respectively.

For example:

  1. Child bottom.yaml has no transforms

  2. Child top_1.yaml has one Translate [ 0, 0, 0.250 ] with offset 0.250 by Z-axis and no offsets by X and Y (we just need to elevate to the bottom.yaml)

  3. Child top_2.yaml has one Translate [ 0.250, 0, 0.250 ]

  4. Child top_3.yaml has one Translate [ 0.470, 0, 0.250 ]

Let’s generate geometry with all blocks into main.geo_unrolled:

python -m gmsh_scripts main.yaml
_images/cross_section_2_geometry_main.png

Geometry with all blocks

Mesh

To generate mesh we should add metadata field to the main.yaml file:

 1 metadata:
 2   run:
 3     factory: geo
 4     strategy:
 5       class: strategy.NoBoolean
 6 data:
 7   class: block.Block
 8   do_register: 0
 9   children: [
10     /bottom.yaml,
11     /top_1.yaml,
12     /top_2.yaml,
13     /top_3.yaml
14   ]
15   children_transforms: [
16     [ ],
17     [ [ 0, 0, 0.250 ] ],
18     [ [ 0.250, 0, 0.250 ] ],
19     [ [ 0.470, 0, 0.250 ] ]
20   ]

File metadata has run sub-field with fields:

  1. factory - Which kernel of gmsh to use for mesh generation? Currently, gmsh has two kernels: geo and occ. We use geo because it’s faster

  2. strategy - Strategy of mesh generation

  3. strategy.class - Class of the strategy. We use NoBoolean because we don’t need boolean operations

Warning

If we need boolean operations we MUST use occ factory with default strategy (just don’t set it in the metadata)

Now mesh generator will return mesh into main.msh2 file (it also returns main.geo_unrolled as before). Generator creates unstructured tetrahedral mesh by default.

python -m gmsh_scripts main.yaml
_images/cross_section_2_mesh_main_default.png

Default mesh

Unstructured Tetrahedral

We can customize unstructured mesh with parameters in input files.

First type of parameters aka point parameters is set in matrix field (e.g. bottom.yaml):

1data:
2  class: block.Matrix
3  matrix: [ [ 0;0.01, 0.250;0.1 ], [ 0;0.01, 1;0.1 ], [ 0;0.01, 0.250;0.1 ] ]

As one can see, for each point a new parameter have been added with ; separator, e.g. 0;0.01 for first point by X-axis or 0.250;0.1 for second point by Z-axis. Parameters 0.01 or 0.1 are approximate sizes of the mesh near the corresponding points.

In this example, mesh is finer near the (0, 0, 0) point with size 0.01 and coarser near the (0.250, 1, 0.250) point with size 0.1.

Let’s add metadata field to bottom.yaml and generate mesh:

python -m gmsh_scripts bottom.yaml

1metadata:
2  run:
3    factory: geo
4    strategy:
5      class: strategy.NoBoolean
6data:
7  class: block.Matrix
8  matrix: [ [ 0;0.01, 0.250;0.1 ], [ 0;0.01, 1;0.1 ], [ 0;0.01, 0.250;0.1 ] ]
_images/cross_section_2_mesh_unstructured_tetrahedral_bottom_1.png

Unstructured tetrahedral mesh of the BOTTOM block

One could fix mesh size along one of the axis (e.g. Y with 0.01):

1metadata:
2  run:
3    factory: geo
4    strategy:
5      class: strategy.NoBoolean
6data:
7  class: block.Matrix
8  matrix: [ [ 0;0.01, 0.250;0.1 ], [ 0;0.01, 1;0.01 ], [ 0;0.01, 0.250;0.1 ] ]
_images/cross_section_2_mesh_unstructured_tetrahedral_bottom_2.png

Unstructured tetrahedral mesh with fixed size along Y-axis of the BOTTOM block

To generate all blocks, one needs to specify point parameters at all blocks and run generator:

python -m gmsh_scripts main.yaml
_images/cross_section_2_mesh_unstructured_tetrahedral_main.png

Unstructured tetrahedral mesh with fixed size along Y-axis at BOTTOM block

Second type of parameters aka global parameters is set in metadata.run.options field (e.g. bottom.yaml):

 1metadata:
 2  run:
 3    factory: geo
 4    strategy:
 5      class: strategy.NoBoolean
 6    options:
 7      Mesh.MeshSizeFactor: 0.5
 8      Mesh.MeshSizeMin: 0
 9      Mesh.MeshSizeMax: 1.0e+22
10      Mesh.MeshSizeFromPoints: 1
11data:
12  class: block.Matrix
13  matrix: [ [ 0;0.01, 0.250;0.1 ], [ 0;0.01, 1;0.01 ], [ 0;0.01, 0.250;0.1 ] ]

Here are 4 options (many other options available, see gmsh documentation): 1. Mesh.MeshSizeFactor - factor applied to all mesh element sizes 2. Mesh.MeshSizeMin - minimum mesh element size 3. Mesh.MeshSizeMax - maximum mesh element size 4. Mesh.MeshSizeFromPoints - compute mesh element sizes from values given at geometry points (e.g. in matrix field)

In this example Mesh.MeshSizeFactor is set to 0.5 that generate mesh that is twice as fine.

_images/cross_section_2_mesh_unstructured_tetrahedral_bottom_global_1.png

Unstructured tetrahedral mesh with Mesh.MeshSizeFactor = 0.5

One could disable Mesh.MeshSizeFromPoints (set to 0) to create uniform mesh whose size is controlled only by global parameters.

 1metadata:
 2  run:
 3    factory: geo
 4    strategy:
 5      class: strategy.NoBoolean
 6    options:
 7      Mesh.MeshSizeFactor: 1
 8      Mesh.MeshSizeMin: 0
 9      Mesh.MeshSizeMax: 1.0e+22
10      Mesh.MeshSizeFromPoints: 0
11data:
12  class: block.Matrix
13  matrix: [ [ 0;0.01, 0.250;0.1 ], [ 0;0.01, 1;0.01 ], [ 0;0.01, 0.250;0.1 ] ]
_images/cross_section_2_mesh_unstructured_tetrahedral_bottom_global_2.png

Unstructured tetrahedral mesh with Mesh.MeshSizeFromPoints = 0

Then we could use to control mesh size, e.g with Mesh.MeshSizeMax = 0.1:

 1metadata:
 2  run:
 3    factory: geo
 4    strategy:
 5      class: strategy.NoBoolean
 6    options:
 7      Mesh.MeshSizeFactor: 1
 8      Mesh.MeshSizeMin: 0
 9      Mesh.MeshSizeMax: 0.1
10      Mesh.MeshSizeFromPoints: 0
11data:
12  class: block.Matrix
13  matrix: [ [ 0, 0.250 ], [ 0, 1 ], [ 0, 0.250 ] ]
_images/cross_section_2_mesh_unstructured_tetrahedral_bottom_global_3.png

Unstructured mesh with Mesh.MeshSizeMax = 0.1

To generate all blocks, one needs to specify global parameters in main.yaml:

 1 metadata:
 2   run:
 3     factory: geo
 4     strategy:
 5       class: strategy.NoBoolean
 6     options:
 7       Mesh.MeshSizeFactor: 1
 8       Mesh.MeshSizeMin: 0
 9       Mesh.MeshSizeMax: 0.1
10       Mesh.MeshSizeFromPoints: 0
11 data:
12   class: block.Block
13   do_register: 0
14   children: [
15     /bottom.yaml,
16     /top_1.yaml,
17     /top_2.yaml,
18     /top_3.yaml
19   ]
20   children_transforms: [
21     [ ],
22     [ [ 0, 0, 0.250 ] ],
23     [ [ 0.250, 0, 0.250 ] ],
24     [ [ 0.470, 0, 0.250 ] ]
25   ]

python -m gmsh_scripts main.yaml
_images/cross_section_2_mesh_unstructured_tetrahedral_main_global.png

Unstructured tetrahedral mesh controlled by global parameters

Unstructured Hexahedral

Warning

Generation of hexahedral unstructured mesh is experimental so not always creates a quality mesh, it depends on the complexity of the geometry.

Unstructured hexahedral parameters are set in metadata.run.options field and have Recombine in their names (see gmsh options)

To generate unstructured hexahedral mesh parameter `Mesh.SubdivisionAlgorithm should be set greater than 1 (see tutorial 11 of gmsh for more information)

 1metadata:
 2  run:
 3    factory: geo
 4    strategy:
 5      class: strategy.NoBoolean
 6    options:
 7      Mesh.MeshSizeFactor: 1
 8      Mesh.MeshSizeMin: 0
 9      Mesh.MeshSizeMax: 0.1
10      Mesh.MeshSizeFromPoints: 0
11      Mesh.SubdivisionAlgorithm: 2
12data:
13  class: block.Matrix
14  matrix: [ [ 0, 0.250 ], [ 0, 1 ], [ 0, 0.250 ] ]

python -m gmsh_scripts bottom.yaml
_images/cross_section_2_mesh_unstructured_hexahedral_bottom_1.png

Unstructured hexahedral mesh of bottom.yaml

To generate unstructured hexahedral mesh of all blocks add parameters to metadata of main.yaml:

 1 metadata:
 2   run:
 3     factory: geo
 4     strategy:
 5       class: strategy.NoBoolean
 6     options:
 7       Mesh.MeshSizeFactor: 1
 8       Mesh.MeshSizeMin: 0
 9       Mesh.MeshSizeMax: 0.1
10       Mesh.MeshSizeFromPoints: 0
11       Mesh.SubdivisionAlgorithm: 2
12 data:
13   class: block.Block
14   do_register: 0
15   children: [
16     /bottom.yaml,
17     /top_1.yaml,
18     /top_2.yaml,
19     /top_3.yaml
20   ]
21   children_transforms: [
22     [ ],
23     [ [ 0, 0, 0.250 ] ],
24     [ [ 0.250, 0, 0.250 ] ],
25     [ [ 0.470, 0, 0.250 ] ]
26   ]

python -m gmsh_scripts main.yaml
_images/cross_section_2_mesh_unstructured_hexahedral_main.png

Unstructured hexahedral mesh

Structured Tetrahedral

To create structured tetrahedral mesh one should add third parameter to the points at matrix field with ; separator, e.g. in bottom.yaml:

1metadata:
2   run:
3     factory: geo
4     strategy:
5       class: strategy.NoBoolean
6
7data:
8  class: block.Matrix
9  matrix: [ [ 0;0.01, 0.250;0.1;4 ], [ 0;0.01, 1;0.1;8 ], [ 0;0.01, 0.250;0.1;16 ] ]

Third argument should be set only for second point and specifies number of nodes along corresponding direction. E.g. 4 nodes by X-axis, 8 nodes by Y and 16 by Z.

python -m gmsh_scripts bottom.yaml
_images/cross_section_2_mesh_structured_tetrahedral_bottom_1.png

Structured tetrahedral mesh of the BOTTOM block

One could disable structured mesh generation by setting items_do_structure_map to 0 (1 by default) in the data field:

 1metadata:
 2   run:
 3     factory: geo
 4     strategy:
 5       class: strategy.NoBoolean
 6
 7data:
 8  class: block.Matrix
 9  matrix: [ [ 0;0.01, 0.250;0.1;4 ], [ 0;0.01, 1;0.1;8 ], [ 0;0.01, 0.250;0.1;16 ] ]
10  items_do_structure_map: 0
_images/cross_section_2_mesh_structured_tetrahedral_bottom_2.png

Unstructured tetrahedral mesh of the BOTTOM block with items_do_structure_map = 0

To create structured tetrahedral mesh with all blocks one should set third parameter in each of the blocks and run main.yaml

Warning

Number of nodes MUST be consistent between adjacent blocks, e.g. all TOP blocks should have the same number of nodes by Y and Z axis

  • top_1.yaml

1 data:
2   class: block.Matrix
3   matrix: [ [ 0, 0.250;0.1;8 ], [ 0, 1;0.1;8 ], [ 0, 0.250;0.1;8 ] ]

  • top_2.yaml

1  data:
2    class: block.Matrix
3    matrix: [ [ 0, 0.220;0.1;8 ], [ 0, 1;0.1;8 ], [ 0, 0.250;0.1;8 ] ]

  • top_3.yaml

1 data:
2   class: block.Matrix
3   matrix: [ [ 0, 0.030;0.1;8 ], [ 0, 1;0.1;8 ], [ 0, 0.250;0.1;8 ] ]

  • bottom.yaml

1 data:
2   class: block.Matrix
3   matrix: [ [ 0, 0.250;0.1;8 ], [ 0, 1;0.1;8 ], [ 0, 0.250;0.1;8 ] ]

python -m gmsh_scripts main.yaml
_images/cross_section_2_mesh_structured_tetrahedral_main_1.png

Structured tetrahedral mesh

To disable generation of structured mesh for all blocks at once one should set children_items_do_structure_map = [0, ..., number of children] at parent block, e.g. for main.yaml:

 1 metadata:
 2   run:
 3     factory: geo
 4     strategy:
 5       class: strategy.NoBoolean
 6 data:
 7   class: block.Block
 8   do_register: 0
 9   children: [
10     /bottom.yaml,
11     /top_1.yaml,
12     /top_2.yaml,
13     /top_3.yaml
14   ]
15   children_transforms: [
16     [ ],
17     [ [ 0, 0, 0.250 ] ],
18     [ [ 0.250, 0, 0.250 ] ],
19     [ [ 0.470, 0, 0.250 ] ]
20   ]
21   children_items_do_structure_map: [0, 0, 0, 0]
_images/cross_section_2_mesh_structured_tetrahedral_main_2.png

Structured tetrahedral mesh with disabled children_items_do_structure_map

Structured Hexahedral

For creating structured hexahedral mesh one could do the same steps as for Structured Tetrahedral but with items_do_quadrate_map = 1 (0 by default) in the data field:

 1metadata:
 2   run:
 3     factory: geo
 4     strategy:
 5       class: strategy.NoBoolean
 6
 7data:
 8  class: block.Matrix
 9  matrix: [ [ 0;0.01, 0.250;0.1;4 ], [ 0;0.01, 1;0.1;8 ], [ 0;0.01, 0.250;0.1;16 ] ]
10  items_do_quadrate_map: 1

python -m gmsh_scripts bottom.yaml
_images/cross_section_2_mesh_structured_hexahedral_bottom_1.png

Structured hexahedral mesh of the BOTTOM block

One could change positions of nodes along axes using one of the two methods:

  1. progression - increase/decrease space between nodes from start point to end point

  2. bump - increase/decrease space between node from center to points

To use progression we should specify 2 additional sub-parameters to the third parameter separated by ::

  1. The first one is 0 (which choose progression type)

  2. The second is a coefficient of the progression - if coefficient > 1 space will be increasing from first point to second else decreasing

For example, progression sub-parameters 0:1.5 for Y-axis:

 1metadata:
 2   run:
 3     factory: geo
 4     strategy:
 5       class: strategy.NoBoolean
 6
 7data:
 8  class: block.Matrix
 9  matrix: [ [ 0;0.01, 0.250;0.1;4 ], [ 0;0.01, 1;0.1;8:0:1.5 ], [ 0;0.01, 0.250;0.1;16 ] ]
10  items_do_quadrate_map: 1
_images/cross_section_2_mesh_structured_hexahedral_bottom_progression_1.png

Structured hexahedral mesh with progression = 1.5

For example, progression sub-parameters 0:0.75 for Y-axis:

 1metadata:
 2   run:
 3     factory: geo
 4     strategy:
 5       class: strategy.NoBoolean
 6
 7data:
 8  class: block.Matrix
 9  matrix: [ [ 0;0.01, 0.250;0.1;4 ], [ 0;0.01, 1;0.1;8:0:0.75 ], [ 0;0.01, 0.250;0.1;16 ] ]
10  items_do_quadrate_map: 1
_images/cross_section_2_mesh_structured_hexahedral_bottom_progression_2.png

Structured hexahedral mesh with progression = 0.75

To use bump we should specify 2 additional sub-parameters to the third parameter separated by ::

  1. The first one is 1 (which choose bump type)

  2. The second is a coefficient of the bump - if coefficient > 1 space will be increasing from the center else decreasing

For example, bump sub-parameters 1:2.0 for Y-axis:

 1metadata:
 2   run:
 3     factory: geo
 4     strategy:
 5       class: strategy.NoBoolean
 6
 7data:
 8  class: block.Matrix
 9  matrix: [ [ 0;0.01, 0.250;0.1;4 ], [ 0;0.01, 1;0.1;8:1:2.0 ], [ 0;0.01, 0.250;0.1;16 ] ]
10  items_do_quadrate_map: 1
_images/cross_section_2_mesh_structured_hexahedral_bottom_bump_1.png

Structured hexahedral mesh with bump = 2.0

For example, bump sub-parameters 1:0.5 for Y-axis:

 1metadata:
 2   run:
 3     factory: geo
 4     strategy:
 5       class: strategy.NoBoolean
 6
 7data:
 8  class: block.Matrix
 9  matrix: [ [ 0;0.01, 0.250;0.1;4 ], [ 0;0.01, 1;0.1;8:1:0.5 ], [ 0;0.01, 0.250;0.1;16 ] ]
10  items_do_quadrate_map: 1
_images/cross_section_2_mesh_structured_hexahedral_bottom_bump_2.png

Structured hexahedral mesh with bump = 0.5

To generate structured hexahedral mesh of all blocks one could set items_do_quadrate_map = 0 at each of the blocks or set children_items_do_quadrate_map = [0, ..., number of children] at parent block, e.g. for main.yaml:

 1 metadata:
 2   run:
 3     factory: geo
 4     strategy:
 5       class: strategy.NoBoolean
 6 data:
 7   class: block.Block
 8   do_register: 0
 9   children: [
10     /bottom.yaml,
11     /top_1.yaml,
12     /top_2.yaml,
13     /top_3.yaml
14   ]
15   children_transforms: [
16     [ ],
17     [ [ 0, 0, 0.250 ] ],
18     [ [ 0.250, 0, 0.250 ] ],
19     [ [ 0.470, 0, 0.250 ] ]
20   ]
21   children_items_do_quadrate_map: [1, 1, 1, 1]

python -m gmsh_scripts main.yaml
_images/cross_section_2_mesh_structured_hexahedral_main.png

Structured hexahedral mesh

Zones

If we want to add names to entities of the mesh (e.g. volumes of surfaces) we should set additional field items_zones in the data field

For example, we can add [ [ Volume, [ NX, X, NY, Y, NZ, Z ] ] ] in the``bottom.yaml``, where:

  1. Volume - volume name

  2. [ NX, X, NY, Y, NZ, Z ] - surfaces names:

    • NX - surface pointing in the opposite direction of X-axis

    • X - surface pointing in the direction of X-axis

    • NY - surface pointing in the opposite direction of Y-axis

    • Y - surface pointing in the direction of Y-axis

    • NZ - surface pointing in the opposite direction of Z-axis

    • Z - surface pointing in the direction of Z-axis

 1metadata:
 2   run:
 3     factory: geo
 4     strategy:
 5       class: strategy.NoBoolean
 6
 7data:
 8  class: block.Matrix
 9  matrix: [ [ 0;0.01, 0.250;0.1;4 ], [ 0;0.01, 1;0.1;8 ], [ 0;0.01, 0.250;0.1;16 ] ]
10  items_zone: [ [ Volume, [ NX, X, NY, Y, NZ, Z ] ] ]
11  items_do_quadrate_map: 1
_images/cross_section_2_mesh_structured_hexahedral_bottom_zones.png

Structured hexahedral with zones

Result

Note

We should define different zone names of bottom surfaces of TOP2 and TOP3, e.g. Top2NZ and Top3NZ respectively

  • top_1.yaml

1data:
2  class: block.Matrix
3  matrix: [ [ 0;0.1, 0.250;0.1;8 ], [ 0;0.1, 1;0.1;8 ], [ 0;0.1, 0.250;0.1;8 ] ]
4  items_zone: [ [ Volume, [ NX, X, NY, Y, NZ, Z ] ] ]

  • top_2.yaml

1data:
2  class: block.Matrix
3  matrix: [ [ 0;0.1, 0.220;0.1;8 ], [ 0;0.1, 1;0.1;8 ], [ 0;.1, 0.250;0.1;8 ] ]
4  items_zone: [ [ Volume, [ NX, X, NY, Y, Top2NZ, Z ] ] ]

  • top_3.yaml

1data:
2  class: block.Matrix
3  matrix: [ [ 0;0.1, 0.030;0.1;8 ], [ 0;0.1, 1;0.1;8 ], [ 0;.1, 0.250;0.1;8 ] ]
4  items_zone: [ [ Volume, [ NX, X, NY, Y, Top3NZ, Z ] ] ]

  • bottom.yaml

1data:
2  class: block.Matrix
3  matrix: [ [ 0;.1, 0.250;.1;8 ], [ 0;.1, 1;.1;8 ], [ 0;.1, 0.250;.1;8 ] ]
4  items_zone: [ [ Volume, [ NX, X, NY, Y, NZ, Z ] ] ]

  • main.yaml

 1metadata:
 2  run:
 3    factory: geo
 4    strategy:
 5      class: strategy.NoBoolean
 6data:
 7  class: block.Block
 8  do_register: 0
 9  children: [
10    /bottom.yaml,
11    /top_1.yaml,
12    /top_2.yaml,
13    /top_3.yaml
14  ]
15  children_transforms: [
16    [ ],
17    [ [ 0, 0, 0.250 ] ],
18    [ [ 0.250, 0, 0.250 ] ],
19    [ [ 0.470, 0, 0.250 ] ]
20  ]
21  children_items_do_quadrate_map: [ 1, 1, 1, 1 ]
22  children_items_do_structure_map: [ 1, 1, 1, 1 ]

python -m gmsh_scripts main.yaml
_images/cross_section_2.png

Mesh