To those interested, there is a quick way to achieve a gradient mesh with one or multiple .stl files, or more generically, multiple volumes with distinct surfaces. The latest version of gmsh (version 4.9.3, released 4 January 2022) includes a new type of "Field" option called "Extend".

An example of this new Field is shown here: https://gitlab.onelab.info/gmsh/gmsh/-/blob/master/examples/boolean/extend_field.geo. Please see my original post on the GitLab page of gmsh for further info: https://gitlab.onelab.info/gmsh/gmsh/-/issues/1678.

For the specific example I posted above, the necessary code (in the format of a .geo file, attached here) is:

Merge "C:\temp\15_microstructure_files\Instantiation103\INSERT_DEFECTS\JAN_3_2022_shifted_defects\att_v2\all_SEM_grains_extend_40_10_1\Grain_1.stl";

Surface Loop(1)={1};

Volume(1)={1};

Physical Volume (1)={1};

Merge "C:\temp\15_microstructure_files\Instantiation103\INSERT_DEFECTS\JAN_3_2022_shifted_defects\att_v2\all_SEM_grains_extend_40_10_1\Grain_2.stl";

Surface Loop(2)={2};

Volume(2)={2};

Physical Volume (2)={2};

Merge "C:\temp\15_microstructure_files\Instantiation103\INSERT_DEFECTS\JAN_3_2022_shifted_defects\att_v2\all_SEM_grains_extend_40_10_1\Grain_3.stl";

Surface Loop(3)={3};

Volume(3)={3};

Physical Volume (3)={3};

Field[1] = Extend;

Field[1].SurfacesList = {1,2,3};

Field[1].DistMax = 40;

Field[1].SizeMax = 10;

Field[1].Power = 1;

Background Field = 1;

Mesh.MeshSizeExtendFromBoundary = 0;

Mesh.Algorithm3D = 10;

For the example above, three .stl files are considered. The user will change:

• The SurfacesList to specify all the surfaces that should be considered.
• DistMax: Maximum distance of the size extension
• SizeMax: Mesh size outside DistMax
• Power: Power exponent used to interpolate the mesh size

Full description of code available at: https://gmsh.info/doc/texinfo/gmsh.html

Big credit to Professor Christophe Geuzaine for his assistance with this!

Hello all,

As mentioned before, the most simple way to do that is indeed to use the Field option. I personally use the Attractor type together with the MathEval function. The first is intended to define a new field, which is computed as the distance from the reference points/curves/surfaces. Then MathEval allow to define size field as a function (of any kind) of the attractor.

Find attached a very basic example of a unit cube, that is meshed so that the elements have a linear increasing size with increasing distance from the bottom face (see figure).

Note: I actually use this method in MTEX2Gmsh [1]

[EDIT]

For recent versions of Gmsh (> 4.8.4), one should use Distance instead of Attractor [2].

[/EDIT]

[1] https://doriandepriester.github.io/MTEX2Gmsh/

[2] https://gitlab.onelab.info/gmsh/gmsh/-/issues/1796

Thank you Dorian Depriester for the answer and the reference to your GitHub/manuscript, very useful!

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