# [Gmsh] Extruded mesh with matching facets in horizontal domain

Christian Helanow christian.helanow at natgeo.su.se
Tue Aug 30 19:29:11 CEST 2016

```Hello,
I wonder if it is possible to start out with a rectangular
(unstructured) mesh that is supposed to be periodic in the x and y
direction and extrude this in the vertical in such a way that the
resulting (tetrahedron) mesh will have matching facets in the
periodic/horizontal directions.
Below is the .geo file that is closest to what I would like.

nz = 10; // vertical resolution
L = 1000; // length of domain [m]
l = 100; // characteristic size of edge
lmid = 10; // characteristic size of mid point
Point(1) = {0, 0, 0, l};
Point(2) = {L, 0, 0, l};
Point(3) = {0, L, 0, l};
Point(4) = {L, L, 0, l};
Line(1) = {1, 2};
Line(2) = {3, 4};
Line(3) = {1, 3};
Line(4) = {2, 4};
Line Loop(5) = {1, 4, -2, -3};
Ruled Surface(5) = {5};
Periodic Line {1} = {-2};
Periodic Line {3} = {-4};
Point(5) = {L/2, L/2, 0, lmid};
Point{5} In Surface{5};
h = 1000.;  // height of domain
Extrude {0,0,h} { Surface{5}; Layers{nz}; } // structured tetrahedrons,
vertical resolution nx

When meshed in 2D, the surfaces of the domain look the way I would like
the surface facets to look when meshing the domain in 3D. However, when
running the 3D algorithm the facets get reordered (switch crossing
pattern) which in my experience is not good for periodic conditions.
I have tried to make the lines/surfaces Transfinite (except top and
bottom), however, this overrides the Extrude command, resulting in a
mesh with good facets on the boundary but not an extruded type of mesh.
Any help would be greatly appreciated.
Best Regards,

Christian Helanow
PhD Student
Dept Physical Geography, Stockholm University

```