# ------------------------------------------------------------------------------
#
# Gmsh Python tutorial 5
#
# Mesh sizes, holes in volumes
#
# ------------------------------------------------------------------------------
import gmsh
import math
import sys
gmsh.initialize()
gmsh.model.add("t5")
lcar1 = .1
lcar2 = .0005
lcar3 = .055
# If we wanted to change these mesh sizes globally (without changing the above
# definitions), we could give a global scaling factor for all mesh sizes with
# e.g.
#
# gmsh.option.setNumber("Mesh.MeshSizeFactor", 0.1);
#
# Since we pass `argc' and `argv' to `gmsh.initialize()', we can also give the
# option on the command line with the `-clscale' switch. For example, with:
#
# > ./t5.exe -clscale 1
#
# this tutorial produces a mesh of approximately 3000 nodes and 14,000
# tetrahedra. With
#
# > ./t5.exe -clscale 0.2
#
# the mesh counts approximately 231,000 nodes and 1,360,000 tetrahedra. You can
# check mesh statistics in the graphical user interface (gmsh.fltk.run()) with
# the `Tools->Statistics' menu.
#
# See `t10.py' for more information about mesh sizes.
# We proceed by defining some elementary entities describing a truncated cube:
gmsh.model.geo.addPoint(0.5, 0.5, 0.5, lcar2, 1)
gmsh.model.geo.addPoint(0.5, 0.5, 0, lcar1, 2)
gmsh.model.geo.addPoint(0, 0.5, 0.5, lcar1, 3)
gmsh.model.geo.addPoint(0, 0, 0.5, lcar1, 4)
gmsh.model.geo.addPoint(0.5, 0, 0.5, lcar1, 5)
gmsh.model.geo.addPoint(0.5, 0, 0, lcar1, 6)
gmsh.model.geo.addPoint(0, 0.5, 0, lcar1, 7)
gmsh.model.geo.addPoint(0, 1, 0, lcar1, 8)
gmsh.model.geo.addPoint(1, 1, 0, lcar1, 9)
gmsh.model.geo.addPoint(0, 0, 1, lcar1, 10)
gmsh.model.geo.addPoint(0, 1, 1, lcar1, 11)
gmsh.model.geo.addPoint(1, 1, 1, lcar1, 12)
gmsh.model.geo.addPoint(1, 0, 1, lcar1, 13)
gmsh.model.geo.addPoint(1, 0, 0, lcar1, 14)
gmsh.model.geo.addLine(8, 9, 1)
gmsh.model.geo.addLine(9, 12, 2)
gmsh.model.geo.addLine(12, 11, 3)
gmsh.model.geo.addLine(11, 8, 4)
gmsh.model.geo.addLine(9, 14, 5)
gmsh.model.geo.addLine(14, 13, 6)
gmsh.model.geo.addLine(13, 12, 7)
gmsh.model.geo.addLine(11, 10, 8)
gmsh.model.geo.addLine(10, 13, 9)
gmsh.model.geo.addLine(10, 4, 10)
gmsh.model.geo.addLine(4, 5, 11)
gmsh.model.geo.addLine(5, 6, 12)
gmsh.model.geo.addLine(6, 2, 13)
gmsh.model.geo.addLine(2, 1, 14)
gmsh.model.geo.addLine(1, 3, 15)
gmsh.model.geo.addLine(3, 7, 16)
gmsh.model.geo.addLine(7, 2, 17)
gmsh.model.geo.addLine(3, 4, 18)
gmsh.model.geo.addLine(5, 1, 19)
gmsh.model.geo.addLine(7, 8, 20)
gmsh.model.geo.addLine(6, 14, 21)
gmsh.model.geo.addCurveLoop([-11, -19, -15, -18], 22)
gmsh.model.geo.addPlaneSurface([22], 23)
gmsh.model.geo.addCurveLoop([16, 17, 14, 15], 24)
gmsh.model.geo.addPlaneSurface([24], 25)
gmsh.model.geo.addCurveLoop([-17, 20, 1, 5, -21, 13], 26)
gmsh.model.geo.addPlaneSurface([26], 27)
gmsh.model.geo.addCurveLoop([-4, -1, -2, -3], 28)
gmsh.model.geo.addPlaneSurface([28], 29)
gmsh.model.geo.addCurveLoop([-7, 2, -5, -6], 30)
gmsh.model.geo.addPlaneSurface([30], 31)
gmsh.model.geo.addCurveLoop([6, -9, 10, 11, 12, 21], 32)
gmsh.model.geo.addPlaneSurface([32], 33)
gmsh.model.geo.addCurveLoop([7, 3, 8, 9], 34)
gmsh.model.geo.addPlaneSurface([34], 35)
gmsh.model.geo.addCurveLoop([-10, 18, -16, -20, 4, -8], 36)
gmsh.model.geo.addPlaneSurface([36], 37)
gmsh.model.geo.addCurveLoop([-14, -13, -12, 19], 38)
gmsh.model.geo.addPlaneSurface([38], 39)
shells = []
sl = gmsh.model.geo.addSurfaceLoop([35, 31, 29, 37, 33, 23, 39, 25, 27])
shells.append(sl)
def cheeseHole(x, y, z, r, lc, shells):
# This function will create a spherical hole in a volume. We don't specify
# tags manually, and let the functions return them automatically:
p1 = gmsh.model.geo.addPoint(x, y, z, lc)
p2 = gmsh.model.geo.addPoint(x + r, y, z, lc)
p3 = gmsh.model.geo.addPoint(x, y + r, z, lc)
p4 = gmsh.model.geo.addPoint(x, y, z + r, lc)
p5 = gmsh.model.geo.addPoint(x - r, y, z, lc)
p6 = gmsh.model.geo.addPoint(x, y - r, z, lc)
p7 = gmsh.model.geo.addPoint(x, y, z - r, lc)
c1 = gmsh.model.geo.addCircleArc(p2, p1, p7)
c2 = gmsh.model.geo.addCircleArc(p7, p1, p5)
c3 = gmsh.model.geo.addCircleArc(p5, p1, p4)
c4 = gmsh.model.geo.addCircleArc(p4, p1, p2)
c5 = gmsh.model.geo.addCircleArc(p2, p1, p3)
c6 = gmsh.model.geo.addCircleArc(p3, p1, p5)
c7 = gmsh.model.geo.addCircleArc(p5, p1, p6)
c8 = gmsh.model.geo.addCircleArc(p6, p1, p2)
c9 = gmsh.model.geo.addCircleArc(p7, p1, p3)
c10 = gmsh.model.geo.addCircleArc(p3, p1, p4)
c11 = gmsh.model.geo.addCircleArc(p4, p1, p6)
c12 = gmsh.model.geo.addCircleArc(p6, p1, p7)
l1 = gmsh.model.geo.addCurveLoop([c5, c10, c4])
l2 = gmsh.model.geo.addCurveLoop([c9, -c5, c1])
l3 = gmsh.model.geo.addCurveLoop([c12, -c8, -c1])
l4 = gmsh.model.geo.addCurveLoop([c8, -c4, c11])
l5 = gmsh.model.geo.addCurveLoop([-c10, c6, c3])
l6 = gmsh.model.geo.addCurveLoop([-c11, -c3, c7])
l7 = gmsh.model.geo.addCurveLoop([-c2, -c7, -c12])
l8 = gmsh.model.geo.addCurveLoop([-c6, -c9, c2])
# We need non-plane surfaces to define the spherical holes. Here we use the
# `gmsh.model.geo.addSurfaceFilling()' function, which can be used for
# surfaces with 3 or 4 curves on their boundary. With the he built-in
# kernel, if the curves are circle arcs, ruled surfaces are created;
# otherwise transfinite interpolation is used.
#
# With the OpenCASCADE kernel, `gmsh.model.occ.addSurfaceFilling()' uses a
# much more general generic surface filling algorithm, creating a BSpline
# surface passing through an arbitrary number of boundary curves. The
# `gmsh.model.geo.addThruSections()' allows to create ruled surfaces (see
# `t19.py').
s1 = gmsh.model.geo.addSurfaceFilling([l1])
s2 = gmsh.model.geo.addSurfaceFilling([l2])
s3 = gmsh.model.geo.addSurfaceFilling([l3])
s4 = gmsh.model.geo.addSurfaceFilling([l4])
s5 = gmsh.model.geo.addSurfaceFilling([l5])
s6 = gmsh.model.geo.addSurfaceFilling([l6])
s7 = gmsh.model.geo.addSurfaceFilling([l7])
s8 = gmsh.model.geo.addSurfaceFilling([l8])
sl = gmsh.model.geo.addSurfaceLoop([s1, s2, s3, s4, s5, s6, s7, s8])
v = gmsh.model.geo.addVolume([sl])
shells.append(sl)
return v
# We create five holes in the cube:
x = 0
y = 0.75
z = 0
r = 0.09
for t in range(1, 6):
x += 0.166
z += 0.166
v = cheeseHole(x, y, z, r, lcar3, shells)
gmsh.model.geo.addPhysicalGroup(3, [v], t)
# The volume of the cube, without the 5 holes, is defined by 6 surface loops:
# the first surface loop defines the exterior surface; the surface loops other
# than the first one define holes:
gmsh.model.geo.addVolume(shells, 186)
gmsh.model.geo.synchronize()
# Note that using solid modelling with the OpenCASCADE CAD kernel, the same
# geometry could be built quite differently: see `t16.py'.
# We finally define a physical volume for the elements discretizing the cube,
# without the holes (for which physical groups were already defined in the
# `cheeseHole()' function):
gmsh.model.addPhysicalGroup(3, [186], 10)
# We could make only part of the model visible to only mesh this subset:
# ent = gmsh.model.getEntities()
# gmsh.model.setVisibility(ent, False)
# gmsh.model.setVisibility([(3, 5(], True, True)
# gmsh.option.setNumber("Mesh.MeshOnlyVisible", 1)
# Meshing algorithms can changed globally using options:
gmsh.option.setNumber("Mesh.Algorithm", 6) # Frontal-Delaunay for 2D meshes
# They can also be set for individual surfaces, e.g. for using `MeshAdapt' on
# surface 1:
gmsh.model.mesh.setAlgorithm(2, 33, 1)
# To generate a curvilinear mesh and optimize it to produce provably valid
# curved elements (see A. Johnen, J.-F. Remacle and C. Geuzaine. Geometric
# validity of curvilinear finite elements. Journal of Computational Physics
# 233, pp. 359-372, 2013; and T. Toulorge, C. Geuzaine, J.-F. Remacle,
# J. Lambrechts. Robust untangling of curvilinear meshes. Journal of
# Computational Physics 254, pp. 8-26, 2013), you can uncomment the following
# lines:
#
# gmsh.option.setNumber("Mesh.ElementOrder", 2)
# gmsh.option.setNumber("Mesh.HighOrderOptimize", 2)
gmsh.model.mesh.generate(3)
gmsh.write("t5.msh")
# Launch the GUI to see the results:
if '-nopopup' not in sys.argv:
gmsh.fltk.run()
gmsh.finalize()