Meshing Example

Introduction

In this example, we will show how to use the mesh module to create a 2D mesh for fem application

Imports

Import necessary module definitions.

from pathlib import Path

from bluemira.base.components import Component, PhysicalComponent
from bluemira.base.file import get_bluemira_path
from bluemira.base.logs import set_log_level
from bluemira.equilibria.shapes import JohnerLCFS
from bluemira.geometry import tools
from bluemira.geometry.face import BluemiraFace
from bluemira.geometry.wire import BluemiraWire
from bluemira.mesh import meshing
from bluemira.mesh.tools import import_mesh, msh_to_xdmf, plot_dolfinx_mesh

set_log_level("DEBUG")

Geometry

Creation of a simple 2-D geometry, i.e. a Johner shape + a coil with casing

p = JohnerLCFS()
lcfs = p.create_shape(label="LCFS")

poly1 = tools.make_polygon(
    [[0, 1, 1], [0, 0, 0], [0, 0, 1]], closed=False, label="poly1"
)
poly2 = tools.make_polygon(
    [[1, 0, 0], [0, 0, 0], [1, 1, 0]], closed=False, label="poly2"
)
poly3 = tools.make_polygon(
    [[0.25, 0.75, 0.75], [0, 0, 0], [0.25, 0.25, 0.75]], closed=False, label="poly3"
)
poly4 = tools.make_polygon(
    [[0.75, 0.25, 0.25], [0, 0, 0], [0.75, 0.75, 0.25]], closed=False, label="poly4"
)
poly_out = BluemiraWire([poly1, poly2], label="poly_out")
poly_in = BluemiraWire([poly3, poly4], label="poly_in")
coil_out = BluemiraFace([poly_out, poly_in], label="coil_out")
coil_in = BluemiraFace([poly_in], label="coil_in")

Mesh setup

setup characteristic mesh length

lcfs.mesh_options = {"lcar": 0.75, "physical_group": "LCFS"}
face = BluemiraFace(lcfs, label="plasma_surface")
face.mesh_options = {"lcar": 0.5, "physical_group": "surface"}

poly1.mesh_options = {"lcar": 0.25, "physical_group": "poly1"}
poly2.mesh_options = {"lcar": 0.25, "physical_group": "poly2"}
poly3.mesh_options = {"lcar": 0.75, "physical_group": "poly3"}
poly4.mesh_options = {"lcar": 0.75, "physical_group": "poly4"}
coil_out.mesh_options = {"lcar": 1, "physical_group": "coil"}
coil_in.mesh_options = {"lcar": 0.3, "physical_group": "coil"}

In order to mesh all the geometry in one, the best solution is to create a component tree as in the following

c_all = Component(name="all")
c_plasma = PhysicalComponent(name="plasma", shape=face, parent=c_all)
c_coil = Component(name="coil", parent=c_all)
c_coil_in = PhysicalComponent(name="coil_in", shape=coil_in, parent=c_coil)
c_coil_out = PhysicalComponent(name="coil_out", shape=coil_out, parent=c_coil)

Initialise and create the mesh

directory = Path(get_bluemira_path("", subfolder="generated_data/"))
directory = directory.joinpath("examples", "mesh_tutorial")
directory.mkdir(parents=True, exist_ok=True)

meshfiles = [Path(directory, p).as_posix() for p in ["Mesh.geo_unrolled", "Mesh.msh"]]
m = meshing.Mesh(meshfile=meshfiles)
buffer = m(c_all)
print(m.get_gmsh_dict(buffer))

Convert to xdmf

msh_to_xdmf("Mesh.msh", dimensions=(0, 2), directory=directory)

mesh, boundaries, subdomains, labels = import_mesh(
    "Mesh", directory=directory, subdomains=True
)

plot_dolfinx_mesh(mesh)

print(mesh.geometry.x)