Specifying resolutions#
When defining entities, ResolutionSpecs can be attached to control the mesh size within or near the entity and its boundaries.
from collections import OrderedDict
import shapely
from meshwell.cad import cad
from meshwell.mesh import mesh
from meshwell.polysurface import PolySurface
from meshwell.resolution import ConstantInField, ExponentialField, ThresholdField
from meshwell.visualization import plot2D
Default characteristic length#
When creating a Model mesh, default_characteristic_length is used to set the default mesh size.
box1 = shapely.box(0, 0, 10, 10)
box2 = shapely.box(2, 2, 4, 4)
box3 = shapely.box(8, 4, 12, 6)
boxes = OrderedDict()
boxes["box3"] = box3
boxes["box2"] = box2
boxes["box1"] = box1
polysurfaces = []
for i, (box_name, box) in enumerate(boxes.items()):
polysurfaces.append(
PolySurface(
polygons=box,
physical_name=box_name,
mesh_order=i,
)
)
cad(
entities_list=polysurfaces,
output_file="model.xao",
)
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for default_characteristic_length in [10, 1, 0.5]:
output_mesh = mesh(
dim=2,
input_file="model.xao",
output_file="default_resolution.msh",
n_threads=1,
default_characteristic_length=default_characteristic_length,
)
plot2D(
output_mesh,
title=f"default_characteristic_length = {default_characteristic_length}",
wireframe=True,
)
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Constant Resolution#
Constant resolution can be assigned within entities or their boundaries using ConstantInField specification.
output_mesh = mesh(
dim=2,
input_file="model.xao",
output_file="constant_resolution.msh",
n_threads=1,
default_characteristic_length=2,
resolution_specs={
"box2": [ConstantInField(resolution=0.3, apply_to="surfaces")],
"box3": [ConstantInField(resolution=0.3, apply_to="curves")],
},
)
plot2D(output_mesh, title="ConstantInField", wireframe=True)
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Threshold-based Resolution#
This creates a mesh that transitions from fine resolution near boundaries to coarse resolution away from them
output_mesh = mesh(
dim=2,
input_file="model.xao",
output_file="threshold_resolution.msh",
n_threads=1,
default_characteristic_length=2,
resolution_specs={
"box2": [
ThresholdField(sizemin=0.3, distmax=5, sizemax=2.0, apply_to="curves"),
ConstantInField(resolution=0.3, apply_to="surfaces"),
],
"box3": [
ThresholdField(sizemin=0.1, distmax=2, sizemax=0.5, apply_to="curves"),
ThresholdField(
sizemin=0.5, distmax=5, sizemax=2, distmin=2, apply_to="curves"
),
],
},
)
plot2D(output_mesh, title="ThresholdField", wireframe=True)
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Exponential Resolution#
Creates a mesh with exponentially varying resolution based on distance from boundaries
output_mesh = mesh(
dim=2,
input_file="model.xao",
output_file="exponential_resolution.msh",
n_threads=1,
default_characteristic_length=2,
resolution_specs={
"box2": [
ExponentialField(
sizemin=0.3, lengthscale=2, growth_factor=2.0, apply_to="curves"
),
ConstantInField(resolution=0.3, apply_to="surfaces"),
],
"box3": [
ExponentialField(
sizemin=0.2, lengthscale=2, growth_factor=2.0, apply_to="curves"
),
],
},
)
plot2D(output_mesh, title="ExponentialField", wireframe=True)
# ## Background mesh
# It is also possible to pass a gmsh .pos file to fully parametrize the size field vs position. This is typically more useful once a physical solution has been calculated on an initial mesh, and a new size field has been calculated from the solution. Many solvers also have built-in remeshing, and hence only need an initial mesh before doing their own refinement
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