discretize.CylindricalMesh#

Inheritance diagram of CylindricalMesh
class discretize.CylindricalMesh(h, origin=None, cartesian_origin=None, **kwargs)[source]#

Class for cylindrical meshes.

CylindricalMesh is a mesh class for problems with rotational symmetry. It supports both cylindrically symmetric and 3D cylindrical meshes where the azimuthal discretization is user-defined. In discretize, the coordinates for cylindrical meshes are as follows:

  • x: radial direction (\(r\))

  • y: azimuthal direction (\(\phi\))

  • z: vertical direction (\(z\))

Parameters
h(dim) iterable of int, numpy.ndarray, or tuple

Defines the cell widths along each axis. The length of the iterable object is equal to the dimension of the mesh (1, 2 or 3). For a 3D mesh, the list would have the form [hr, hphi, hz] . Note that the sum of cell widths in the phi direction must equal \(2\pi\). You can also use a flat value of hphi = 1 to define a cylindrically symmetric mesh.

Along each axis, the user has 3 choices for defining the cells widths:

  • int -> A unit interval is equally discretized into N cells.

  • numpy.ndarray -> The widths are explicity given for each cell

  • the widths are defined as a list of tuple of the form (dh, nc, [npad]) where dh is the cell width, nc is the number of cells, and npad (optional)is a padding factor denoting exponential increase/decrease in the cell width or each cell; e.g. [(2., 10, -1.3), (2., 50), (2., 10, 1.3)]

origin(dim) iterable, default: 0

Define the origin or ‘anchor point’ of the mesh; i.e. the bottom-left-frontmost corner. By default, the mesh is anchored such that its origin is at [0, 0, 0].

For each dimension (r, theta or z), The user may set the origin 2 ways:

  • a scalar which explicitly defines origin along that dimension.

  • {‘0’, ‘C’, ‘N’} a str specifying whether the zero coordinate along each axis is the first node location (‘0’), in the center (‘C’) or the last node location (‘N’).

Examples

To create a general 3D cylindrical mesh, we discretize along the radial, azimuthal and vertical axis. For example:

>>> from discretize import CylindricalMesh
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> ncr = 10  # number of mesh cells in r
>>> ncp = 8   # number of mesh cells in phi
>>> ncz = 15  # number of mesh cells in z
>>> dr = 15   # cell width r
>>> dz = 10   # cell width z
>>> hr = dr * np.ones(ncr)
>>> hp = (2 * np.pi / ncp) * np.ones(ncp)
>>> hz = dz * np.ones(ncz)
>>> mesh1 = CylindricalMesh([hr, hp, hz])
>>> mesh1.plot_grid()
>>> plt.show()

(Source code, png, pdf)

../../_images/discretize-CylindricalMesh-1_00_00.png

For a cylindrically symmetric mesh, the disretization along the azimuthal direction is set with a flag of 1. This reduces the size of numerical systems given that the derivative along the azimuthal direction is 0. For example:

>>> ncr = 10      # number of mesh cells in r
>>> ncz = 15      # number of mesh cells in z
>>> dr = 15       # cell width r
>>> dz = 10       # cell width z
>>> npad_r = 4    # number of padding cells in r
>>> npad_z = 4    # number of padding cells in z
>>> exp_r = 1.25  # expansion rate of padding cells in r
>>> exp_z = 1.25  # expansion rate of padding cells in z

A value of 1 is used to define the discretization in phi for this case.

>>> hr = [(dr, ncr), (dr, npad_r, exp_r)]
>>> hz = [(dz, npad_z, -exp_z), (dz, ncz), (dz, npad_z, exp_z)]
>>> mesh2 = CylindricalMesh([hr, 1, hz])
>>> mesh2.plot_grid()
>>> plt.show()

(png, pdf)

../../_images/discretize-CylindricalMesh-1_01_00.png

Attributes

area

area has been deprecated.

areaFx

areaFx has been deprecated.

areaFy

areaFy has been deprecated.

areaFz

areaFz has been deprecated.

average_cell_to_edge

Averaging operator from cell centers to edges (scalar quantities).

average_cell_to_face

Averaging operator from cell centers to faces (scalar quantities).

average_cell_vector_to_face

Averaging operator from cell centers to faces (vector quantities).

average_edge_to_cell

Averaging operator from edges to cell centers (scalar quantities).

average_edge_to_cell_vector

Averaging operator from edges to cell centers (vector quantities).

average_edge_to_face_vector

Averaging operator from edges to faces (vector quantities).

average_edge_x_to_cell

Averaging operator from x-edges to cell centers (scalar quantities).

average_edge_y_to_cell

Averaging operator from y-edges to cell centers (scalar quantities).

average_edge_z_to_cell

Averaging operator from z-edges to cell centers (scalar quantities).

average_face_to_cell

Averaging operator from faces to cell centers (scalar quantities).

average_face_to_cell_vector

Averaging operator from faces to cell centers (vector quantities).

average_face_x_to_cell

Averaging operator from x-faces to cell centers (scalar quantities).

average_face_y_to_cell

Averaging operator from y-faces to cell centers (scalar quantities).

average_face_z_to_cell

Averaging operator from z-faces to cell centers (scalar quantities).

average_node_to_cell

Averaging operator from nodes to cell centers (scalar quantities).

average_node_to_edge

Averaging operator from nodes to edges (scalar quantities).

average_node_to_face

Averaging operator from nodes to faces (scalar quantities).

axis_u

Orientation of the first axis.

axis_v

Orientation of the second axis.

axis_w

Orientation of the third axis.

boundary_edge_vector_integral

Integrate a vector function on the boundary.

boundary_edges

Boundary edge locations.

boundary_face_outward_normals

Outward normal vectors of boundary faces.

boundary_face_scalar_integral

Represent the operation of integrating a scalar function on the boundary.

boundary_faces

Boundary face locations.

boundary_node_vector_integral

Integrate a vector function dotted with the boundary normal.

boundary_nodes

Boundary node locations.

cartesianOrigin

cartesianOrigin has been deprecated.

cartesian_origin

Cartesian origin of the mesh.

cellGrad

cellGrad has been deprecated.

cellGradBC

cellGradBC has been deprecated.

cellGradx

cellGradx has been deprecated.

cellGrady

cellGrady has been deprecated.

cellGradz

cellGradz has been deprecated.

cell_centers

Return gridded cell center locations.

cell_centers_x

Return the x-positions of cell centers along the x-direction.

cell_centers_y

Return the y-positions of cell centers along the y-direction (azimuthal).

cell_centers_z

Return z-coordinates of the cell centers along the z-direction.

cell_gradient

Cell gradient operator (cell centers to faces).

cell_gradient_BC

Boundary conditions matrix for the cell gradient operator (Deprecated).

cell_gradient_x

X-derivative operator (cell centers to x-faces).

cell_gradient_y

Y-derivative operator (cell centers to y-faces).

cell_gradient_z

Z-derivative operator (cell centers to z-faces).

cell_volumes

Volumes of all mesh cells.

dim

The dimension of the mesh (1, 2, or 3).

edge

edge has been deprecated.

edgeCurl

edgeCurl has been deprecated.

edgeEx

edgeEx has been deprecated.

edgeEy

edgeEy has been deprecated.

edgeEz

edgeEz has been deprecated.

edge_curl

Edge curl operator (edges to faces).

edge_lengths

Lengths of all mesh edges.

edge_tangents

Unit tangent vectors for all mesh edges.

edge_x_lengths

Lengths of each x edge for the entire mesh.

edge_y_lengths

Arc-lengths of each y-edge for the entire mesh.

edge_z_lengths

Lengths of each z-edges for the entire mesh.

edges

Gridded edge locations.

edges_x

Gridded x-edge locations.

edges_y

Gridded y-edge (azimuthal edge) locations.

edges_z

Gridded z-edge (vertical edge) locations.

faceDiv

faceDiv has been deprecated.

faceDivx

faceDivx has been deprecated.

faceDivy

faceDivy has been deprecated.

faceDivz

faceDivz has been deprecated.

face_areas

Face areas for the entire mesh.

face_divergence

Face divergence operator (faces to cell-centres).

face_normals

Unit normal vectors for all mesh faces.

face_x_areas

Areas of each x-face for the entire mesh.

face_x_divergence

X-derivative operator (x-faces to cell-centres).

face_y_areas

Areas of each y-face for the entire mesh.

face_y_divergence

Y-derivative operator (y-faces to cell-centres).

face_z_areas

Areas of each z-face for the entire mesh.

face_z_divergence

Z-derivative operator (z-faces to cell-centres).

faces

Gridded face locations.

faces_x

Gridded x-face (radial face) locations.

faces_y

Gridded y-face locations.

faces_z

Gridded z-face locations.

h

Cell widths along each axis direction.

h_gridded

Return dimensions of all mesh cells as staggered grid.

hx

Width of cells in the x direction.

hy

Width of cells in the y direction.

hz

Width of cells in the z direction.

isSymmetric

isSymmetric has been deprecated.

is_symmetric

Validate whether mesh is symmetric.

nCx

Number of cells in the x direction.

nCy

Number of cells in the y direction.

nCz

Number of cells in the z direction.

nNx

Number of nodes in the x-direction.

nNy

Number of nodes in the y-direction.

nNz

Number of nodes in the z-direction.

n_cells

Total number of cells in the mesh.

n_edges

Total number of edges in the mesh.

n_edges_per_direction

The number of edges in each direction.

n_edges_x

Number of x-edges in the mesh.

n_edges_y

Number of y-edges in the mesh.

n_edges_z

Total number of z-edges in the mesh.

n_faces

Total number of faces in the mesh.

n_faces_per_direction

The number of faces in each axis direction.

n_faces_x

Number of x-faces in the mesh.

n_faces_y

Number of y-faces in the mesh.

n_faces_z

Number of z-faces in the mesh.

n_nodes

Return total number of mesh nodes.

nodalGrad

nodalGrad has been deprecated.

nodalLaplacian

nodalLaplacian has been deprecated.

nodal_gradient

Nodal gradient operator (nodes to edges).

nodal_laplacian

Nodal scalar Laplacian operator (nodes to nodes).

nodes

Gridded node locations.

nodes_x

Return the x-positions of nodes along the x-direction (radial).

nodes_y

Return the y-positions of nodes along the y-direction (azimuthal).

nodes_z

Return z-coordinates of the nodes along the z-direction.

normals

normals has been deprecated.

orientation

Rotation matrix defining mesh axes relative to Cartesian.

origin

Origin or 'anchor point' of the mesh.

project_edge_to_boundary_edge

Projection matrix from all edges to boundary edges.

project_face_to_boundary_face

Projection matrix from all faces to boundary faces.

project_node_to_boundary_node

Projection matrix from all nodes to boundary nodes.

reference_is_rotated

Indicate whether mesh uses standard coordinate axes.

reference_system

Coordinate reference system.

rotation_matrix

Alias for orientation.

shape_cells

Number of cells in each coordinate direction.

shape_edges_x

Number of x-edges along each axis direction.

shape_edges_y

Number of y-edges along each axis direction.

shape_edges_z

Number of z-edges along each axis direction.

shape_faces_x

Number of x-faces along each axis direction.

shape_faces_y

Number of y-faces along each axis direction.

shape_faces_z

Number of z-faces along each axis direction.

shape_nodes

Return the number of nodes along each axis.

stencil_cell_gradient

Stencil for cell gradient operator (cell centers to faces).

stencil_cell_gradient_x

Differencing operator along x-direction (cell centers to x-faces).

stencil_cell_gradient_y

Differencing operator along y-direction (cell centers to y-faces).

stencil_cell_gradient_z

Differencing operator along z-direction (cell centers to z-faces).

tangents

tangents has been deprecated.

vectorCCx

vectorCCx has been deprecated.

vectorCCy

vectorCCy has been deprecated.

vectorCCz

vectorCCz has been deprecated.

vectorNx

vectorNx has been deprecated.

vectorNy

vectorNy has been deprecated.

vectorNz

vectorNz has been deprecated.

vol

vol has been deprecated.

x0

Alias for the origin.

Methods

cartesianGrid(*args, **kwargs)

cartesianGrid has been deprecated.

cartesian_grid([location_type, theta_shift])

Return the specified grid in cartesian coordinates.

cell_gradient_weak_form_robin([alpha, beta, ...])

Create Robin conditions pieces for weak form of the cell gradient operator (cell centers to faces).

closest_points_index(locations[, grid_loc, ...])

Find the indicies for the nearest grid location for a set of points.

copy()

Make a copy of the current mesh.

deserialize(items, **kwargs)

Create this mesh from a dictionary of attributes.

edge_divergence_weak_form_robin([alpha, ...])

Create Robin conditions pieces for weak form of the edge divergence operator (edges to nodes).

equals(other_mesh)

Compare the current mesh with another mesh to determine if they are identical.

from_omf(element)

Convert an omf object to a discretize mesh.

getBCProjWF(*args, **kwargs)

getBCProjWF has been deprecated.

getBCProjWF_simple(*args, **kwargs)

getBCProjWF_simple has been deprecated.

getEdgeInnerProduct(*args, **kwargs)

getEdgeInnerProduct has been deprecated.

getEdgeInnerProductDeriv(*args, **kwargs)

getEdgeInnerProductDeriv has been deprecated.

getFaceInnerProduct(*args, **kwargs)

getFaceInnerProduct has been deprecated.

getFaceInnerProductDeriv(*args, **kwargs)

getFaceInnerProductDeriv has been deprecated.

getInterpolationMat(*args, **kwargs)

getInterpolationMat has been deprecated.

getInterpolationMatCartMesh(*args, **kwargs)

getInterpolationMatCartMesh has been deprecated.

getTensor(*args, **kwargs)

getTensor has been deprecated.

get_BC_projections(BC[, discretization])

Create the weak form boundary condition projection matrices.

get_BC_projections_simple([discretization])

Create weak form boundary condition projection matrices for mixed boundary condition.

get_edge_inner_product([model, ...])

Generate the edge inner product matrix or its inverse.

get_edge_inner_product_deriv(model[, ...])

Get a function handle to multiply vector with derivative of edge inner product matrix (or its inverse).

get_face_inner_product([model, ...])

Generate the face inner product matrix or its inverse.

get_face_inner_product_deriv(model[, ...])

Get a function handle to multiply a vector with derivative of face inner product matrix (or its inverse).

get_interpolation_matrix(loc[, ...])

Construct interpolation matrix from mesh.

get_interpolation_matrix_cartesian_mesh(Mrect)

Construct projection matrix from CylindricalMesh to other mesh.

get_tensor(key)

Return the base 1D arrays for a specified mesh tensor.

isInside(*args, **kwargs)

isInside has been deprecated.

is_inside(pts[, location_type])

Determine which points lie within the mesh.

plotGrid(*args, **kwargs)

plotGrid has been deprecated.

plotImage(*args, **kwargs)

plotImage has been deprecated.

plotSlice(*args, **kwargs)

plotSlice has been deprecated.

plot_3d_slicer(v[, xslice, yslice, zslice, ...])

Plot slices of a 3D volume, interactively (scroll wheel).

plot_grid([ax, nodes, faces, centers, ...])

Plot the grid for nodal, cell-centered and staggered grids.

plot_image(v[, v_type, grid, view, ax, ...])

Plot quantities defined on a given mesh.

plot_slice(v[, v_type, normal, ind, ...])

Plot a slice of fields on the given 3D mesh.

point2index(locs)

Find cells that contain the given points.

projectEdgeVector(*args, **kwargs)

projectEdgeVector has been deprecated.

projectFaceVector(*args, **kwargs)

projectFaceVector has been deprecated.

project_edge_vector(edge_vectors)

Project vectors to the edges of the mesh.

project_face_vector(face_vectors)

Project vectors onto the faces of the mesh.

r(*args, **kwargs)

r has been deprecated.

reshape(x[, x_type, out_type, return_format])

Reshape tensor quantities.

save([file_name, verbose])

Save the mesh to json.

serialize()

Represent the mesh's attributes as a dictionary.

setCellGradBC(*args, **kwargs)

setCellGradBC has been deprecated.

set_cell_gradient_BC(BC)

Set boundary conditions for derivative operators acting on cell-centered quantities.

toVTK([models])

Convert mesh (and models) to corresponding VTK or PyVista data object.

to_dict()

Represent the mesh's attributes as a dictionary.

to_omf([models])

Convert to an omf data object.

to_vtk([models])

Convert mesh (and models) to corresponding VTK or PyVista data object.

validate()

Return the validation state of the mesh.

writeVTK(file_name[, models, directory])

Convert mesh (and models) to corresponding VTK or PyVista data object then writes to file.

write_vtk(file_name[, models, directory])

Convert mesh (and models) to corresponding VTK or PyVista data object then writes to file.

Galleries and Tutorials using discretize.CylindricalMesh#

Plot Mirrored Cylindrically Symmetric Model

Plot Mirrored Cylindrically Symmetric Model

Plot Mirrored Cylindrically Symmetric Model
Cylindrical meshes

Cylindrical meshes

Cylindrical meshes