4.2.5. pde.grids.cylindrical module¶
Cylindrical grids with azimuthal symmetry
- class CylindricalSymGrid(radius, bounds_z, shape, periodic_z=False)[source]¶
Bases:
GridBase
3-dimensional cylindrical grid assuming polar symmetry
The polar symmetry implies that states only depend on the radial and axial coordinates \(r\) and \(z\), respectively. These are discretized uniformly as
\begin{align*} r_i &= \left(i + \frac12\right) \Delta r &&\quad \text{for} \quad i = 0, \ldots, N_r - 1 &&\quad \text{with} \quad \Delta r = \frac{R}{N_r} \\ z_j &= z_\mathrm{min} + \left(j + \frac12\right) \Delta z &&\quad \text{for} \quad j = 0, \ldots, N_z - 1 &&\quad \text{with} \quad \Delta z = \frac{z_\mathrm{max} - z_\mathrm{min}}{N_z} \end{align*}where \(R\) is the radius of the cylindrical grid, \(z_\mathrm{min}\) and \(z_\mathrm{max}\) denote the respective lower and upper bounds of the axial direction, so that \(z_\mathrm{max} - z_\mathrm{min}\) is the total height. The two axes are discretized by \(N_r\) and \(N_z\) support points, respectively.
Warning
The order of components in the vector and tensor fields defined on this grid is different than in ordinary math. While it is common to use \((r, \phi, z)\), we here use the order \((r, z, \phi)\). It might thus be best to access components by name instead of index, e.g., use
field['z']
instead offield[1]
.- Parameters
radius (float) – The radius of the cylinder
bounds_z (tuple) – The lower and upper bound of the z-axis
shape (tuple) – The number of support points in r and z direction, respectively. The same number is used for both if a single value is given.
periodic_z (bool) – Determines whether the z-axis has periodic boundary conditions.
- axes_symmetric: List[str] = ['phi']¶
The names of the additional axes that the fields do not depend on, e.g. along which they are constant.
- Type
- boundary_names: Dict[str, Tuple[int, bool]] = {'bottom': (1, False), 'inner': (0, False), 'outer': (0, True), 'top': (1, True)}¶
Names of boundaries to select them conveniently
- Type
- cell_volume_data: Sequence[FloatNumerical]¶
Information about the size of discretization cells
- Type
- classmethod from_bounds(bounds, shape, periodic)[source]¶
- Parameters
bounds (tuple) – Give the coordinate range for each axis. This should be a tuple of two number (lower and upper bound) for each axis. The length of bounds must be 2.
shape (tuple) – The number of support points for each axis. The length of shape needs to be 2.
periodic (bool or list) – Specifies which axes possess periodic boundary conditions. The first entry is ignored.
- Returns
CylindricalGrid representing the region chosen by bounds
- Return type
- classmethod from_state(state)[source]¶
create a field from a stored state.
- Parameters
state (dict) – The state from which the grid is reconstructed.
- Return type
- get_cartesian_grid(mode='valid')[source]¶
return a Cartesian grid for this Cylindrical one
- Parameters
mode (str) – Determines how the grid is determined. Setting it to ‘valid’ only returns points that are fully resolved in the cylindrical grid, e.g., the cylinder is circumscribed. Conversely, ‘full’ returns all data, so the cylinder is inscribed.
- Returns
The requested grid
- Return type
- get_line_data(data, extract='auto')[source]¶
return a line cut for the cylindrical grid
- Parameters
data (
ndarray
) – The values at the grid pointsextract (str) –
Determines which cut is done through the grid. Possible choices are (default is cut_axial):
cut_z or cut_axial: values along the axial coordinate for \(r=0\).
project_z or project_axial: average values for each axial position (radial average).
project_r or project_radial: average values for each radial position (axial average)
- Returns
A dictionary with information about the line cut, which is convenient for plotting.
- Return type
- get_random_point(*, boundary_distance=0, avoid_center=False, coords='cartesian', rng=None)[source]¶
return a random point within the grid
Note that these points will be uniformly distributed on the radial axis, which implies that they are not uniformly distributed in the volume.
- Parameters
boundary_distance (float) – The minimal distance this point needs to have from all boundaries.
avoid_center (bool) – Determines whether the boundary distance should also be kept from the center, i.e., whether points close to the center are returned.
coords (str) – Determines the coordinate system in which the point is specified. Valid values are cartesian, cell, and grid; see
transform()
.rng (
Generator
) – Random number generator (default:default_rng()
)
- Returns
The coordinates of the point
- Return type
- iter_mirror_points(point, with_self=False, only_periodic=True)[source]¶
generates all mirror points corresponding to point
- point_from_cartesian(points)[source]¶
convert points given in Cartesian coordinates to this grid
This function returns points restricted to the x-z plane, i.e., the y-coordinate will be zero.
- point_to_cartesian(points, *, full=False)[source]¶
convert coordinates of a point to Cartesian coordinates
- polar_coordinates_real(origin, *, ret_angle=False)[source]¶
return spherical coordinates associated with the grid
- Parameters
origin (
ndarray
) – Coordinates of the origin at which the polar coordinate system is anchored. Note that this must be of the form [0, 0, z_val], where only z_val can be chosen freely.ret_angle (bool) – Determines whether the azimuthal angle is returned alongside the distance. If False only the distance to the origin is returned for each support point of the grid. If True, the distance and angles are returned.
- Return type
- slice(indices)[source]¶
return a subgrid of only the specified axes
- Parameters
indices (list) – Indices indicating the axes that are retained in the subgrid
- Returns
CartesianGrid
orPolarSymGrid
: The subgrid- Return type