bluemira.equilibria.grid

Grid object and operations for equilibria.

Classes

Grid

A rectangular Grid object with regular rectangular cells for use in finite

Functions

`integrate_dx_dz`(func, d_x, d_z)	Get the double-integral of a function over the space.
`volume_integral`(func, x, d_x, d_z)	Calculate the volume integral of a field in quasi-cylindrical coordinates.
`revolved_volume`(x, z)	Calculate the revolved volume of a set of x, z coordinates. Revolution about

Module Contents

class bluemira.equilibria.grid.Grid(x_min: float, x_max: float, z_min: float, z_max: float, nx: int, nz: int)

A rectangular Grid object with regular rectangular cells for use in finite difference calculations.

Parameters:

x_min (float) – Minimum x grid coordinate (>0) [m]
x_max (float) – Maximum x grid coordinate [m]
z_min (float) – Minimum z grid coordinate [m]
z_max (float) – Maximum z grid coordinate [m]
nx (int) – Number of x grid points
nz (int) – Number of z grid points

__slots__ = ('bounds', 'dx', 'dz', 'edges', 'nx', 'nz', 'step', 'x', 'x_1d', 'x_max', 'x_mid', 'x_min',...

x_min

x_max

x_size

x_mid

z_min

z_max

z_size

z_mid

x_1d

z_1d

dx: float

dz: float

bounds

edges

step

regrid(nx: int, nz: int) → Grid

Reinitialise the grid with different x and z discretisation

Parameters:

nx (int) – number of x grid points
nz (int) – number of z grid points

Returns:

New grid object

Return type:

Grid

classmethod from_eqdict(e) → Grid

Initialise a Grid object from an EQDSK dictionary.

Parameters:: e (dict) – EQDSK dictionary
Return type:: Grid

classmethod from_eqdsk(e: eqdsk.EQDSKInterface) → Grid

Initialise a Grid object from an EQDSKInterface.

Parameters:: e (eqdsk.EQDSKInterface)
Return type:: Grid

point_inside(x: float | collections.abc.Iterable[float], z: float | None = None) → bool

Determine if a point is inside the rectangular grid (includes edges).

Parameters:

x (float | collections.abc.Iterable[float]) – The x coordinate of the point. Or the 2-D point.
z (float | None) – The z coordinate of the point

Returns:

inside – Whether or not the point is inside the grid

Return type:

bool

distance_to(x: float | collections.abc.Iterable[float], z: float | None = None) → numpy.typing.NDArray[numpy.float64]

Get the distances of a point to the edges of the Grid.

Parameters:

x (float | collections.abc.Iterable[float]) – The x coordinate of the point. Or the 2-D point.
z (float | None) – The z coordinate of the point

Returns:

Distances to the edges of the Grid.

Return type:

distances

plot(ax=None, **kwargs)

Plot the Grid object onto an ax.

Returns:: The plot axis

bluemira.equilibria.grid.integrate_dx_dz(func, d_x, d_z)

Get the double-integral of a function over the space.

\(\int_Z\int_X f(x, z) dXdZ\)

Parameters:

func (np.array(N, M)) – A 2-D function map
d_x (float) – The discretisation size in the X coordinate
d_z (float) – The discretisation size in the Z coordinate

Returns:

integral – The integral value of the field in 2-D

Return type:

float

bluemira.equilibria.grid.volume_integral(func, x, d_x, d_z)

Calculate the volume integral of a field in quasi-cylindrical coordinates.

Parameters:

func (2-D np.array) – Field to volume integrate
x (2-D np.array) – X coordinate grid
d_x (float) – Grid X cell size
d_z (float) – Grid Z cell size

Returns:

integral – The integral value of the field in 3-D space

Return type:

float

bluemira.equilibria.grid.revolved_volume(x, z)

Calculate the revolved volume of a set of x, z coordinates. Revolution about [0, 0, 1].

Parameters:

x (np.array) – The x coordinates
z (np.array) – The z coordinates

Returns:

volume – The volume of the revolved x, z coordinates

Return type:

float