Grid

Grid#

class fridom.framework.grid.cartesian.grid.Grid(N: list[int], L: list[float], periodic_bounds: list[bool] | None = None, domain_decomp: DomainDecomposition | None = None, diff_mod: DiffModule | None = None, interp_mod: InterpolationModule | None = None)[source]#

Bases: GridBase

An n-dimensional cartesian grid with capabilities for fourier transforms.

Description#

The cartesian grid is a regular grid with constant grid spacing in each direction. The grid can be periodic in some directions and non-periodic in others.

Parameters#

Ntuple[int]

Number of grid points in each direction.

Ltuple[float]

Domain size in meters in each direction.

periodic_boundstuple[bool], (default: None)

A list of booleans that indicate whether the axis is periodic. If True, the axis is periodic, if False, the axis is non-periodic. Default is True for all axes.

shared_axeslist[int], (default: None)

A list of integers that indicate which axes are shared among MPI ranks. Default is None, which means that no fourier transforms are available.

diff_modDiffModule, (default: None)

A module that contains the differentiation operators. If None, the finite differences module is used.

interp_modInterpolationModule, (default: None)

A module that contains the interpolation methods. If None, the linear interpolation module is used.

Examples#

import fridom.framework as fr
# construct a 3D grid:
grid = fr.grid.CartesianGrid(
    N=(32, 32, 8),  # 32x32x8 grid points
    L=(100.0, 100.0, 10.0),  # 100m x 100m x 10m domain
    periodic_bounds=(True, True, False),  # non-periodic in z
    shared_axes=[0, 1]  # slab decomposition, shared in x and y
    )
# setup the grid using the model settings
mset = fr.ModelSettingsBase(grid)
mset.setup()
# get the meshgrids
X, Y, Z = grid.X  # physical meshgrid of the local domain
KX, KY, KZ = grid.K  # spectral meshgrid of the local domain
# get the grid spacing
dx, dy, dz = grid.dx
__init__(N: list[int], L: list[float], periodic_bounds: list[bool] | None = None, domain_decomp: DomainDecomposition | None = None, diff_mod: DiffModule | None = None, interp_mod: InterpolationModule | None = None) → None[source]#

Methods

__init__(N, L[, periodic_bounds, ...])

create_array([pad, spectral, topo])

Create an array.

create_random_array([seed, pad, spectral, topo])

Create a random array.

cumulative_integral(field, axis[, direction])

Compute the cumulative integral of a field along a given axis.

fft(arr[, padding, bc_types, positions, axes])

Perform a (fast) fourier transform on the input array.

get_mesh([position, spectral])

Get the meshgrid of the grid points.

ifft(arr[, padding, bc_types, positions, axes])

Perform an inverse (fast) fourier transform on the input array.

integrate(field[, axes])

Integrate a scalar field over a given domain.

max(field[, axes])

Compute the maximum of a field over the given axes.

min(field[, axes])

Compute the minimum of a field over the given axes.

omega(k[, use_discrete])

Compute the dispersion relation of the model.

pad(arr)

Add halo padding to an array.

setup(mset[, req_halo, fft_module])

Initialize the grid from the model settings.

sum(field[, axes])

Sum a field over the given axes.

sync(arr[, flat_axes])

Synchronize the halo (boundary) points of an array across all MPI ranks.

sync_multi(arrs)

Synchronize the halo (boundary) points of multiple arrays across all MPI ranks.

unpad(arr)

Remove the halo padding from an array.

vec_p(s[, use_discrete])

Computes the projection vector of the linear operator of the mode s.

vec_q(s[, use_discrete])

Computes the eigenvector of the linear operator of the mode s.

Attributes

K

Spectral meshgrid on the local domain.

L

Domain size in each direction.

N

Grid points in each direction.

X

The meshgrid of the grid points.

cell_center

The position of the cell centers.

characteristic_function

The characteristic function of the grid (1 inside the domain, 0 outside).

dV

The volume element of the grid.

diff_module

The differential operator module.

domain_decomp

The domain decomposition object.

dx

The grid spacing in each dimension.

fourier_transform_available

Indicates whether the grid supports fast fourier transforms.

halo

The halo size of the grid.

info

Return a dictionary with information about the grid.

interp_module

The interpolation operator module.

k_global

Global spectral k-vectors.

k_local

Spectral k-vectors on the local domain.

mpi_available

Indicates whether the grid supports MPI parallelization.

mset

The model settings object.

n_dims

The number of dimensions of the grid.

omega_analytical

Analytical dispersion relation.

omega_space_discrete

Dispersion relation with space-discretization effects.

omega_time_discrete

Dispersion relation with space-time-discretization effects.

periodic_bounds

A tuple of booleans indicating whether the grid is periodic in each dimension.

spectral_grid

Indicates whether the grid is a spectral grid.

total_grid_points

The total number of grid points in the grid.

water_mask

Get the water mask.

x_global

The x-vector of the global grid points.

Examples using fridom.framework.grid.cartesian.Grid#

Barotropic Jet

Barotropic Jet

Convection and Closures

Convection and Closures

Dancing Eddies

Dancing Eddies

Internal Gravity Wave Maker

Internal Gravity Wave Maker

Multiple Wave Makers

Multiple Wave Makers

Rayleigh-Bénard Convection

Rayleigh-Bénard Convection

Rayleigh-Taylor Instability

Rayleigh-Taylor Instability

Single Internal Wave

Single Internal Wave

Symmetric Instability

Symmetric Instability

Tracers and Eddies

Tracers and Eddies

Reflecting Wave Package

Reflecting Wave Package

Barotropic Instability.

Barotropic Instability.

Equatorial Waves.

Equatorial Waves.
setup(mset: ModelSettingsBase, req_halo: int | None = None, fft_module: FFT | None = None) → None[source]#

Initialize the grid from the model settings.

Parameters#

msetModelSettingsBase

The model settings object. This is for example needed to determine the required halo size.

get_mesh(position: Position | None = None, spectral: bool = False) → tuple[ndarray][source]#

Get the meshgrid of the grid points.

Parameters#

positionPosition or None (default: None)

The position of the field.

spectralbool (default: False)

Whether to return the meshgrid of the spectral domain.

Returns#

tuple[ndarray]

The meshgrid of the grid points.

fft(arr: ndarray, padding=FFTPadding.NOPADDING, bc_types: tuple[BCType] | None = None, positions: tuple[AxisPosition] | None = None, axes: tuple[int] | None = None) → ndarray[source]#

Perform a (fast) fourier transform on the input array.

Parameters#

arrndarray

The input array.

paddingFFTPadding (default: FFTPadding.NOPADDING)

The padding to apply to the array.

bc_typestuple[BCType] or None (default: None)

The boundary conditions to apply to each axis.

positionstuple[AxisPosition] or None (default: None)

The position of the field.

axestuple[int] or None (default: None)

The axes to transform.

Returns#

ndarray

The transformed array.

ifft(arr: ndarray, padding=FFTPadding.NOPADDING, bc_types: tuple[BCType] | None = None, positions: tuple[AxisPosition] | None = None, axes: tuple[int] | None = None) → ndarray[source]#

Perform an inverse (fast) fourier transform on the input array.

Parameters#

arrndarray

The input array.

paddingFFTPadding (default: FFTPadding.NOPADDING)

The padding to apply to the array.

bc_typestuple[BCType] or None (default: None)

The boundary conditions to apply to each axis.

positionstuple[AxisPosition] or None (default: None)

The position of the field.

axestuple[int] or None (default: None)

The axes to transform.

Returns#

ndarray

The transformed array.

sync_multi(arrs: tuple[ndarray]) → tuple[ndarray][source]#

Synchronize the halo (boundary) points of multiple arrays across all MPI ranks.

Parameters#

arrslist[ndarray]

The list of arrays to synchronize.

Returns#

list[ndarray]

The synchronized list of arrays.

sum(field: ScalarField, axes: tuple[int] | None = None) → ScalarField[source]#

Sum a field over the given axes.

Parameters#

fieldScalarField

The field to sum.

axestuple[int] or None (default: None)

The axes to sum over. If None, all axes are summed over.

Returns#

ScalarField

The summed field with no extend in the summed axes.

max(field: ScalarField, axes: tuple[int] | None = None) → ScalarField[source]#

Compute the maximum of a field over the given axes.

Parameters#

fieldScalarField

The field to compute the maximum.

axestuple[int] or None (default: None)

The axes to compute the maximum over. If None, all axes are used.

Returns#

ScalarField

The field with the maximum value in the given axes.

min(field: ScalarField, axes: tuple[int] | None = None) → ScalarField[source]#

Compute the minimum of a field over the given axes.

Parameters#

fieldScalarField

The field to compute the minimum.

axestuple[int] or None (default: None)

The axes to compute the minimum over. If None, all axes are used.

Returns#

ScalarField

The field with the minimum value in the given axes.

integrate(field: ScalarField, axes: tuple[int] | None = None) → ScalarField[source]#

Integrate a scalar field over a given domain.

Parameters#

fieldScalarField

The field to integrate.

axestuple[int] or None (default: None)

The axes to integrate over.

Returns#

ScalarField

The integrated field with no extend in the integrated axes.

cumulative_integral(field: ScalarField, axis: int, direction: Literal['forward', 'backward'] = 'forward') → ScalarField[source]#

Compute the cumulative integral of a field along a given axis.

Description#

The cumulative integral computes the integral starting at one end of the domain and accumulates the integral along the specified axis. The integral is computed in either the forward or backward direction.

Forward integral:

\[F(x) = \int_{x_0}^{x} f(x') dx'\]

with axis \(x\) and \(x_0\) the lower bound of the domain.

Backward integral:

\[F(x) = \int_{x}^{x_1} f(x') dx'\]

with axis \(x\) and \(x_1\) the upper bound of the domain.

Parameters#

fieldScalarField

The field to integrate.

axisint

The axis to integrate over.

directionstr (default is “forward”)

The direction of the integration. Can be “forward” or “backward”.

Returns#

ScalarField

The cumulative integral of the field along the given axis.

property info: dict#

Return a dictionary with information about the grid.

Description#

This method should be overridden by the child class to return a dictionary with information about the grid. This information is used to print the grid in the __repr__ method.

property L: tuple#

Domain size in each direction.

property N: tuple#

Grid points in each direction.

property K: tuple | None#

Spectral meshgrid on the local domain.

property k_local: tuple | None#

Spectral k-vectors on the local domain.

property k_global: tuple | None#

Global spectral k-vectors.

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