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)

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

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.
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.
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.
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.
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.
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

Reflecting Wave Package

Reflecting Wave Package

Internal Gravity Wave Maker

Internal Gravity Wave Maker

Convection and Closures

Convection and Closures

Multiple Wave Makers

Multiple Wave Makers

Rayleigh-Taylor Instability

Rayleigh-Taylor Instability

Rayleigh-Bénard Convection

Rayleigh-Bénard Convection

Single Internal Wave

Single Internal Wave

Dancing Eddies

Dancing Eddies

Symmetric Instability

Symmetric Instability

Tracers and Eddies

Tracers and Eddies

Barotropic Instability

Barotropic Instability

setup(mset: ModelSettingsBase, req_halo: int | None = None, fft_module: FFT | None = None) → None

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]

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

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

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]

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.

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.