DiffModule

class fridom.framework.grid.DiffModule

Bases: Module

Base class for differentiation modules.

Description

A differentiation module is a class that computes derivatives of a field, for example the partial derivative in a specific direction, or the gradient of a field, or divergence of a vector etc.

__init__() → None

Methods

__init__()
diff(f, axis[, order])	Compute the partial derivative of a field along an axis.
disable()	Enabling the module means that it will be executed at each time step.
div(vec)	Compute the divergence of a vector field.
enable()	Enabling the module means that it will be executed at each time step.
grad(f[, axes])	Compute the gradient of a field.
is_enabled()	Return whether the module is enabled or not.
laplacian(f[, axes])	Compute the Laplacian of a scalar field.
reset()	Stop and start the module.
setup(mset)	Start the module
start()	Start the module
stop()	Stop the module
update(mz)	Update the module

Attributes

diff_module	The differentiation module to be used by this module.
grid	The grid of the model settings
info	Return a dictionary with information about the time stepper.
interp_module	The interpolation module to be used by this module.
mset	The model settings
name
required_halo

name = 'Diff. Module'

abstract diff(f: FieldVariable, axis: int, order: int = 1) → FieldVariable

Compute the partial derivative of a field along an axis.

\[\partial_i^n f\]

with axis \(i\) and order \(n\).

Parameters

ffr.FieldVariable

The field to differentiate.

axisint

The axis along which to differentiate.

orderint

The order of the derivative. Default is 1.

Returns

fr.FieldVariable

The derivative of the field along the specified axis.

grad(f: FieldVariable, axes: list[int] | None = None) → tuple[FieldVariable | None]

Compute the gradient of a field.

\[\begin{split}\nabla f = \begin{pmatrix} \partial_1 f \\ \dots \\ \partial_n f \end{pmatrix}\end{split}\]

Parameters

ffr.FieldVariable

The field to differentiate.

axeslist[int] | None (default is None)

The axes along which to compute the gradient. If None, the gradient is computed along all axes.

Returns

tuple[fr.FieldVariable | None]

The gradient of the field along the specified axes. The list contains the gradient components along each axis. Axis which are not included in axes will have a value of None. E.g. for a 3D grid, diff.grad(f, axes=[0, 2]) will return [df/dx, None, df/dz].

div(vec: tuple[FieldVariable | None]) → FieldVariable

Compute the divergence of a vector field.

\[\nable \cdot \boldsymbol{v} = \sum_{i=1}^n \partial_i v_i\]

Parameters

vectuple[fr.FieldVariable | None]

The vector field to compute the divergence of. Tuple entries that are None are ignored (for example to calculate 2D divergence in a 3D system).

Returns

fr.FieldVariable

The divergence of the field.

Examples

# Create diff module (Let mset be a ModelSettingsBase object)
diff = DiffModule(...)
diff.setup(mset)
# let u, v, w be the components of the vector field
# Calculate 3D divergence
div = diff.div((u, v, w))
# Calculate 2D horizontal divergence
div = diff.div((u, v, None))

laplacian(f: FieldVariable, axes: tuple[int] | None = None) → FieldVariable

Compute the Laplacian of a scalar field.

\[\nabla^2 f = \sum_{i=1}^n \partial_i^2 f\]

Parameters

ffr.FieldVariable

The field to differentiate.

axestuple[int] | None (default is None)

The axes along which to compute the Laplacian. If None, the Laplacian is computed along all axes.

Returns

fr.FieldVariable

The Laplacian of the field.