DiffModule

DiffModule#

class fridom.framework.grid.DiffModule[source]#

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()

Disable the module.

div(vec)

Compute the divergence of a vector field.

enable()

Enable the module.

grad(f[, axes])

Compute the gradient of a field.

is_enabled()

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[, setup_mode])

Set the module up.

start()

Start the module.

stop()

Stop the module.

update(mz)

Update the model state.

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.

is_setup

Whether the module is set up.

mset

The model settings.

name

required_halo

The required halo points for this module.
name = 'Diff. Module'#
abstract diff(f: ScalarField, axis: int, order: int = 1) → ScalarField[source]#

Compute the partial derivative of a field along an axis.

\[\partial_i^n f\]

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

Parameters#

ffr.ScalarField

The field to differentiate.

axisint

The axis along which to differentiate.

orderint

The order of the derivative. Default is 1.

Returns#

fr.ScalarField

The derivative of the field along the specified axis.

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

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.ScalarField

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.ScalarField | 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[ScalarField | None]) → ScalarField[source]#

Compute the divergence of a vector field.

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

Parameters#

vectuple[fr.ScalarField | 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.ScalarField

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

Compute the Laplacian of a scalar field.

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

Parameters#

ffr.ScalarField

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.ScalarField

The Laplacian of the field.

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