HarmonicDiffusion

class fridom.framework.modules.closures.harmonic_diffusion.HarmonicDiffusion(field_flags: list[str], diffusion_coefficients: list[float | ScalarField])

Bases: Module

Harmonic diffusion module.

Description

The harmonic diffusion operator \(\mathcal{H}\) on a scalar field \(u\) is given by:

\[\mathcal{H}(u) = \nabla \cdot \left (\mathbf{A} \cdot \nabla u \right)\]

with the diagonal diffusion tensor \(\mathbf{A}\) given by:

\[\begin{split}\mathbf{A} = \begin{pmatrix} \kappa_1 & \dots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \dots & \kappa_n \end{pmatrix}\end{split}\]

where \(\kappa_i\) is the harmonic diffusion coefficient in the \(i\)-th direction.

Parameters

field_flagslist[str]

A list of strings that indicate which fields should be diffused. For example, if field_flags=[“ENABLE_MIXING”], all fields with the flag “ENABLE_MIXING” will be diffused. For more information on possible flags, see fridom.framework.ScalarField.

diffusion_coefficientstuple[float | fr.ScalarField]

A tuple of diffusion coefficients. The length of the tuple must match the number of dimensions of the grid.

namestr, (default=”Harmonic Diffusion”)

Name of the module.

__init__(field_flags: list[str], diffusion_coefficients: list[float | ScalarField]) → None

Methods

__init__(field_flags, diffusion_coefficients)
diffuse(z, dz)
diffusion_operator(u)	Apply the harmonic diffusion operator on a scalar field \(u\).
disable()	Disable the module.
enable()	Enable the module.
is_enabled()	Whether the module is enabled or not.
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.
diffusion_coefficients	A list of diffusion coefficients.
field_flags	A list of field flags that indicate which fields should be diffused.
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.

Examples using fridom.framework.modules.closures.HarmonicDiffusion

Convection and Closures

Convection and Closures

Dancing Eddies

Dancing Eddies

Barotropic Instability.

Barotropic Instability.

name = 'Harmonic Diffusion'

diffusion_operator(u: ScalarField) → ScalarField

Apply the harmonic diffusion operator on a scalar field \(u\).

diffuse(z: VectorField, dz: VectorField) → VectorField

update(mz: ModelState) → ModelState

Update the model state.

Description

This method is called by the model at each time step. Child classes should overwrite this method to update the module. Make sure to decorate the method with the @module_method decorator.

Parameters

mzfr.ModelState

The model state at the current time step.

Returns

fr.ModelState

The updated model state.

property field_flags: list[str]

A list of field flags that indicate which fields should be diffused.

property diffusion_coefficients: list[float | ScalarField]

A list of diffusion coefficients.