HarmonicDiffusion

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

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.FieldVariable.

diffusion_coefficientstuple[float | fr.FieldVariable]

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 | FieldVariable])

Methods

__init__(field_flags, diffusion_coefficients)
diffuse(z, dz)
diffusion_operator(u)	Applies the harmonic diffusion operator on a scalar field \(u\).
disable()	Enabling the module means that it will be executed at each time step.
enable()	Enabling the module means that it will be executed at each time step.
is_enabled()	Return whether the module is enabled or not.
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.
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.
mset	The model settings
name
required_halo

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: FieldVariable) → FieldVariable

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

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

update(mz: ModelState) → ModelState

Update the module

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 | FieldVariable]

A list of diffusion coefficients.