Relaxation

class fridom.framework.modules.forcings.relaxation.Relaxation(tau: float, field_name: str, target: float | ScalarField, domain_function: callable)

Bases: Module

A relaxation module for scalar fields.

Description

This module implements the relaxation operator \(\mathcal{R}(\phi)\) for a scalar field \(\phi\). The relaxation operator is defined as:

\[\mathcal{R}(\phi) = \frac{\phi^* - \phi}{\tau} \delta_\Omega\]

where \(\phi^*\) is the target value of the field, \(\tau\) is the relaxation time scale, and \(\delta_\Omega\) is one on the domain \(\Omega\) and zero elsewhere. At each time step, \(\mathcal{R}(\phi)\) is added to the tendency of the field \(\phi\). The analytical solution of the relaxation operator with no other forcing terms is:

\[ \begin{align}\begin{aligned}\partial_t \phi = \frac{\phi^* - \phi}{\tau}\\\Rightarrow \phi(t) = \phi^* + C e^{-t/\tau}\end{aligned}\end{align} \]

with a constant \(C\).

The relaxation operator can be used to add heating or cooling to a fluid, but also for example for wind stress forcing.

Parameters

taufloat

The relaxation time scale \(\tau\).

field_namestr

The name of the field that should be relaxed.

targetfloat | fr.ScalarField

The target value of the field.

domain_functioncallable

A function that takes the mesh as input and returns a boolean array that indicates the domain where the relaxation should be applied.

__init__(tau: float, field_name: str, target: float | ScalarField, domain_function: callable) → None

Methods

__init__(tau, field_name, target, ...)
disable()	Disable the module.
enable()	Enable the module.
is_enabled()	Whether the module is enabled or not.
relax(z, dz)
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.

Examples using fridom.framework.modules.forcings.Relaxation

Rayleigh-Bénard Convection

Rayleigh-Bénard Convection

name = 'Relaxation'

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.

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