BiharmonicDiffusion

BiharmonicDiffusion#

class fridom.framework.modules.closures.biharmonic_diffusion.BiharmonicDiffusion(field_flags: list[str], diffusion_coefficients: list[float | ScalarField])[source]#

Bases: HarmonicDiffusion

Biharmonic diffusion module.

Description#

Following Griffiies et al. (2000), the biharmonic mixing operator \(\mathcal{B}\) iterates twice over the harmonic mixing operator \(\mathcal{H}\). For a scalar field \(u\) it is given by:

\[\mathcal{B}(u) = - \mathcal{H} \left( \mathcal{H}(u) \right)\]

where we use the biharmonic diffusion coefficient \(\sqrt{|\kappa_i|}\). The index \(i\) refers to the direction of the diffusion.

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.

__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 biharmonic 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.