CenteredAdvection

class fridom.framework.modules.advection.centered_advection.CenteredAdvection

Bases: AdvectionBase

Centered advection scheme.

Description

For the centered advection scheme, we assume that the velocity field is divergence-free. The advection term can then be written as:

\[\mathcal{A}(\boldsymbol{v}, q) = -\boldsymbol{v} \cdot \nabla q = - \nabla \cdot (\boldsymbol{v} q)\]

where \(q\) is the quantity to be advected and \(\boldsymbol{v}\) is the velocity field. The flux divergence \(\nabla \cdot (\boldsymbol{v} q)\) is calculated using forward or backward differences. For that the flux is interpolated to the cell faces of the quantity \(q\):

            Position of the quantity q
                        ↓
|       x       |       x       |       x       |
                ↑
    Position of the flux Fx

__init__() → None

Methods

__init__()
advect_state(z, dz)
advection(velocity, quantity)	Advect a quantity using the given velocity field.
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

background	The background state.
diff_module	The differentiation module to be used by this module.
disable_nonlinear	Whether to disable advection by the state vector itself.
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
scaling	A scaling factor for the nonlinear terms (default: 1.0)

name = 'Centered Advection'

advection(velocity: tuple[FieldVariable], quantity: FieldVariable) → FieldVariable

Advect a quantity using the given velocity field.