PerronNLDiffuse: Model soil creep using implicit solution to nonlinear diffusion law#

class PerronNLDiffuse(*args, **kwds)[source]#

Bases: Component

Nonlinear diffusion, following Perron (2011).

This module uses Taylor Perron’s implicit (2011) method to solve the nonlinear hillslope diffusion equation across a rectangular, regular grid for a single timestep. Note it works with the mass flux implicitly, and thus does not actually calculate it. Grid must be at least 5x5.

Boundary condition handling assumes each edge uses the same BC for each of its nodes. This component cannot yet handle looped boundary conditions, but all others should be fine.

This component has KNOWN STABILITY ISSUES which will be resolved in a future release; use at your own risk.

The primary method of this class is run_one_step.

Examples

>>> from landlab.components import PerronNLDiffuse
>>> from landlab import RasterModelGrid
>>> import numpy as np
>>> mg = RasterModelGrid((5, 5))
>>> z = mg.add_zeros("topographic__elevation", at="node")
>>> nl = PerronNLDiffuse(mg, nonlinear_diffusivity=1.)
>>> dt = 100.
>>> nt = 20
>>> uplift_rate = 0.001
>>> for i in range(nt):
...     z[mg.core_nodes] += uplift_rate*dt
...     nl.run_one_step(dt)
>>> z_target = np.array(
...     [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,
...       0.        ,  0.00778637,  0.0075553 ,  0.00778637,  0.        ,
...       0.        ,  0.0075553 ,  0.0078053 ,  0.0075553 ,  0.        ,
...       0.        ,  0.00778637,  0.0075553 ,  0.00778637,  0.        ,
...       0.        ,  0.        ,  0.        ,  0.        ,  0.        ])
>>> np.allclose(z, z_target)
True

References

Required Software Citation(s) Specific to this Component

None Listed

Additional References

Perron, J. (2011). Numerical methods for nonlinear hillslope transport laws. Journal of Geophysical Research 116(F2), 23 - 13. https://dx.doi.org/10.1029/2010jf001801

Parameters
  • grid (RasterModelGrid) – A Landlab raster grid

  • nonlinear_diffusivity (float, array or field name) – The nonlinear diffusivity

  • S_crit (float (radians)) – The critical hillslope angle

  • rock_density (float (kg*m**-3)) – The density of intact rock

  • sed_density (float (kg*m**-3)) – The density of the mobile (sediment) layer

__init__(grid, nonlinear_diffusivity=0.01, S_crit=0.5759586531581288, rock_density=2700.0, sed_density=2700.0)[source]#
Parameters
  • grid (RasterModelGrid) – A Landlab raster grid

  • nonlinear_diffusivity (float, array or field name) – The nonlinear diffusivity

  • S_crit (float (radians)) – The critical hillslope angle

  • rock_density (float (kg*m**-3)) – The density of intact rock

  • sed_density (float (kg*m**-3)) – The density of the mobile (sediment) layer

run_one_step(dt)[source]#

Run the diffuser for one timestep, dt.

This is the primary method of the class.

Parameters

dt (float (time)) – The imposed timestep.

updated_boundary_conditions()[source]#

Call if grid BCs are updated after component instantiation.