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