def main():
"""
In this simple tutorial example, the main function does all the work:
it sets the parameter values, creates and initializes a grid, sets up
the state variables, runs the main loop, and cleans up.
"""
import time
start_time = time.time()
# INITIALIZE
# User-defined parameter values
num_shells=10 # number of radial "shells" in the grid
#numcols = 30 # not needed for a radial model grid
dr = 10.0 # grid cell spacing
kd = 0.01 # diffusivity coefficient, in m2/yr
uplift_rate = 0.0001 # baselevel/uplift rate, in m/yr
num_time_steps = 1000 # number of time steps in run
# Derived parameters
dt = 0.1*dr**2 / kd # time-step size set by CFL condition
# Create and initialize a radial model grid
mg = RadialModelGrid(num_shells, dr)
# Set up scalar values: elevation and time rate of change of elevation.
# Note use of CSDMS standard names for these variables.
z = mg.add_zeros('node', 'Land_surface__elevation')
dzdt = mg.add_zeros('node', 'Land_surface__time_derivative_of_elevation')
# Get a list of the core nodes
core_nodes = mg.core_nodes
# Display a message
print( 'Running diffusion_with_radial_model_grid.py' )
print( 'Time-step size has been set to ' + str( dt ) + ' years.' )
# RUN
# Main loop
for i in range(0, num_time_steps):
# Calculate the gradients and sediment fluxes
g = mg.calculate_gradients_at_active_links(z)
qs = -kd*g
# Calculate the net deposition/erosion rate at each node
dqsds = mg.calculate_flux_divergence_at_nodes(qs)
# Calculate the total rate of elevation change
dzdt = uplift_rate - dqsds
# Update the elevations
z[core_nodes] = z[core_nodes] + dzdt[core_nodes] * dt
# FINALIZE
# Plot the points, colored by elevation
import numpy
maxelev = numpy.amax(z)
for i in range(mg.number_of_nodes):
mycolor = str(z[i]/maxelev)
pylab.plot(mg.node_x[i], mg.node_y[i], 'o', color=mycolor, ms=10)
mg.display_grid()
# Plot the points from the side, with analytical solution
pylab.figure(3)
L = num_shells*dr
xa = numpy.arange(-L, L+dr, dr)
z_analytical = (uplift_rate/(4*kd))*(L*L-xa*xa)
pylab.plot(mg.node_x, z, 'o')
pylab.plot(xa, z_analytical, 'r-')
pylab.xlabel('Distance from center (m)')
pylab.ylabel('Height (m)')
pylab.show()
end_time = time.time()
print 'Elapsed time',end_time-start_time
def main():
"""
In this simple tutorial example, the main function does all the work:
it sets the parameter values, creates and initializes a grid, sets up
the state variables, runs the main loop, and cleans up.
"""
import time
start_time = time.time()
# INITIALIZE
# User-defined parameter values
num_shells = 10 # number of radial "shells" in the grid
#numcols = 30 # not needed for a radial model grid
dr = 10.0 # grid cell spacing
kd = 0.01 # diffusivity coefficient, in m2/yr
uplift_rate = 0.0001 # baselevel/uplift rate, in m/yr
num_time_steps = 1000 # number of time steps in run
# Derived parameters
dt = 0.1 * dr**2 / kd # time-step size set by CFL condition
# Create and initialize a radial model grid
mg = RadialModelGrid(num_shells, dr)
# Set up scalar values: elevation and time rate of change of elevation.
# Note use of CSDMS standard names for these variables.
z = mg.add_zeros('node', 'Land_surface__elevation')
dzdt = mg.add_zeros('node', 'Land_surface__time_derivative_of_elevation')
# Get a list of the core nodes
core_nodes = mg.core_nodes
# Display a message
print('Running diffusion_with_radial_model_grid.py')
print('Time-step size has been set to ' + str(dt) + ' years.')
# RUN
# Main loop
for i in range(0, num_time_steps):
# Calculate the gradients and sediment fluxes
g = mg.calculate_gradients_at_active_links(z)
qs = -kd * g
# Calculate the net deposition/erosion rate at each node
dqsds = mg.calculate_flux_divergence_at_nodes(qs)
# Calculate the total rate of elevation change
dzdt = uplift_rate - dqsds
# Update the elevations
z[core_nodes] = z[core_nodes] + dzdt[core_nodes] * dt
# FINALIZE
# Plot the points, colored by elevation
import numpy
maxelev = numpy.amax(z)
for i in range(mg.number_of_nodes):
mycolor = str(z[i] / maxelev)
pylab.plot(mg.node_x[i], mg.node_y[i], 'o', color=mycolor, ms=10)
mg.display_grid()
# Plot the points from the side, with analytical solution
pylab.figure(3)
L = num_shells * dr
xa = numpy.arange(-L, L + dr, dr)
z_analytical = (uplift_rate / (4 * kd)) * (L * L - xa * xa)
pylab.plot(mg.node_x, z, 'o')
pylab.plot(xa, z_analytical, 'r-')
pylab.xlabel('Distance from center (m)')
pylab.ylabel('Height (m)')
pylab.show()
end_time = time.time()
print 'Elapsed time', end_time - start_time
