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. """ # INITIALIZE # User-defined parameter values numrows = 7 # number of rows in the grid basenumcols = 6 # number of columns in the grid dx = 10.0 # grid cell spacing kd = 0.01 # diffusivity coefficient, in m2/yr uplift_rate = 0.001 # baselevel/uplift rate, in m/yr num_time_steps = 1000 # number of time steps in run # Derived parameters dt = 0.1*dx**2 / kd # time-step size set by CFL condition # Create and initialize a raster model grid mg = HexModelGrid(numrows, basenumcols, dx) # Set up scalar values: elevation and elevation time derivative 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_model_hex_grid.py' ) print( 'Time-step size has been set to ' + str( dt ) + ' years.' ) start_time = time.time() # 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 import numpy # Test solution for a 1-cell hex grid if mg.number_of_nodes==7: # single cell with 6 boundaries perimeter = dx*6*(numpy.sqrt(3.)/3.) flux = kd*(numpy.amax(z)/dx) total_outflux = perimeter*flux total_influx = mg.cell_areas*uplift_rate # just one cell ... print 'total influx=',total_influx,'total outflux=',total_outflux print('Run time = '+str(time.time()-start_time)+' seconds') # Plot the points, colored by elevation pylab.figure() 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=50) pylab.show() mg.display_grid()