import importlib
import numpy as np
import matplotlib.pyplot as plt
import advection.advective_fluxes as flx
import mesh.patch as patch
from simulation_null import NullSimulation, grid_setup, bc_setup
[docs]class Simulation(NullSimulation):
[docs] def initialize(self):
"""
Initialize the grid and variables for advection and set the initial
conditions for the chosen problem.
"""
my_grid = grid_setup(self.rp, ng=4)
# create the variables
my_data = patch.CellCenterData2d(my_grid)
bc = bc_setup(self.rp)[0]
my_data.register_var("density", bc)
my_data.create()
self.cc_data = my_data
# now set the initial conditions for the problem
problem = importlib.import_module("advection.problems.{}".format(self.problem_name))
problem.init_data(self.cc_data, self.rp)
[docs] def method_compute_timestep(self):
"""
Compute the advective timestep (CFL) constraint. We use the
driver.cfl parameter to control what fraction of the CFL
step we actually take.
"""
cfl = self.rp.get_param("driver.cfl")
u = self.rp.get_param("advection.u")
v = self.rp.get_param("advection.v")
# the timestep is min(dx/|u|, dy/|v|)
xtmp = self.cc_data.grid.dx/max(abs(u), self.SMALL)
ytmp = self.cc_data.grid.dy/max(abs(v), self.SMALL)
self.dt = cfl*min(xtmp, ytmp)
[docs] def evolve(self):
"""
Evolve the linear advection equation through one timestep. We only
consider the "density" variable in the CellCenterData2d object that
is part of the Simulation.
"""
dtdx = self.dt/self.cc_data.grid.dx
dtdy = self.dt/self.cc_data.grid.dy
flux_x, flux_y = flx.unsplit_fluxes(self.cc_data, self.rp, self.dt, "density")
"""
do the differencing for the fluxes now. Here, we use slices so we
avoid slow loops in python. This is equivalent to:
myPatch.data[i,j] = myPatch.data[i,j] + \
dtdx*(flux_x[i,j] - flux_x[i+1,j]) + \
dtdy*(flux_y[i,j] - flux_y[i,j+1])
"""
dens = self.cc_data.get_var("density")
dens.v()[:, :] = dens.v() + dtdx*(flux_x.v() - flux_x.ip(1)) + \
dtdy*(flux_y.v() - flux_y.jp(1))
# increment the time
self.cc_data.t += self.dt
self.n += 1
[docs] def dovis(self):
"""
Do runtime visualization.
"""
plt.clf()
dens = self.cc_data.get_var("density")
myg = self.cc_data.grid
plt.imshow(np.transpose(dens.v()),
interpolation="nearest", origin="lower",
extent=[myg.xmin, myg.xmax, myg.ymin, myg.ymax],
cmap=self.cm)
plt.xlabel("x")
plt.ylabel("y")
plt.title("density")
plt.colorbar()
plt.figtext(0.05, 0.0125, "t = {:10.5f}".format(self.cc_data.t))
plt.pause(0.001)
plt.draw()