import matplotlib.pyplot as plt
import numpy as np
import pyro.mesh.boundary as bnd
import pyro.swe.unsplit_fluxes as flx
from pyro.particles import particles
from pyro.simulation_null import NullSimulation, bc_setup, grid_setup
from pyro.swe import derives
from pyro.util import plot_tools
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class Variables:
"""
a container class for easy access to the different swe
variables by an integer key
"""
def __init__(self, myd):
self.nvar = len(myd.names)
# conserved variables -- we set these when we initialize for
# they match the CellCenterData2d object
self.ih = myd.names.index("height")
self.ixmom = myd.names.index("x-momentum")
self.iymom = myd.names.index("y-momentum")
# if there are any additional variables, we treat them as
# passively advected scalars
self.naux = self.nvar - 3
if self.naux > 0:
self.ihx = 3
else:
self.ihx = -1
# primitive variables
self.nq = 3 + self.naux
self.ih = 0
self.iu = 1
self.iv = 2
if self.naux > 0:
self.ix = 3 # advected scalar
else:
self.ix = -1
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def cons_to_prim(U, ivars, myg):
"""
Convert an input vector of conserved variables
:math:`U = (h, hu, hv, {hX})`
to primitive variables :math:`q = (h, u, v, {X})`.
"""
q = myg.scratch_array(nvar=ivars.nq)
q[:, :, ivars.ih] = U[:, :, ivars.ih]
q[:, :, ivars.iu] = U[:, :, ivars.ixmom]/U[:, :, ivars.ih]
q[:, :, ivars.iv] = U[:, :, ivars.iymom]/U[:, :, ivars.ih]
if ivars.naux > 0:
for nq, nu in zip(range(ivars.ix, ivars.ix+ivars.naux),
range(ivars.ihx, ivars.ihx+ivars.naux)):
q[:, :, nq] = U[:, :, nu]/q[:, :, ivars.ih]
return q
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def prim_to_cons(q, ivars, myg):
"""
Convert an input vector of primitive variables :math:`q = (h, u, v, {X})`
to conserved variables :math:`U = (h, hu, hv, {hX})`
"""
U = myg.scratch_array(nvar=ivars.nvar)
U[:, :, ivars.ih] = q[:, :, ivars.ih]
U[:, :, ivars.ixmom] = q[:, :, ivars.iu]*U[:, :, ivars.ih]
U[:, :, ivars.iymom] = q[:, :, ivars.iv]*U[:, :, ivars.ih]
if ivars.naux > 0:
for nq, nu in zip(range(ivars.ix, ivars.ix+ivars.naux),
range(ivars.ihx, ivars.ihx+ivars.naux)):
U[:, :, nu] = q[:, :, nq]*q[:, :, ivars.ih]
return U
[docs]
class Simulation(NullSimulation):
"""The main simulation class for the corner transport upwind
swe hydrodynamics solver
"""
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def initialize(self, *, extra_vars=None, ng=4):
"""
Initialize the grid and variables for swe flow and set
the initial conditions for the chosen problem.
"""
my_grid = grid_setup(self.rp, ng=ng)
my_data = self.data_class(my_grid)
bc, bc_xodd, bc_yodd = bc_setup(self.rp)
# are we dealing with solid boundaries? we'll use these for
# the Riemann solver
self.solid = bnd.bc_is_solid(bc)
# density and energy
my_data.register_var("height", bc)
my_data.register_var("x-momentum", bc_xodd)
my_data.register_var("y-momentum", bc_yodd)
my_data.register_var("fuel", bc)
# any extras?
if extra_vars is not None:
for v in extra_vars:
my_data.register_var(v, bc)
# store the gravitational acceration g as an auxiliary quantity
# so we can have a
# self-contained object stored in output files to make plots.
# store grav because we'll need that in some BCs
my_data.set_aux("g", self.rp.get_param("swe.grav"))
my_data.create()
self.cc_data = my_data
if self.rp.get_param("particles.do_particles") == 1:
n_particles = self.rp.get_param("particles.n_particles")
particle_generator = self.rp.get_param("particles.particle_generator")
self.particles = particles.Particles(self.cc_data, bc, n_particles, particle_generator)
# some auxiliary data that we'll need to fill GC in, but isn't
# really part of the main solution
aux_data = self.data_class(my_grid)
aux_data.register_var("ymom_src", bc_yodd)
aux_data.create()
self.aux_data = aux_data
self.ivars = Variables(my_data)
# derived variables
self.cc_data.add_derived(derives.derive_primitives)
# initial conditions for the problem
self.problem_func(self.cc_data, self.rp)
if self.verbose > 0:
print(my_data)
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def method_compute_timestep(self):
"""
The timestep function computes the advective timestep (CFL)
constraint. The CFL constraint says that information cannot
propagate further than one zone per timestep.
We use the driver.cfl parameter to control what fraction of the
CFL step we actually take.
"""
cfl = self.rp.get_param("driver.cfl")
# get the variables we need
u, v, cs = self.cc_data.get_var(["velocity", "soundspeed"])
# the timestep is min(dx/(|u| + cs), dy/(|v| + cs))
xtmp = self.cc_data.grid.dx/(abs(u) + cs)
ytmp = self.cc_data.grid.dy/(abs(v) + cs)
self.dt = cfl*float(min(xtmp.min(), ytmp.min()))
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def evolve(self):
"""
Evolve the equations of swe hydrodynamics through a
timestep dt.
"""
tm_evolve = self.tc.timer("evolve")
tm_evolve.begin()
myg = self.cc_data.grid
Flux_x, Flux_y = flx.unsplit_fluxes(self.cc_data, self.rp, self.ivars,
self.solid, self.tc, self.dt)
# conservative update
dtdx = self.dt/myg.dx
dtdy = self.dt/myg.dy
for n in range(self.ivars.nvar):
var = self.cc_data.get_var_by_index(n)
var.v()[:, :] += \
dtdx*(Flux_x.v(n=n) - Flux_x.ip(1, n=n)) + \
dtdy*(Flux_y.v(n=n) - Flux_y.jp(1, n=n))
if self.particles is not None:
self.particles.update_particles(self.dt)
# increment the time
self.cc_data.t += self.dt
self.n += 1
tm_evolve.end()
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def dovis(self):
"""
Do runtime visualization.
"""
plt.clf()
plt.rc("font", size=10)
# we do this even though ivars is in self, so this works when
# we are plotting from a file
ivars = Variables(self.cc_data)
q = cons_to_prim(self.cc_data.data, ivars, self.cc_data.grid)
h = q[:, :, ivars.ih]
u = q[:, :, ivars.iu]
v = q[:, :, ivars.iv]
fuel = q[:, :, ivars.ix]
magvel = np.sqrt(u**2 + v**2)
myg = self.cc_data.grid
vort = myg.scratch_array()
dv = 0.5*(v.ip(1) - v.ip(-1))/myg.dx
du = 0.5*(u.jp(1) - u.jp(-1))/myg.dy
vort.v()[:, :] = dv - du
fields = [h, magvel, fuel, vort]
field_names = [r"$h$", r"$|U|$", r"$X$", r"$\nabla\times U$"]
_, axes, cbar_title = plot_tools.setup_axes(myg, len(fields))
for n, ax in enumerate(axes):
v = fields[n]
img = ax.imshow(np.transpose(v.v()),
interpolation="nearest", origin="lower",
extent=[myg.xmin, myg.xmax, myg.ymin, myg.ymax],
cmap=self.cm)
ax.set_xlabel("x")
ax.set_ylabel("y")
# needed for PDF rendering
cb = axes.cbar_axes[n].colorbar(img)
cb.solids.set_rasterized(True)
cb.solids.set_edgecolor("face")
if cbar_title:
cb.ax.set_title(field_names[n])
else:
ax.set_title(field_names[n])
if self.particles is not None:
ax = axes[0]
particle_positions = self.particles.get_positions()
# dye particles
colors = self.particles.get_init_positions()[:, 0]
# plot particles
ax.scatter(particle_positions[:, 0],
particle_positions[:, 1], s=5, c=colors, alpha=0.8, cmap="Greys")
ax.set_xlim([myg.xmin, myg.xmax])
ax.set_ylim([myg.ymin, myg.ymax])
plt.figtext(0.05, 0.0125, f"t = {self.cc_data.t:10.5g}")
plt.pause(0.001)
plt.draw()
