e = p/rho/(gamma - 1.0)
# output the solution
with open(outfile, "w") as f:
f.write("# left: {}\n".format(left))
f.write("# right: {}\n".format(right))
f.write("# gamma = {}\n".format(gamma))
f.write("# time = {}\n".format(time))
f.write("# {:^20} {:^20} {:^20} {:^20} {:^20}\n".format("x", "rho", "u", "p", "e"))
for n in range(len(x)):
f.write(" {:20.10g} {:20.10g} {:20.10g} {:20.10g} {:20.10g}\n".format(x[n], rho[n], u[n], p[n], e[n]))
# Sod
left = riemann.State(p=1.0, u=0.0, rho=1.0)
right = riemann.State(p=0.1, u=0.0, rho=0.125)
time = 0.2
gamma = 1.4
outfile = "sod_exact.out"
store(left, right, time, gamma, outfile=outfile)
# double rarefaction
left = riemann.State(p=0.4, u=-2.0, rho=1.0)
right = riemann.State(p=0.4, u=2.0, rho=1.0)
time = 0.15
gamma = 1.4
outfile = "double_rarefaction_exact.out"
store(left, right, time, gamma, outfile=outfile)
mpl.rcParams['mathtext.fontset'] = 'cm'
mpl.rcParams['mathtext.rm'] = 'serif'
mpl.rcParams['font.size'] = 12
mpl.rcParams['legend.fontsize'] = 'large'
mpl.rcParams['figure.titlesize'] = 'medium'
if __name__ == "__main__":
# setup the problem -- slow shock
# stationary shock
#left = riemann.State(p=100.0, u=-1.9336, rho=5.6698)
#right = riemann.State(p=1.0, u=-10.9636, rho=1.0)
# slow shock
left = riemann.State(p=100.0, u=-1.4701, rho=5.6698)
right = riemann.State(p=1.0, u=-10.5, rho=1.0)
rp = riemann.RiemannProblem(left, right)
rp.find_star_state()
x, rho, u, p = rp.sample_solution(1.0, 128)
plt.subplot(311)
plt.plot(x, rho)
plt.ylabel(r"$\rho$")
plt.xlim(0, 1)
plt.tick_params(axis="x", labelbottom="off")
def draw_var_avg(self, var, scale=1.0):
for n in range(self.gr.nx):
self.vars[var].draw_cell_avg(n, color="r")
#-----------------------------------------------------------------------------
# multipage PDF
# http://matplotlib.org/examples/pylab_examples/multipage_pdf.html
# left state
q_l = riemann.State(rho=1.0, u=0.0, p=1.0)
# right state
q_r = riemann.State(rho=0.125, u=0.0, p=0.1)
r = RiemannProblem(q_l, q_r)
subidx = [311, 312, 313]
states = ["rho", "u", "p"]
state_labels = [r"$\rho$", r"$u$", r"$p$"]
#-----------------------------------------------------------------------------
# plot 1: initial state
plt.clf()
# plot the Hugoniot loci for a compressible Riemann problem
from __future__ import print_function
import matplotlib.pyplot as plt
import numpy as np
import riemann
import matplotlib as mpl
# Use LaTeX for rendering
mpl.rcParams['mathtext.fontset'] = 'cm'
mpl.rcParams['mathtext.rm'] = 'serif'
mpl.rcParams['font.size'] = 12
mpl.rcParams['legend.fontsize'] = 'large'
mpl.rcParams['figure.titlesize'] = 'medium'
if __name__ == "__main__":
# setup the problem -- Sod
left = riemann.State(p=1.0, u=0.0, rho=1.0)
right = riemann.State(p=0.1, u=0.0, rho=0.125)
rp = riemann.RiemannProblem(left, right)
rp.find_star_state()
rp.plot_hugoniot()
plt.savefig("riemann-phase.pdf")
print(rp.pstar, rp.ustar)
mpl.rcParams['mathtext.fontset'] = 'cm'
mpl.rcParams['mathtext.rm'] = 'serif'
mpl.rcParams['font.size'] = 12
mpl.rcParams['legend.fontsize'] = 'large'
mpl.rcParams['figure.titlesize'] = 'medium'
if __name__ == "__main__":
# setup the problem -- slow shock
# stationary shock
#left = riemann.State(p=100.0, u=-1.9336, rho=5.6698)
#right = riemann.State(p=1.0, u=-10.9636, rho=1.0)
# slow shock
left = riemann.State(p=100.0, u=-1.5336, rho=5.6698)
right = riemann.State(p=1.0, u=-10.5636, rho=1.0)
rp = riemann.RiemannProblem(left, right)
rp.find_star_state()
x, rho, u, p = rp.sample_solution(0.2, 128)
plt.subplot(311)
plt.plot(x, rho)
plt.ylabel(r"$\rho$")
plt.xlim(0, 1)
plt.tick_params(axis="x", labelbottom="off")