Updated the 3D Sod shock example to use the new glass files. Added script to...

Updated the 3D Sod shock example to use the new glass files. Added script to plot solution. Removed old glass files.

examples/SedovBlast_3D/getGlass.sh

+#!/bin/bash
+wget http://virgodb.cosma.dur.ac.uk/swift-webstorage/ICs/glassCube_64.hdf5

examples/SedovBlast_3D/plotSolution.py

+###############################################################################
+ # This file is part of SWIFT.
+ # Copyright (c) 2015 Bert Vandenbroucke (bert.vandenbroucke@ugent.be)
+ #                    Matthieu Schaller (matthieu.schaller@durham.ac.uk)
+ # 
+ # This program is free software: you can redistribute it and/or modify
+ # it under the terms of the GNU Lesser General Public License as published
+ # by the Free Software Foundation, either version 3 of the License, or
+ # (at your option) any later version.
+ # 
+ # This program is distributed in the hope that it will be useful,
+ # but WITHOUT ANY WARRANTY; without even the implied warranty of
+ # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ # GNU General Public License for more details.
+ # 
+ # You should have received a copy of the GNU Lesser General Public License
+ # along with this program.  If not, see <http://www.gnu.org/licenses/>.
+ # 
+ ##############################################################################
+
+# Computes the analytical solution of the 2D Sedov blast wave.
+# The script works for a given initial box and dumped energy and computes the solution at a later time t.
+
+# Parameters
+rho_0 = 1.          # Background Density
+P_0 = 1.e-6         # Background Pressure
+E_0 = 1.            # Energy of the explosion
+gas_gamma = 5./3.   # Gas polytropic index
+
+
+# ---------------------------------------------------------------
+# Don't touch anything after this.
+# ---------------------------------------------------------------
+
+import matplotlib
+matplotlib.use("Agg")
+from pylab import *
+import h5py
+
+# Plot parameters
+params = {'axes.labelsize': 10,
+'axes.titlesize': 10,
+'font.size': 12,
+'legend.fontsize': 12,
+'xtick.labelsize': 10,
+'ytick.labelsize': 10,
+'text.usetex': True,
+ 'figure.figsize' : (9.90,6.45),
+'figure.subplot.left'    : 0.045,
+'figure.subplot.right'   : 0.99,
+'figure.subplot.bottom'  : 0.05,
+'figure.subplot.top'     : 0.99,
+'figure.subplot.wspace'  : 0.15,
+'figure.subplot.hspace'  : 0.12,
+'lines.markersize' : 6,
+'lines.linewidth' : 3.,
+'text.latex.unicode': True
+}
+rcParams.update(params)
+rc('font',**{'family':'sans-serif','sans-serif':['Times']})
+
+
+snap = int(sys.argv[1])
+
+
+# Read the simulation data
+sim = h5py.File("sedov_%03d.hdf5"%snap, "r")
+boxSize = sim["/Header"].attrs["BoxSize"][0]
+time = sim["/Header"].attrs["Time"][0]
+scheme = sim["/HydroScheme"].attrs["Scheme"]
+kernel = sim["/HydroScheme"].attrs["Kernel function"]
+neighbours = sim["/HydroScheme"].attrs["Kernel target N_ngb"]
+eta = sim["/HydroScheme"].attrs["Kernel eta"]
+git = sim["Code"].attrs["Git Revision"]
+
+pos = sim["/PartType0/Coordinates"][:,:]
+x = pos[:,0] - boxSize / 2
+y = pos[:,1] - boxSize / 2
+z = pos[:,2] - boxSize / 2
+vel = sim["/PartType0/Velocities"][:,:]
+r = sqrt(x**2 + y**2 + z**2)
+v_r = (x * vel[:,0] + y * vel[:,1] + z * vel[:,2]) / r
+u = sim["/PartType0/InternalEnergy"][:]
+S = sim["/PartType0/Entropy"][:]
+P = sim["/PartType0/Pressure"][:]
+rho = sim["/PartType0/Density"][:]
+
+
+# Now, work our the solution....
+
+from scipy.special import gamma as Gamma
+from numpy import *
+
+def calc_a(g,nu=3):
+    """ 
+    exponents of the polynomials of the sedov solution
+    g - the polytropic gamma
+    nu - the dimension
+    """
+    a = [0]*8
+   
+    a[0] = 2.0 / (nu + 2)
+    a[2] = (1-g) / (2*(g-1) + nu)
+    a[3] = nu / (2*(g-1) + nu)
+    a[5] = 2 / (g-2)
+    a[6] = g / (2*(g-1) + nu)
+   
+    a[1] = (((nu+2)*g)/(2.0+nu*(g-1.0)) ) * ( (2.0*nu*(2.0-g))/(g*(nu+2.0)**2) - a[2])
+    a[4] = a[1]*(nu+2) / (2-g)
+    a[7] = (2 + nu*(g-1))*a[1]/(nu*(2-g))
+    return a
+
+def calc_beta(v, g, nu=3):
+    """ 
+    beta values for the sedov solution (coefficients of the polynomials of the similarity variables) 
+    v - the similarity variable
+    g - the polytropic gamma
+    nu- the dimension
+    """
+
+    beta = (nu+2) * (g+1) * array((0.25, (g/(g-1))*0.5,
+            -(2 + nu*(g-1))/2.0 / ((nu+2)*(g+1) -2*(2 + nu*(g-1))),
+     -0.5/(g-1)), dtype=float64)
+
+    beta = outer(beta, v)
+
+    beta += (g+1) * array((0.0,  -1.0/(g-1),
+                           (nu+2) / ((nu+2)*(g+1) -2.0*(2 + nu*(g-1))),
+                           1.0/(g-1)), dtype=float64).reshape((4,1))
+
+    return beta
+
+
+def sedov(t, E0, rho0, g, n=1000, nu=3):
+    """ 
+    solve the sedov problem
+    t - the time
+    E0 - the initial energy
+    rho0 - the initial density
+    n - number of points (10000)
+    nu - the dimension
+    g - the polytropic gas gamma
+    """
+    # the similarity variable
+    v_min = 2.0 / ((nu + 2) * g)
+    v_max = 4.0 / ((nu + 2) * (g + 1))
+
+    v = v_min + arange(n) * (v_max - v_min) / (n - 1.0)
+
+    a = calc_a(g, nu)
+    beta = calc_beta(v, g=g, nu=nu)
+    lbeta = log(beta)
+    
+    r = exp(-a[0] * lbeta[0] - a[2] * lbeta[1] - a[1] * lbeta[2])
+    rho = ((g + 1.0) / (g - 1.0)) * exp(a[3] * lbeta[1] + a[5] * lbeta[3] + a[4] * lbeta[2])
+    p = exp(nu * a[0] * lbeta[0] + (a[5] + 1) * lbeta[3] + (a[4] - 2 * a[1]) * lbeta[2])
+    u = beta[0] * r * 4.0 / ((g + 1) * (nu + 2))
+    p *= 8.0 / ((g + 1) * (nu + 2) * (nu + 2))
+
+    # we have to take extra care at v=v_min, since this can be a special point.
+    # It is not a singularity, however, the gradients of our variables (wrt v) are.
+    # r -> 0, u -> 0, rho -> 0, p-> constant
+
+    u[0] = 0.0; rho[0] = 0.0; r[0] = 0.0; p[0] = p[1]
+
+    # volume of an n-sphere
+    vol = (pi ** (nu / 2.0) / Gamma(nu / 2.0 + 1)) * power(r, nu)
+
+    # note we choose to evaluate the integral in this way because the
+    # volumes of the first few elements (i.e near v=vmin) are shrinking 
+    # very slowly, so we dramatically improve the error convergence by 
+    # finding the volumes exactly. This is most important for the
+    # pressure integral, as this is on the order of the volume.
+
+    # (dimensionless) energy of the model solution
+    de = rho * u * u * 0.5 + p / (g - 1)
+    # integrate (trapezium rule)
+    q = inner(de[1:] + de[:-1], diff(vol)) * 0.5
+
+    # the factor to convert to this particular problem
+    fac = (q * (t ** nu) * rho0 / E0) ** (-1.0 / (nu + 2))
+
+    # shock speed
+    shock_speed = fac * (2.0 / (nu + 2))
+    rho_s = ((g + 1) / (g - 1)) * rho0                                                                            
+    r_s = shock_speed * t * (nu + 2) / 2.0
+    p_s = (2.0 * rho0 * shock_speed * shock_speed) / (g + 1)
+    u_s = (2.0 * shock_speed) / (g + 1)
+    
+    r *= fac * t
+    u *= fac
+    p *= fac * fac * rho0
+    rho *= rho0
+    return r, p, rho, u, r_s, p_s, rho_s, u_s, shock_speed
+
+
+# The main properties of the solution
+r_s, P_s, rho_s, v_s, r_shock, _, _, _, _ = sedov(time, E_0, rho_0, gas_gamma, 1000, 3)
+
+# Append points for after the shock
+r_s = np.insert(r_s, np.size(r_s), [r_shock, r_shock*1.5])
+rho_s = np.insert(rho_s, np.size(rho_s), [rho_0, rho_0])
+P_s = np.insert(P_s, np.size(P_s), [P_0, P_0])
+v_s = np.insert(v_s, np.size(v_s), [0, 0])
+
+# Additional arrays
+u_s = P_s / (rho_s * (gas_gamma - 1.))  #internal energy
+s_s = P_s / rho_s**gas_gamma # entropic function
+
+
+
+# Plot the interesting quantities
+figure()
+
+# Velocity profile --------------------------------
+subplot(231)
+plot(r, v_r, '.', color='r', ms=1.)
+plot(r_s, v_s, '--', color='k', alpha=0.8, lw=1.2)
+xlabel("${\\rm{Radius}}~r$", labelpad=0)
+ylabel("${\\rm{Radial~velocity}}~v_r$", labelpad=0)
+xlim(0, 1.3 * r_shock)
+ylim(-0.2, 3.8)
+
+# Density profile --------------------------------
+subplot(232)
+plot(r, rho, '.', color='r', ms=1.)
+plot(r_s, rho_s, '--', color='k', alpha=0.8, lw=1.2)
+xlabel("${\\rm{Radius}}~r$", labelpad=0)
+ylabel("${\\rm{Density}}~\\rho$", labelpad=2)
+xlim(0, 1.3 * r_shock)
+ylim(-0.2, 5.2)
+
+# Pressure profile --------------------------------
+subplot(233)
+plot(r, P, '.', color='r', ms=1.)
+plot(r_s, P_s, '--', color='k', alpha=0.8, lw=1.2)
+xlabel("${\\rm{Radius}}~r$", labelpad=0)
+ylabel("${\\rm{Pressure}}~P$", labelpad=0)
+xlim(0, 1.3 * r_shock)
+ylim(-1, 12.5)
+
+# Internal energy profile -------------------------
+subplot(234)
+plot(r, u, '.', color='r', ms=1.)
+plot(r_s, u_s, '--', color='k', alpha=0.8, lw=1.2)
+xlabel("${\\rm{Radius}}~r$", labelpad=0)
+ylabel("${\\rm{Internal~Energy}}~u$", labelpad=0)
+xlim(0, 1.3 * r_shock)
+ylim(-2, 22)
+
+# Entropy profile ---------------------------------
+subplot(235)
+plot(r, S, '.', color='r', ms=1.)
+plot(r_s, s_s, '--', color='k', alpha=0.8, lw=1.2)
+xlabel("${\\rm{Radius}}~r$", labelpad=0)
+ylabel("${\\rm{Entropy}}~S$", labelpad=0)
+xlim(0, 1.3 * r_shock)
+ylim(-5, 50)
+
+# Information -------------------------------------
+subplot(236, frameon=False)
+
+text(-0.49, 0.9, "Sedov blast with  $\\gamma=%.3f$ in 2D at $t=%.2f$"%(gas_gamma,time), fontsize=10)
+text(-0.49, 0.8, "Background $\\rho_0=%.2f$"%(rho_0), fontsize=10)
+text(-0.49, 0.7, "Energy injected $E_0=%.2f$"%(E_0), fontsize=10)
+plot([-0.49, 0.1], [0.62, 0.62], 'k-', lw=1)
+text(-0.49, 0.5, "$\\textsc{Swift}$ %s"%git, fontsize=10)
+text(-0.49, 0.4, scheme, fontsize=10)
+text(-0.49, 0.3, kernel, fontsize=10)
+text(-0.49, 0.2, "$%.2f$ neighbours ($\\eta=%.3f$)"%(neighbours, eta), fontsize=10)
+xlim(-0.5, 0.5)
+ylim(0, 1)
+xticks([])
+yticks([])
+
+
+savefig("Sedov.png", dpi=200)
+
+
+
+

examples/SodShock_1D/plotSolution.py

@@ -22,8 +22,6 @@
 
 # Generates the analytical  solution for the Sod shock test case
 # The script works for a given left (x<0) and right (x>0) state and computes the solution at a later time t.
-# The code writes five files rho.dat, P.dat, v.dat, u.dat and s.dat with the density, pressure, internal energy and
-# entropic function on N points between x_min and x_max.
 # This follows the solution given in (Toro, 2009)
 
 

examples/SodShock_2D/plotSolution.py

@@ -22,8 +22,6 @@
 
 # Generates the analytical  solution for the Sod shock test case
 # The script works for a given left (x<0) and right (x>0) state and computes the solution at a later time t.
-# The code writes five files rho.dat, P.dat, v.dat, u.dat and s.dat with the density, pressure, internal energy and
-# entropic function on N points between x_min and x_max.
 # This follows the solution given in (Toro, 2009)
 
 

examples/SodShock_3D/getGlass.sh

+#!/bin/bash
+wget http://virgodb.cosma.dur.ac.uk/swift-webstorage/ICs/glassCube_64.hdf5
+wget http://virgodb.cosma.dur.ac.uk/swift-webstorage/ICs/glassCube_32.hdf5

examples/SodShock_3D/makeIC.py

 ###############################################################################
  # This file is part of SWIFT.
- # Copyright (c) 2012 Pedro Gonnet (pedro.gonnet@durham.ac.uk),
- #                    Matthieu Schaller (matthieu.schaller@durham.ac.uk)
+ # Copyright (c) 2016 Matthieu Schaller (matthieu.schaller@durham.ac.uk)
  # 
  # This program is free software: you can redistribute it and/or modify
  # it under the terms of the GNU Lesser General Public License as published
@@ -21,84 +20,75 @@
 import h5py
 from numpy import *
 
-# Generates a swift IC file for the Sod Shock in a periodic box
+# Generates a swift IC file for the 3D Sod Shock in a periodic box
 
 # Parameters
-periodic= 1      # 1 For periodic box
-factor = 8
-boxSize = [ 1.0 , 1.0/factor , 1.0/factor ]
-L = 100           # Number of particles along one axis
-P1 = 1.           # Pressure left state
-P2 = 0.1795       # Pressure right state
-gamma = 5./3.     # Gas adiabatic index
+gamma = 5./3.          # Gas adiabatic index
+x_min = -1.
+x_max = 1.
+rho_L = 1.             # Density left state
+rho_R = 0.125          # Density right state
+v_L = 0.               # Velocity left state
+v_R = 0.               # Velocity right state
+P_L = 1.               # Pressure left state
+P_R = 0.1              # Pressure right state
 fileName = "sodShock.hdf5" 
-vol = boxSize[0] * boxSize[1] * boxSize[2]
 
 
 #---------------------------------------------------
-
-#Read in high density glass
-# glass1 = h5py.File("../Glass/glass_200000.hdf5")
-glass1 = h5py.File("glass_001.hdf5")
-pos1 = glass1["/PartType0/Coordinates"][:,:]
-pos1 = pos1 / factor # Particles are in [0:0.25, 0:0.25, 0:0.25]
-glass_h1 = glass1["/PartType0/SmoothingLength"][:] / factor
-
-#Read in high density glass
-# glass2 = h5py.File("../Glass/glass_50000.hdf5")
-glass2 = h5py.File("glass_002.hdf5")
-pos2 = glass2["/PartType0/Coordinates"][:,:]
-pos2 = pos2 / factor # Particles are in [0:0.25, 0:0.25, 0:0.25]
-glass_h2 = glass2["/PartType0/SmoothingLength"][:] / factor
-
-#Generate high density region
-rho1 = 1.
-coord1 = append(pos1, pos1 + [0.125, 0, 0], 0)
-coord1 = append(coord1, coord1 + [0.25, 0, 0], 0)
-# coord1 = append(pos1, pos1 + [0, 0.5, 0], 0)
-# coord1 = append(coord1, pos1 + [0, 0, 0.5], 0)
-# coord1 = append(coord1, pos1 + [0, 0.5, 0.5], 0)
-N1 = size(coord1)/3
-v1 = zeros((N1, 3))
-u1 = ones(N1) * P1 / ((gamma - 1.) * rho1)
-m1 = ones(N1) * vol * 0.5 * rho1 / N1
-h1 = append(glass_h1, glass_h1, 0)
-h1 = append(h1, h1, 0)
-
-#Generate low density region
-rho2 = 0.25
-coord2 = append(pos2, pos2 + [0.125, 0, 0], 0)
-coord2 = append(coord2, coord2 + [0.25, 0, 0], 0)
-# coord2 = append(pos2, pos2 + [0, 0.5, 0], 0)
-# coord2 = append(coord2, pos2 + [0, 0, 0.5], 0)
-# coord2 = append(coord2, pos2 + [0, 0.5, 0.5], 0)
-N2 = size(coord2)/3
-v2 = zeros((N2, 3))
-u2 = ones(N2) * P2 / ((gamma - 1.) * rho2)
-m2 = ones(N2) * vol * 0.5 * rho2 / N2
-h2 = append(glass_h2, glass_h2, 0)
-h2 = append(h2, h2, 0)
-
-#Merge arrays
-numPart = N1 + N2
-coords = append(coord1, coord2+[0.5, 0., 0.], 0)
-v = append(v1, v2,0)
-h = append(h1, h2,0)
-u = append(u1, u2,0)
-m = append(m1, m2,0)
-ids = zeros(numPart, dtype='L')
-for i in range(1, numPart+1):
-    ids[i-1] = i
-
-#Final operation since we come from Gadget-2 cubic spline ICs
-h /= 1.825752
+boxSize = (x_max - x_min)
+
+glass_L = h5py.File("glassCube_64.hdf5", "r")
+glass_R = h5py.File("glassCube_32.hdf5", "r")
+
+pos_L = glass_L["/PartType0/Coordinates"][:,:] * 0.5
+pos_R = glass_R["/PartType0/Coordinates"][:,:] * 0.5
+h_L = glass_L["/PartType0/SmoothingLength"][:] * 0.5
+h_R = glass_R["/PartType0/SmoothingLength"][:] * 0.5
+
+# Merge things
+aa = pos_L - array([0.5, 0., 0.])
+pos_LL = append(pos_L, pos_L + array([0.5, 0., 0.]), axis=0)
+pos_RR = append(pos_R, pos_R + array([0.5, 0., 0.]), axis=0)
+pos = append(pos_LL - array([1.0, 0., 0.]), pos_RR, axis=0)
+h_LL = append(h_L, h_L)
+h_RR = append(h_R, h_R)
+h = append(h_LL, h_RR)
+
+numPart_L = size(h_LL)
+numPart_R = size(h_RR)
+numPart = size(h)
+
+vol_L = 0.25
+vol_R = 0.25
+
+# Generate extra arrays
+v = zeros((numPart, 3))
+ids = linspace(1, numPart, numPart)
+m = zeros(numPart)
+u = zeros(numPart)
+
+for i in range(numPart):
+    x = pos[i,0]
+
+    if x < 0: #left
+        u[i] = P_L / (rho_L * (gamma - 1.))
+        m[i] = rho_L * vol_L / numPart_L
+        v[i,0] = v_L
+    else:     #right
+        u[i] = P_R / (rho_R * (gamma - 1.))
+        m[i] = rho_R * vol_R / numPart_R
+        v[i,0] = v_R
+        
+# Shift particles
+pos[:,0] -= x_min
 
 #File
 file = h5py.File(fileName, 'w')
 
 # Header
 grp = file.create_group("/Header")
-grp.attrs["BoxSize"] = boxSize
+grp.attrs["BoxSize"] = [boxSize, 0.5, 0.5]
 grp.attrs["NumPart_Total"] =  [numPart, 0, 0, 0, 0, 0]
 grp.attrs["NumPart_Total_HighWord"] = [0, 0, 0, 0, 0, 0]
 grp.attrs["NumPart_ThisFile"] = [numPart, 0, 0, 0, 0, 0]
@@ -109,7 +99,7 @@ grp.attrs["Flag_Entropy_ICs"] = 0
 
 #Runtime parameters
 grp = file.create_group("/RuntimePars")
-grp.attrs["PeriodicBoundariesOn"] = periodic
+grp.attrs["PeriodicBoundariesOn"] = 1
 
 #Units
 grp = file.create_group("/Units")
@@ -121,7 +111,7 @@ grp.attrs["Unit temperature in cgs (U_T)"] = 1.
 
 #Particle group
 grp = file.create_group("/PartType0")
-grp.create_dataset('Coordinates', data=coords, dtype='d')
+grp.create_dataset('Coordinates', data=pos, dtype='d')
 grp.create_dataset('Velocities', data=v, dtype='f')
 grp.create_dataset('Masses', data=m, dtype='f')
 grp.create_dataset('SmoothingLength', data=h, dtype='f')
@@ -130,5 +120,3 @@ grp.create_dataset('ParticleIDs', data=ids, dtype='L')
 
 
 file.close()
-
-

examples/SodShock_3D/solution.py → examples/SodShock_3D/plotSolution.py

 ###############################################################################
  # This file is part of SWIFT.
- # Copyright (c) 2012 Pedro Gonnet (pedro.gonnet@durham.ac.uk),
- #                    Matthieu Schaller (matthieu.schaller@durham.ac.uk)
+ # Copyright (c) 2016 Matthieu Schaller (matthieu.schaller@durham.ac.uk)
  # 
  # This program is free software: you can redistribute it and/or modify
  # it under the terms of the GNU Lesser General Public License as published
@@ -18,61 +17,105 @@
  # 
  ##############################################################################
 
-import random
-from numpy import *
+# Computes the analytical solution of the Sod shock and plots the SPH answer
+ 
 
 # Generates the analytical  solution for the Sod shock test case
 # The script works for a given left (x<0) and right (x>0) state and computes the solution at a later time t.
-# The code writes five files rho.dat, P.dat, v.dat, u.dat and s.dat with the density, pressure, internal energy and
-# entropic function on N points between x_min and x_max.
 # This follows the solution given in (Toro, 2009)
 
 
 # Parameters
-rho_L = 1
-P_L = 1
-v_L = 0.
+gas_gamma = 5./3.      # Polytropic index
+rho_L = 1.             # Density left state
+rho_R = 0.125          # Density right state
+v_L = 0.               # Velocity left state
+v_R = 0.               # Velocity right state
+P_L = 1.               # Pressure left state
+P_R = 0.1              # Pressure right state
 
-rho_R = 0.25
-P_R = 0.1795
-v_R = 0.
 
-gamma = 5./3. # Polytropic index
+import matplotlib
+matplotlib.use("Agg")
+from pylab import *
+import h5py
 
-t = 0.12  # Time of the evolution
+# Plot parameters
+params = {'axes.labelsize': 10,
+'axes.titlesize': 10,
+'font.size': 12,
+'legend.fontsize': 12,
+'xtick.labelsize': 10,
+'ytick.labelsize': 10,
+'text.usetex': True,
+ 'figure.figsize' : (9.90,6.45),
+'figure.subplot.left'    : 0.045,
+'figure.subplot.right'   : 0.99,
+'figure.subplot.bottom'  : 0.05,
+'figure.subplot.top'     : 0.99,
+'figure.subplot.wspace'  : 0.15,
+'figure.subplot.hspace'  : 0.12,
+'lines.markersize' : 6,
+'lines.linewidth' : 3.,
+'text.latex.unicode': True
+}
+rcParams.update(params)
+rc('font',**{'family':'sans-serif','sans-serif':['Times']})
+
+
+snap = int(sys.argv[1])
+
+
+# Read the simulation data
+sim = h5py.File("sodShock_%03d.hdf5"%snap, "r")
+boxSize = sim["/Header"].attrs["BoxSize"][0]
+time = sim["/Header"].attrs["Time"][0]
+scheme = sim["/HydroScheme"].attrs["Scheme"]
+kernel = sim["/HydroScheme"].attrs["Kernel function"]
+neighbours = sim["/HydroScheme"].attrs["Kernel target N_ngb"]
+eta = sim["/HydroScheme"].attrs["Kernel eta"]
+git = sim["Code"].attrs["Git Revision"]
+
+x = sim["/PartType0/Coordinates"][:,0]
+v = sim["/PartType0/Velocities"][:,0]
+u = sim["/PartType0/InternalEnergy"][:]
+S = sim["/PartType0/Entropy"][:]
+P = sim["/PartType0/Pressure"][:]
+rho = sim["/PartType0/Density"][:]
 
 N = 1000  # Number of points
-x_min = -0.25
-x_max = 0.25
+x_min = -1.
+x_max = 1.
 
+x += x_min
 
 # ---------------------------------------------------------------
 # Don't touch anything after this.
 # ---------------------------------------------------------------
 
-c_L = sqrt(gamma * P_L / rho_L)   # Speed of the rarefaction wave
-c_R = sqrt(gamma * P_R / rho_R)   # Speed of the shock front
+c_L = sqrt(gas_gamma * P_L / rho_L)   # Speed of the rarefaction wave
+c_R = sqrt(gas_gamma * P_R / rho_R)   # Speed of the shock front
 
 # Helpful variable