Merge branch 'master' into disk-patch

.gitignore

@@ -29,6 +29,7 @@ examples/used_parameters.yml
 examples/energy.txt
 examples/*/*.xmf
 examples/*/*.hdf5
+examples/*/*.png
 examples/*/*.txt
 examples/*/used_parameters.yml
 examples/*/*/*.xmf

configure.ac

@@ -469,7 +469,7 @@ if test "$enable_warn" != "no"; then
              CFLAGS="$CFLAGS -Wall"
           ;;
 	  intel)
-             CFLAGS="$CFLAGS -w2"
+             CFLAGS="$CFLAGS -w2 -Wunused-variable"
           ;;
 	  *)
 	     AX_CFLAGS_WARN_ALL

examples/GreshoVortex/solution.py

-###############################################################################
- # This file is part of SWIFT.
- # Copyright (c) 2012 Pedro Gonnet (pedro.gonnet@durham.ac.uk),
- #                    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/>.
- # 
- ##############################################################################
-
-import random
-from numpy import *
-
-# Computes the analytical solution of the Gresho-Chan vortex
-# The script works for a given initial box and background pressure and computes the solution for any time t (The solution is constant over time).
-# 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 radial points between r=0 and r=R_max.
-
-# Parameters
-rho0 = 1.         # Background Density
-P0 = 0.           # Background Pressure
-gamma = 5./3.     # Gas polytropic index
-N = 1000          # Number of radial points
-R_max = 1.        # Maximal radius
-
-# ---------------------------------------------------------------
-# Don't touch anything after this.
-# ---------------------------------------------------------------
-
-r = arange(0, R_max, R_max / N)
-rho = ones(N)
-P = zeros(N)
-v = zeros(N)
-u = zeros(N)
-s = zeros(N)
-
-
-for i in range(N):
-    if r[i] < 0.2:
-        P[i] = P0 + 5. + 12.5*r[i]**2
-        v[i] = 5.*r[i]
-    elif r[i] < 0.4:
-        P[i] = P0 + 9. + 12.5*r[i]**2 - 20.*r[i] + 4.*log(r[i]/0.2)
-        v[i] = 2. -5.*r[i]
-    else:
-        P[i] = P0 + 3. + 4.*log(2.)
-        v[i] = 0.
-    rho[i] = rho0
-    s[i] = P[i] / rho[i]**gamma
-    u[i] = P[i] /((gamma - 1.)*rho[i])
-
-savetxt("rho.dat", column_stack((r, rho)))
-savetxt("P.dat", column_stack((r, P)))
-savetxt("v.dat", column_stack((r, v)))
-savetxt("u.dat", column_stack((r, u)))
-savetxt("s.dat", column_stack((r, s)))
-
-
-

examples/GreshoVortex_2D/getGlass.sh

+#!/bin/bash
+wget http://virgodb.cosma.dur.ac.uk/swift-webstorage/ICs/glassPlane_128.hdf5

examples/GreshoVortex_2D/gresho.yml

+# Define the system of units to use internally. 
+InternalUnitSystem:
+  UnitMass_in_cgs:     1   # Grams
+  UnitLength_in_cgs:   1   # Centimeters
+  UnitVelocity_in_cgs: 1   # Centimeters per second
+  UnitCurrent_in_cgs:  1   # Amperes
+  UnitTemp_in_cgs:     1   # Kelvin
+
+# Parameters governing the time integration
+TimeIntegration:
+  time_begin: 0.    # The starting time of the simulation (in internal units).
+  time_end:   1.    # The end time of the simulation (in internal units).
+  dt_min:     1e-6  # The minimal time-step size of the simulation (in internal units).
+  dt_max:     1e-2  # The maximal time-step size of the simulation (in internal units).
+
+# Parameters governing the snapshots
+Snapshots:
+  basename:            gresho # Common part of the name of output files
+  time_first:          0.     # Time of the first output (in internal units)
+  delta_time:          1e-1   # Time difference between consecutive outputs (in internal units)
+
+# Parameters governing the conserved quantities statistics
+Statistics:
+  delta_time:          1e-2 # Time between statistics output
+
+# Parameters for the hydrodynamics scheme
+SPH:
+  resolution_eta:        1.2348   # Target smoothing length in units of the mean inter-particle separation (1.2348 == 48Ngbs with the cubic spline kernel).
+  delta_neighbours:      0.1      # The tolerance for the targetted number of neighbours.
+  max_smoothing_length:  0.02     # Maximal smoothing length allowed (in internal units).
+  CFL_condition:         0.1      # Courant-Friedrich-Levy condition for time integration.
+  
+# Parameters related to the initial conditions
+InitialConditions:
+  file_name:  ./greshoVortex.hdf5     # The file to read

examples/GreshoVortex_2D/makeIC.py

+###############################################################################
+ # This file is part of SWIFT.
+ # 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
+ # 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/>.
+ # 
+ ##############################################################################
+
+import h5py
+from numpy import *
+
+# Generates a swift IC file for the Gresho-Chan vortex in a periodic box
+
+# Parameters
+gamma = 5./3.     # Gas adiabatic index
+rho0 = 1           # Gas density
+P0 = 0.           # Constant additional pressure (should have no impact on the dynamics)
+fileOutputName = "greshoVortex.hdf5" 
+fileGlass = "glassPlane_128.hdf5"
+#---------------------------------------------------
+
+# Get position and smoothing lengths from the glass
+fileInput = h5py.File(fileGlass, 'r')
+coords = fileInput["/PartType0/Coordinates"][:,:]
+h = fileInput["/PartType0/SmoothingLength"][:]
+ids = fileInput["/PartType0/ParticleIDs"][:]
+boxSize = fileInput["/Header"].attrs["BoxSize"][0]
+numPart = size(h)
+fileInput.close()
+
+# Now generate the rest
+m = ones(numPart) * rho0 * boxSize**2 / numPart
+u = zeros(numPart)
+v = zeros((numPart, 3))
+
+for i in range(numPart):
+    
+    x = coords[i,0]
+    y = coords[i,1]
+
+    r2 = (x - boxSize / 2)**2 + (y - boxSize / 2)**2
+    r = sqrt(r2)
+
+    v_phi = 0.
+    if r < 0.2:
+        v_phi = 5.*r
+    elif r < 0.4:
+        v_phi = 2. - 5.*r
+    else:
+        v_phi = 0.
+    v[i,0] = -v_phi * (y - boxSize / 2) / r
+    v[i,1] =  v_phi * (x - boxSize / 2) / r
+    v[i,2] = 0.
+
+    P = P0
+    if r < 0.2:
+        P = P + 5. + 12.5*r2
+    elif r < 0.4:
+        P = P + 9. + 12.5*r2 - 20.*r + 4.*log(r/0.2)
+    else:
+        P = P + 3. + 4.*log(2.)
+    u[i] = P / ((gamma - 1.)*rho0)
+    
+
+
+#File
+fileOutput = h5py.File(fileOutputName, 'w')
+
+# Header
+grp = fileOutput.create_group("/Header")
+grp.attrs["BoxSize"] = [boxSize, boxSize, 0.2]
+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]
+grp.attrs["Time"] = 0.0
+grp.attrs["NumFileOutputsPerSnapshot"] = 1
+grp.attrs["MassTable"] = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+grp.attrs["Flag_Entropy_ICs"] = [0, 0, 0, 0, 0, 0]
+
+#Runtime parameters
+grp = fileOutput.create_group("/RuntimePars")
+grp.attrs["PeriodicBoundariesOn"] = 1
+
+#Units
+grp = fileOutput.create_group("/Units")
+grp.attrs["Unit length in cgs (U_L)"] = 1.
+grp.attrs["Unit mass in cgs (U_M)"] = 1.
+grp.attrs["Unit time in cgs (U_t)"] = 1.
+grp.attrs["Unit current in cgs (U_I)"] = 1.
+grp.attrs["Unit temperature in cgs (U_T)"] = 1.
+
+#Particle group
+grp = fileOutput.create_group("/PartType0")
+ds = grp.create_dataset('Coordinates', (numPart, 3), 'd')
+ds[()] = coords
+ds = grp.create_dataset('Velocities', (numPart, 3), 'f')
+ds[()] = v
+ds = grp.create_dataset('Masses', (numPart, 1), 'f')
+ds[()] = m.reshape((numPart,1))
+ds = grp.create_dataset('SmoothingLength', (numPart,1), 'f')
+ds[()] = h.reshape((numPart,1))
+ds = grp.create_dataset('InternalEnergy', (numPart,1), 'f')
+ds[()] = u.reshape((numPart,1))
+ds = grp.create_dataset('ParticleIDs', (numPart,1), 'L')
+ds[()] = ids.reshape((numPart,1))
+
+fileOutput.close()
+
+

examples/GreshoVortex_2D/plotSolution.py

+###############################################################################
+ # This file is part of SWIFT.
+ # 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
+ # 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 Gresho-Chan vortex and plots the SPH answer
+
+# Parameters
+gas_gamma = 5./3.     # Gas adiabatic index
+rho0 = 1          # Gas density
+P0 = 0.           # Constant additional pressure (should have no impact on the dynamics)
+
+# ---------------------------------------------------------------
+# 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])
+
+# Generate the analytic solution at this time
+N = 200
+R_max = 0.8
+solution_r = arange(0, R_max, R_max / N)
+solution_P = zeros(N)
+solution_v_phi = zeros(N)
+solution_v_r = zeros(N)
+
+for i in range(N):
+    if solution_r[i] < 0.2:
+        solution_P[i] = P0 + 5. + 12.5*solution_r[i]**2
+        solution_v_phi[i] = 5.*solution_r[i]
+    elif solution_r[i] < 0.4:
+        solution_P[i] = P0 + 9. + 12.5*solution_r[i]**2 - 20.*solution_r[i] + 4.*log(solution_r[i]/0.2)
+        solution_v_phi[i] = 2. -5.*solution_r[i]
+    else:
+        solution_P[i] = P0 + 3. + 4.*log(2.)
+        solution_v_phi[i] = 0.
+
+solution_rho = ones(N) * rho0
+solution_s = solution_P / solution_rho**gas_gamma
+solution_u = solution_P /((gas_gamma - 1.)*solution_rho)
+
+# Read the simulation data
+sim = h5py.File("gresho_%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
+vel = sim["/PartType0/Velocities"][:,:]
+r = sqrt(x**2 + y**2)
+v_r = (x * vel[:,0] + y * vel[:,1]) / r
+v_phi = (-y * vel[:,0] + x * vel[:,1]) / r
+v_norm = sqrt(vel[:,0]**2 + vel[:,1]**2)
+rho = sim["/PartType0/Density"][:]
+u = sim["/PartType0/InternalEnergy"][:]
+S = sim["/PartType0/Entropy"][:]
+P = sim["/PartType0/Pressure"][:]
+
+# Plot the interesting quantities
+figure()
+
+
+# Azimuthal velocity profile -----------------------------
+subplot(231)
+
+plot(r, v_phi, '.', color='r', ms=0.5)
+plot(solution_r, solution_v_phi, '--', color='k', alpha=0.8, lw=1.2)
+plot([0.2, 0.2], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
+plot([0.4, 0.4], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
+xlabel("${\\rm{Radius}}~r$", labelpad=0)
+ylabel("${\\rm{Azimuthal~velocity}}~v_\\phi$", labelpad=0)
+xlim(0,R_max)
+ylim(-0.1, 1.2)
+
+# Radial density profile --------------------------------
+subplot(232)
+
+plot(r, rho, '.', color='r', ms=0.5)
+plot(solution_r, solution_rho, '--', color='k', alpha=0.8, lw=1.2)
+plot([0.2, 0.2], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
+plot([0.4, 0.4], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
+xlabel("${\\rm{Radius}}~r$", labelpad=0)
+ylabel("${\\rm{Density}}~\\rho$", labelpad=0)
+xlim(0,R_max)
+ylim(rho0-0.3, rho0 + 0.3)
+#yticks([-0.2, -0.1, 0., 0.1, 0.2])
+
+# Radial pressure profile --------------------------------
+subplot(233)
+
+plot(r, P, '.', color='r', ms=0.5)
+plot(solution_r, solution_P, '--', color='k', alpha=0.8, lw=1.2)
+plot([0.2, 0.2], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
+plot([0.4, 0.4], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
+xlabel("${\\rm{Radius}}~r$", labelpad=0)
+ylabel("${\\rm{Pressure}}~P$", labelpad=0)
+xlim(0, R_max)
+ylim(4.9 + P0, P0 + 6.1)
+
+# Internal energy profile --------------------------------
+subplot(234)
+
+plot(r, u, '.', color='r', ms=0.5)
+plot(solution_r, solution_u, '--', color='k', alpha=0.8, lw=1.2)
+plot([0.2, 0.2], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
+plot([0.4, 0.4], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
+xlabel("${\\rm{Radius}}~r$", labelpad=0)
+ylabel("${\\rm{Internal~Energy}}~u$", labelpad=0)
+xlim(0,R_max)
+ylim(7.3, 9.1)
+
+
+# Radial entropy profile --------------------------------
+subplot(235)
+
+plot(r, S, '.', color='r', ms=0.5)
+plot(solution_r, solution_s, '--', color='k', alpha=0.8, lw=1.2)
+plot([0.2, 0.2], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
+plot([0.4, 0.4], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
+xlabel("${\\rm{Radius}}~r$", labelpad=0)
+ylabel("${\\rm{Entropy}}~S$", labelpad=0)
+xlim(0, R_max)
+ylim(4.9 + P0, P0 + 6.1)
+
+# Image --------------------------------------------------
+#subplot(234)
+#scatter(pos[:,0], pos[:,1], c=v_norm, cmap="PuBu", edgecolors='face', s=4, vmin=0, vmax=1)
+#text(0.95, 0.95, "$|v|$", ha="right", va="top")
+#xlim(0,1)
+#ylim(0,1)
+#xlabel("$x$", labelpad=0)
+#ylabel("$y$", labelpad=0)
+
+# Information -------------------------------------
+subplot(236, frameon=False)
+
+text(-0.49, 0.9, "Gresho-Chan vortex with  $\\gamma=%.3f$ at $t=%.2f$"%(gas_gamma,time), fontsize=10)
+text(-0.49, 0.8, "Background $\\rho_0=%.3f$"%rho0, fontsize=10)
+text(-0.49, 0.7, "Background $P_0=%.3f$"%P0, 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("GreshoVortex.png", dpi=200)

examples/GreshoVortex_2D/run.sh

+#!/bin/bash
+
+ # Generate the initial conditions if they are not present.
+if [ ! -e glassPlane_128.hdf5 ]
+then
+    echo "Fetching initial glass file for the Gresho-Chan vortex example..."
+    ./getGlass.sh
+fi
+if [ ! -e greshoVortex.hdf5 ]
+then
+    echo "Generating initial conditions for the Gresho-Chan vortex example..."
+    python makeIC.py
+fi
+
+# Run SWIFT
+../swift -s -t 1 gresho.yml
+
+# Plot the solution
+python plotSolution.py 11

examples/KelvinHelmoltz_2D/kelvinHelmholtz.yml

+# Define the system of units to use internally. 
+InternalUnitSystem:
+  UnitMass_in_cgs:     1   # Grams
+  UnitLength_in_cgs:   1   # Centimeters
+  UnitVelocity_in_cgs: 1   # Centimeters per second
+  UnitCurrent_in_cgs:  1   # Amperes
+  UnitTemp_in_cgs:     1   # Kelvin
+
+# Parameters governing the time integration
+TimeIntegration:
+  time_begin: 0.    # The starting time of the simulation (in internal units).
+  time_end:   1.5   # The end time of the simulation (in internal units).
+  dt_min:     1e-6  # The minimal time-step size of the simulation (in internal units).
+  dt_max:     1e-2  # The maximal time-step size of the simulation (in internal units).
+
+# Parameters governing the snapshots
+Snapshots:
+  basename:            kelvinHelmholtz  # Common part of the name of output files
+  time_first:          0.               # Time of the first output (in internal units)
+  delta_time:          0.25      # Time difference between consecutive outputs (in internal units)
+
+# Parameters governing the conserved quantities statistics
+Statistics:
+  delta_time:          1e-2 # Time between statistics output
+
+# Parameters for the hydrodynamics scheme
+SPH:
+  resolution_eta:        1.2348   # Target smoothing length in units of the mean inter-particle separation (1.2348 == 48Ngbs with the cubic spline kernel).
+  delta_neighbours:      0.1      # The tolerance for the targetted number of neighbours.
+  max_smoothing_length:  0.01      # Maximal smoothing length allowed (in internal units).
+  CFL_condition:         0.1      # Courant-Friedrich-Levy condition for time integration.
+  
+# Parameters related to the initial conditions
+InitialConditions:
+  file_name:  ./kelvinHelmholtz.hdf5     # The file to read

examples/KelvinHelmoltz_2D/makeIC.py

+###############################################################################
+ # This file is part of SWIFT.
+ # 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
+ # 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/>.
+ # 
+ ##############################################################################
+
+import h5py
+from numpy import *
+import sys
+
+# Generates a swift IC file for the Kelvin-Helmholtz vortex in a periodic box
+
+# Parameters
+L2    = 128       # Particles along one edge in the low-density region
+gamma = 5./3.     # Gas adiabatic index
+P1    = 2.5       # Central region pressure
+P2    = 2.5       # Outskirts pressure
+v1    = 0.5       # Central region velocity
+v2    = -0.5      # Outskirts vlocity
+rho1  = 2         # Central density
+rho2  = 1         # Outskirts density
+omega0 = 0.1
+sigma = 0.05 / sqrt(2)
+fileOutputName = "kelvinHelmholtz.hdf5" 
+#---------------------------------------------------
+
+# Start by generating grids of particles at the two densities
+numPart2 = L2 * L2
+L1 = int(sqrt(numPart2 / rho2 * rho1))
+numPart1 = L1 * L1
+
+#print "N2 =", numPart2, "N1 =", numPart1
+#print "L2 =", L2, "L1 = ", L1
+#print "rho2 =", rho2, "rho1 =", (float(L1*L1)) / (float(L2*L2))
+
+coords1 = zeros((numPart1, 3))
+coords2 = zeros((numPart2, 3))
+h1 = ones(numPart1) * 1.2348 / L1
+h2 = ones(numPart2) * 1.2348 / L2
+m1 = zeros(numPart1)
+m2 = zeros(numPart2)
+u1 = zeros(numPart1)
+u2 = zeros(numPart2)
+vel1 = zeros((numPart1, 3))
+vel2 = zeros((numPart2, 3))
+
+# Particles in the central region
+for i in range(L1):
+    for j in range(L1):
+
+        index = i * L1 + j
+        
+        x = i / float(L1) + 1. / (2. * L1)
+        y = j / float(L1) + 1. / (2. * L1)
+
+        coords1[index, 0] = x
+        coords1[index, 1] = y
+        u1[index] = P1 / (rho1 * (gamma-1.))
+        vel1[index, 0] = v1
+        
+# Particles in the outskirts
+for i in range(L2):
+    for j in range(L2):
+
+        index = i * L2 + j
+        
+        x = i / float(L2) + 1. / (2. * L2)
+        y = j / float(L2) + 1. / (2. * L2)
+
+        coords2[index, 0] = x
+        coords2[index, 1] = y
+        u2[index] = P2 / (rho2 * (gamma-1.))
+        vel2[index, 0] = v2
+
+
+# Now concatenate arrays