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
+where1 = abs(coords1[:,1]-0.5) < 0.25
+where2 = abs(coords2[:,1]-0.5) > 0.25
+
+coords = append(coords1[where1, :], coords2[where2, :], axis=0)
+
+#print L2*(L2/2), L1*(L1/2)
+#print shape(coords), shape(coords1[where1,:]), shape(coords2[where2,:])
+#print shape(coords), shape(logical_not(coords1[where1,:])), shape(logical_not(coords2[where2,:]))
+
+vel = append(vel1[where1, :], vel2[where2, :], axis=0)
+h = append(h1[where1], h2[where2], axis=0)
+m = append(m1[where1], m2[where2], axis=0)
+u = append(u1[where1], u2[where2], axis=0)
+numPart = size(h)
+ids = linspace(1, numPart, numPart)
+m[:] = (0.5 * rho1 + 0.5 * rho2) / float(numPart)
+
+# Velocity perturbation
+vel[:,1] = omega0 * sin(4*pi*coords[:,0]) * (exp(-(coords[:,1]-0.25)**2 / (2 * sigma**2)) + exp(-(coords[:,1]-0.75)**2 / (2 * sigma**2)))
+            
+#File
+fileOutput = h5py.File(fileOutputName, 'w')
+
+# Header
+grp = fileOutput.create_group("/Header")
+grp.attrs["BoxSize"] = [1., 1., 0.1]
+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[()] = vel
+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/KelvinHelmoltz_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
+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
+
+# ---------------------------------------------------------------
+# 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("kelvinHelmholtz_%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"][:,:]
+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)
+scatter(pos[:,0], pos[:,1], c=vel[:,0], cmap="PuBu", edgecolors='face', s=4, vmin=-1., vmax=1.)
+text(0.97, 0.97, "${\\rm{Velocity~along}}~x$", ha="right", va="top", backgroundcolor="w")
+xlabel("${\\rm{Position}}~x$", labelpad=0)
+ylabel("${\\rm{Position}}~y$", labelpad=0)
+xlim(0, 1)
+ylim(0, 1)
+
+# Radial density profile --------------------------------
+subplot(232)
+scatter(pos[:,0], pos[:,1], c=rho, cmap="PuBu", edgecolors='face', s=4, vmin=0.8, vmax=2.2)
+text(0.97, 0.97, "${\\rm{Density}}$", ha="right", va="top", backgroundcolor="w")
+xlabel("${\\rm{Position}}~x$", labelpad=0)
+ylabel("${\\rm{Position}}~y$", labelpad=0)
+xlim(0, 1)
+ylim(0, 1)
+
+# Radial pressure profile --------------------------------
+subplot(233)
+scatter(pos[:,0], pos[:,1], c=P, cmap="PuBu", edgecolors='face', s=4, vmin=1, vmax=4)
+text(0.97, 0.97, "${\\rm{Pressure}}$", ha="right", va="top", backgroundcolor="w")
+xlabel("${\\rm{Position}}~x$", labelpad=0)
+ylabel("${\\rm{Position}}~y$", labelpad=0)
+xlim(0, 1)
+ylim(0, 1)
+
+# Internal energy profile --------------------------------
+subplot(234)
+scatter(pos[:,0], pos[:,1], c=u, cmap="PuBu", edgecolors='face', s=4, vmin=1.5, vmax=5.)
+text(0.97, 0.97, "${\\rm{Internal~energy}}$", ha="right", va="top", backgroundcolor="w")
+xlabel("${\\rm{Position}}~x$", labelpad=0)
+ylabel("${\\rm{Position}}~y$", labelpad=0)
+xlim(0, 1)
+ylim(0, 1)
+
+# Radial entropy profile --------------------------------
+subplot(235)
+scatter(pos[:,0], pos[:,1], c=S, cmap="PuBu", edgecolors='face', s=4, vmin=0.5, vmax=3.)
+text(0.97, 0.97, "${\\rm{Entropy}}$", ha="right", va="top", backgroundcolor="w")
+xlabel("${\\rm{Position}}~x$", labelpad=0)
+ylabel("${\\rm{Position}}~y$", labelpad=0)
+xlim(0, 1)
+ylim(0, 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, "Kelvin-Helmholtz instability at $t=%.2f$"%(time), fontsize=10)
+text(-0.49, 0.8, "Centre:~~~ $(P, \\rho, v) = (%.3f, %.3f, %.3f)$"%(P1, rho1, v1), fontsize=10)
+text(-0.49, 0.7, "Outskirts: $(P, \\rho, v) = (%.3f, %.3f, %.3f)$"%(P2, rho2, v2), 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("KelvinHelmholtz.png", dpi=200)

examples/KelvinHelmoltz_2D/run.sh

+#!/bin/bash
+
+ # Generate the initial conditions if they are not present.
+if [ ! -e kelvinHelmholtz.hdf5 ]
+then
+    echo "Generating initial conditions for the Kelvin-Helmholtz example..."
+    python makeIC.py
+fi
+
+# Run SWIFT
+../swift -s -t 1 kelvinHelmholtz.yml
+
+# Plot the solution
+python plotSolution.py 6

examples/GreshoVortex/makeIC.py → examples/PerturbedBox_2D/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
@@ -19,28 +18,28 @@
  ##############################################################################
 
 import h5py
+import sys
 import random
 from numpy import *
 
-# Generates a swift IC file for the Gresho Vortex in a periodic box
+# Generates a swift IC file containing a perturbed cartesian distribution of particles
+# at a constant density and pressure in a cubic box
 
 # Parameters
-periodic= 1      # 1 For periodic box
-factor = 3
-boxSize = [ 1.0 , 1.0, 1.0/factor ]
-L = 120           # Number of particles along one axis
-gamma = 5./3.     # Gas adiabatic index
-eta = 1.2349      # 48 ngbs with cubic spline kernel
-rho = 1           # Gas density
-P0 = 0.           # Constant additional pressure (should have no impact on the dynamics)
-fileName = "greshoVortex.hdf5" 
-vol = boxSize[0] * boxSize[1] * boxSize[2]
+periodic= 1          # 1 For periodic box
+boxSize = 1.
+L = int(sys.argv[1]) # Number of particles along one axis
+rho = 1.             # Density
+P = 1.               # Pressure
+gamma = 5./3.        # Gas adiabatic index
+pert = 0.1          # Perturbation scale (in units of the interparticle separation)
+fileName = "perturbedPlane.hdf5" 
 
 
 #---------------------------------------------------
-
-numPart = L**3 / factor
-mass = boxSize[0]*boxSize[1]*boxSize[2] * rho / numPart
+numPart = L**2
+mass = boxSize**2 * rho / numPart
+internalEnergy = P / ((gamma - 1.)*rho)
 
 #Generate particles
 coords = zeros((numPart, 3))
@@ -50,43 +49,26 @@ h      = zeros((numPart, 1))
 u      = zeros((numPart, 1))
 ids    = zeros((numPart, 1), dtype='L')
 
-partId=0
 for i in range(L):
     for j in range(L):
-        for k in range(L/factor):
-            index = i*L*L/factor + j*L/factor + k
-            x = i * boxSize[0] / L + boxSize[0] / (2*L)
-            y = j * boxSize[0] / L + boxSize[0] / (2*L)
-            z = k * boxSize[0] / L + boxSize[0] / (2*L)
-            r2 = (x - boxSize[0] / 2)**2 + (y - boxSize[1] / 2)**2
-            r = sqrt(r2)
-            coords[index,0] = x
-            coords[index,1] = y
-            coords[index,2] = z
-            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[index,0] = -v_phi * (y - boxSize[0] / 2) / r
-            v[index,1] =  v_phi * (x - boxSize[0] / 2) / r
-            v[index,2] = 0.
-            m[index] = mass
-            h[index] = eta * boxSize[0] / L
-            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[index] = P / ((gamma - 1.)*rho)
-            ids[index] = partId + 1
-            partId = partId + 1
-
-
+        index = i*L + j
+        x = i * boxSize / L + boxSize / (2*L) + random.random() * pert * boxSize/(2.*L)
+        y = j * boxSize / L + boxSize / (2*L) + random.random() * pert * boxSize/(2.*L)
+        z = 0
+        coords[index,0] = x
+        coords[index,1] = y
+        coords[index,2] = z
+        v[index,0] = 0.
+        v[index,1] = 0.
+        v[index,2] = 0.
+        m[index] = mass
+        h[index] = 1.23485 * boxSize / L
+        u[index] = internalEnergy
+        ids[index] = index
+            
+            
+
+#--------------------------------------------------
 
 #File
 file = h5py.File(fileName, 'w')
@@ -101,6 +83,7 @@ grp.attrs["Time"] = 0.0
 grp.attrs["NumFilesPerSnapshot"] = 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]
+grp.attrs["NumPart_Total"] = numPart
 
 #Runtime parameters
 grp = file.create_group("/RuntimePars")
@@ -126,9 +109,7 @@ ds = grp.create_dataset('SmoothingLength', (numPart,1), 'f')
 ds[()] = h
 ds = grp.create_dataset('InternalEnergy', (numPart,1), 'f')
 ds[()] = u
-ds = grp.create_dataset('ParticleIDs', (numPart,1), 'L')
-ds[()] = ids[:]
+ds = grp.create_dataset('ParticleIDs', (numPart, 1), 'L')
+ds[()] = ids + 1
 
 file.close()
-
-

examples/PerturbedBox_2D/perturbedPlane.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:   10.   # 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:            perturbedPlane # 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-3 # 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:  0.1      # 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:  ./perturbedPlane.hdf5     # The file to read

examples/SedovBlast/profile.py

-###############################################################################
- # This file is part of SWIFT.
- # Copyright (c) 2015 Bert Vandenbroucke (bert.vandenbroucke@ugent.be)
- # 
- # 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 numpy as np
-import h5py
-import matplotlib
-matplotlib.use('Agg')
-import pylab as pl
-import glob
-import sedov
-
-# plot the radial density profile for all snapshots in the current directory,
-# as well as the analytical solution of Sedov
-
-for f in sorted(glob.glob("output*.hdf5")):
-    file = h5py.File(f, "r")
-    t = file["/Header"].attrs["Time"]
-    coords = np.array(file["/PartType0/Coordinates"])
-    rho = np.array(file["/PartType0/Density"])
-
-    radius = np.sqrt( (coords[:,0]-5.)**2 + (coords[:,1]-5.)**2 + \
-                      (coords[:,2]-5.)**2 )
-    
-    r_theory, rho_theory = sedov.get_analytical_solution(100., 5./3., 3, t,
-                                                         max(radius))
-    
-    pl.plot(r_theory, rho_theory, "r-")
-    pl.plot(radius, rho, "k.")
-    pl.savefig("{name}.png".format(name = f[:-5]))
-    pl.close()

examples/SedovBlast/rdf.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 h5py
-import random
-import sys
-import math
-from numpy import *
-
-# Reads the HDF5 output of SWIFT and generates a radial density profile
-# of the different physical values.
-
-# Input values?
-if len(sys.argv) < 3 :
-    print "Usage: " , sys.argv[0] , " <filename> <nr. bins>"
-    exit()
-    
-# Get the input arguments
-fileName = sys.argv[1];
-nr_bins = int( sys.argv[2] );
-
-
-# Open the file
-fileName = sys.argv[1];
-file = h5py.File( fileName , 'r' )
-
-# Get the space dimensions.
-grp = file[ "/Header" ]
-boxsize = grp.attrs[ 'BoxSize' ]
-if len( boxsize ) > 0:
-    boxsize = boxsize[0]
-
-# Get the particle data
-grp = file.get( '/PartType0' )
-ds = grp.get( 'Coordinates' )
-coords = ds[...]
-ds = grp.get( 'Velocities' )
-v = ds[...]
-ds = grp.get( 'Masses' )
-m = ds[...]
-ds = grp.get( 'SmoothingLength' )
-h = ds[...]
-ds = grp.get( 'InternalEnergy' )
-u = ds[...]
-ds = grp.get( 'ParticleIDs' )
-ids = ds[...]
-ds = grp.get( 'Density' )
-rho = ds[...]
-
-# Set the origin to be the middle of the box
-origin = [ boxsize / 2 , boxsize / 2 , boxsize / 2 ]
-
-# Get the maximum radius
-r_max = boxsize / 2
-
-# Init the bins
-nr_parts = coords.shape[0]
-bins_v = zeros( nr_bins )
-bins_m = zeros( nr_bins )
-bins_h = zeros( nr_bins )
-bins_u = zeros( nr_bins )
-bins_rho = zeros( nr_bins )
-bins_count = zeros( nr_bins )
-bins_P = zeros( nr_bins )
-
-# Loop over the particles and fill the bins.
-for i in range( nr_parts ):
-
-    # Get the box index.
-    r = coords[i] - origin
-    r = sqrt( r[0]*r[0] + r[1]*r[1] + r[2]*r[2] )
-    ind = floor( r / r_max * nr_bins )
-    
-    # Update the bins
-    if ( ind < nr_bins ):
-        bins_count[ind] += 1
-        bins_v[ind] += sqrt( v[i,0]*v[i,0] + v[i,1]*v[i,1] + v[i,2]*v[i,2] )
-        bins_m[ind] += m[i]
-        bins_h[ind] += h[i]
-        bins_u[ind] += u[i]
-        bins_rho[ind] += rho[i]
-        bins_P[ind] += (2.0/3)*u[i]*rho[i]
-    
-# Loop over the bins and dump them
-print "# bucket left right count v m h u rho"
-for i in range( nr_bins ):
-
-    # Normalize by the bin volume.
-    r_left = r_max * i / nr_bins
-    r_right = r_max * (i+1) / nr_bins
-    vol = 4/3*math.pi*(r_right*r_right*r_right - r_left*r_left*r_left)
-    ivol = 1.0 / vol
-
-    print "%i %.3e %.3e %.3e %.3e %.3e %.3e %.3e %.3e %.3e" % \
-        ( i , r_left , r_right , \
-          bins_count[i] * ivol , \
-          bins_v[i] / bins_count[i] , \
-          bins_m[i] * ivol , \
-          bins_h[i] / bins_count[i] , \
-          bins_u[i] / bins_count[i] , \
-          bins_rho[i] / bins_count[i] ,
-          bins_P[i] / bins_count[i] )
-    
-    

examples/SedovBlast/sedov.py

-###############################################################################
- # This file is part of SWIFT.
- # Copyright (c) 2015 Bert Vandenbroucke (bert.vandenbroucke@ugent.be)
- # 
- # 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 numpy as np
-import scipy.integrate as integrate
-import scipy.optimize as optimize
-import os
-
-# Calculate the analytical solution of the Sedov-Taylor shock wave for a given
-# number of dimensions, gamma and time. We assume dimensionless units and a
-# setup with constant density 1, pressure and velocity 0. An energy 1 is
-# inserted in the center at t 0.
-#
-# The solution is a self-similar shock wave, which was described in detail by
-# Sedov (1959). We follow his notations and solution method.
-#
-# The position of the shock at time t is given by
-#  r2 = (E/rho1)^(1/(2+nu)) * t^(2/(2+nu))
-# the energy E is related to the inserted energy E0 by E0 = alpha*E, with alpha
-# a constant which has to be calculated by imposing energy conservation.
-#
-# The density for a given radius at a certain time is determined by introducing
-# the dimensionless position coordinate lambda = r/r2. The density profile as
-# a function of lambda is constant in time and given by
-#  rho = rho1 * R(V, gamma, nu)
-# and
-#  V = V(lambda, gamma, nu)
-#
-# The function V(lambda, gamma, nu) is found by solving a differential equation
-# described in detail in Sedov (1959) chapter 4, section 5. Alpha is calculated
-# from the integrals in section 11 of the same chapter.
-#
-# Numerically, the complete solution requires the use of 3 quadratures and 1
-# root solver, which are implemented using the GNU Scientific Library (GSL).
-# Since some quadratures call functions that themselves contain quadratures,
-# the problem is highly non-linear and complex and takes a while to converge.
-# Therefore, we tabulate the alpha values and profile values the first time
-# a given set of gamma and nu values is requested and reuse these tabulated
-# values.
-#
-# Reference:
-#  Sedov (1959): Sedov, L., Similitude et dimensions en mecanique (7th ed.;
-#                Moscou: Editions Mir) - french translation of the original
-#                book from 1959.
-
-# dimensionless variable z = gamma*P/R as a function of V (and gamma and nu)
-# R is a dimensionless density, while P is a dimensionless pressure
-# z is hence a sort of dimensionless sound speed
-# The expression below corresponds to eq. 11.9 in Sedov (1959), chapter 4
-def _z(V, gamma, nu):
-    if V == 2./(nu+2.)/gamma:
-        return 0.
-    else:
-        return (gamma-1.)*V*V*(V-2./(2.+nu))/2./(2./(2.+nu)/gamma-V)
-
-# differential equation that needs to be solved to obtain lambda for a given V
-# corresponds to eq. 5.11 in Sedov (1959), chapter 4 (omega = 0)
-def _dlnlambda_dV(V, gamma, nu):
-    nom = _z(V, gamma, nu) - (V-2./(nu+2.))*(V-2./(nu+2.))
-    denom = V*(V-1.)*(V-2./(nu+2.))+nu*(2./(nu+2.)/gamma-V)*_z(V, gamma, nu)
-    return nom/denom
-
-# dimensionless variable lambda = r/r2 as a function of V (and gamma and nu)
-# found by solving differential equation 5.11 in Sedov (1959), chapter 4
-# (omega = 0)
-def _lambda(V, gamma, nu):
-    if V == 2./(nu+2.)/gamma:
-        return 0.
-    else:
-        V0 = 4./(nu+2.)/(gamma+1.)
-        integral, err = integrate.quad(_dlnlambda_dV, V, V0, (gamma, nu),
-                                       limit = 8000)
-        return np.exp(-integral)
-
-# dimensionless variable R = rho/rho1 as a function of V (and gamma and nu)
-# found by inverting eq. 5.12 in Sedov (1959), chapter 4 (omega = 0)
-# the integration constant C is found by inserting the R, V and z values
-# at the shock wave, where lambda is 1. These correspond to eq. 11.8 in Sedov
-# (1959), chapter 4.
-def _R(V, gamma, nu):
-    if V == 2./(nu+2.)/gamma:
-        return 0.
-    else:
-        C = 8.*gamma*(gamma-1.)/(nu+2.)/(nu+2.)/(gamma+1.)/(gamma+1.) \
-                *((gamma-1.)/(gamma+1.))**(gamma-2.) \
-                *(4./(nu+2.)/(gamma+1.)-2./(nu+2.))
-        lambda1 = _lambda(V, gamma, nu)
-        lambda5 = lambda1**(nu+2)
-        return (_z(V, gamma, nu)*(V-2./(nu+2.))*lambda5/C)**(1./(gamma-2.))
-
-# function of which we need to find the zero point to invert lambda(V)
-def _lambda_min_lambda(V, lambdax, gamma, nu):
-    return _lambda(V, gamma, nu) - lambdax
-
-# dimensionless variable V = v*t/r as a function of lambda (and gamma and nu)
-# found by inverting the function lamdba(V) which is found by solving
-# differential equation 5.11 in Sedov (1959), chapter 4 (omega = 0)
-# the invertion is done by searching the zero point of the function
-# lambda_min_lambda defined above
-def _V_inv(lambdax, gamma, nu):
-    if lambdax == 0.:
-        return 2./(2.+nu)/gamma;
-    else:
-        return optimize.brentq(_lambda_min_lambda, 2./(nu+2.)/gamma, 
-                               4./(nu+2.)/(gamma+1.), (lambdax, gamma, nu))
-
-# integrand of the first integral in eq. 11.24 in Sedov (1959), chapter 4
-def _integrandum1(lambdax, gamma, nu):
-    V = _V_inv(lambdax, gamma, nu)
-    if nu == 2:
-        return _R(V, gamma, nu)*V**2*lambdax**3
-    else:
-        return _R(V, gamma, nu)*V**2*lambdax**4
-
-# integrand of the second integral in eq. 11.24 in Sedov (1959), chapter 4
-def _integrandum2(lambdax, gamma, nu):
-    V = _V_inv(lambdax, gamma, nu)
-    if V == 2./(nu+2.)/gamma:
-        P = 0.
-    else:
-        P = _z(V, gamma, nu)*_R(V, gamma, nu)/gamma
-    if nu == 2:
-        return P*lambdax**3
-    else:
-        return P*lambdax**4
-
-# calculate alpha = E0/E
-# this corresponds to eq. 11.24 in Sedov (1959), chapter 4
-def get_alpha(gamma, nu):
-  integral1, err1 = integrate.quad(_integrandum1, 0., 1., (gamma, nu))
-  integral2, err2 = integrate.quad(_integrandum2, 0., 1., (gamma, nu))
-  
-  if nu == 2:
-    return np.pi*integral1+2.*np.pi/(gamma-1.)*integral2
-  else:
-    return 2.*np.pi*integral1+4.*np.pi/(gamma-1.)*integral2
-
-# get the analytical solution for the Sedov-Taylor blastwave given an input
-# energy E, adiabatic index gamma, and number of dimensions nu, at time t and
-# with a maximal outer region radius maxr
-def get_analytical_solution(E, gamma, nu, t, maxr = 1.):
-    # we check for the existance of a datafile with precomputed alpha and
-    # profile values
-    # if it does not exist, we calculate it here and write it out
-    # calculation of alpha and the profile takes a while...
-    lvec = np.zeros(1000)
-    Rvec = np.zeros(1000)
-    fname = "sedov_profile_gamma_{gamma}_nu_{nu}.dat".format(gamma = gamma,
-                                                             nu = nu)
-    if os.path.exists(fname):
-        file = open(fname, "r")
-        lines = file.readlines()
-        alpha = float(lines[0])
-        for i in range(len(lines)-1):
-            data = lines[i+1].split()
-            lvec[i] = float(data[0])
-            Rvec[i] = float(data[1])
-    else:
-        alpha = get_alpha(gamma, nu)
-        for i in range(1000):
-            lvec[i] = (i+1)*0.001
-            V = _V_inv(lvec[i], gamma, nu)
-            Rvec[i] = _R(V, gamma, nu)
-        file = open(fname, "w")
-        file.write("{alpha}\n".format(alpha = alpha))
-        for i in range(1000):
-            file.write("{l}\t{R}\n".format(l = lvec[i], R = Rvec[i]))
-
-    xvec = np.zeros(1002)
-    rhovec = np.zeros(1002)
-    if nu == 2:
-        r2 = (E/alpha)**0.25*np.sqrt(t)
-    else:
-        r2 = (E/alpha)**0.2*t**0.4
-
-    for i in range(1000):
-        xvec[i] = lvec[i]*r2
-        rhovec[i] = Rvec[i]
-    xvec[1000] = 1.001*r2
-    xvec[1001] = maxr
-    rhovec[1000] = 1.
-    rhovec[1001] = 1.
-    
-    return xvec, rhovec
-
-def main():
-    E = 1.
-    gamma = 1.66667
-    nu = 3
-    t = 0.001
-    x, rho = get_analytical_solution(E, gamma, nu, t)
-    for i in range(len(x)):
-        print x[i], rho[i]
-
-if __name__ == "__main__":
-    main()