Added a 1D Sedov-Taylor blast example

examples/SedovBlast_1D/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 Sedov blast test in a periodic cubic box
+
+# Parameters
+numPart = 1000   
+gamma = 5./3.      # Gas adiabatic index
+rho0 = 1.          # Background density
+P0 = 1.e-6         # Background pressure
+E0= 1.             # Energy of the explosion
+N_inject = 3     # Number of particles in which to inject energy
+fileName = "sedov.hdf5" 
+
+#---------------------------------------------------
+coords = zeros((numPart, 3))
+h = zeros(numPart)
+vol = 1.
+
+for i in range(numPart):
+    coords[i,0] = i * vol/numPart + vol/(2.*numPart)
+    h[i] = 1.2348 * vol / numPart
+
+# Generate extra arrays
+v = zeros((numPart, 3))
+ids = linspace(1, numPart, numPart)
+m = zeros(numPart)
+u = zeros(numPart)
+r = zeros(numPart)
+
+r = abs(coords[:,0] - 0.5)
+m[:] = rho0 * vol / numPart    
+u[:] = P0 / (rho0 * (gamma - 1))
+
+# Make the central particle detonate
+index = argsort(r)
+u[index[0:N_inject]] = E0 / (N_inject * m[0])
+
+#--------------------------------------------------
+
+#File
+file = h5py.File(fileName, 'w')
+
+# Header
+grp = file.create_group("/Header")
+grp.attrs["BoxSize"] = [1., 1., 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["NumFilesPerSnapshot"] = 1
+grp.attrs["MassTable"] = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+grp.attrs["Flag_Entropy_ICs"] = 0
+
+#Runtime parameters
+grp = file.create_group("/RuntimePars")
+grp.attrs["PeriodicBoundariesOn"] = 1
+
+#Units
+grp = file.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 = file.create_group("/PartType0")
+grp.create_dataset('Coordinates', data=coords, 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')
+grp.create_dataset('InternalEnergy', data=u, dtype='f')
+grp.create_dataset('ParticleIDs', data=ids, dtype='L')
+
+file.close()

examples/SedovBlast_1D/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
+vel = sim["/PartType0/Velocities"][:,:]
+r = abs(x)
+v_r = x * vel[:,0] / 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, 1)
+
+# 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=2.)
+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=2.)
+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=2.)
+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=2.)
+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=2.)
+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 1D 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/SedovBlast_1D/run.sh

+#!/bin/bash
+
+ # Generate the initial conditions if they are not present.
+if [ ! -e sedov.hdf5 ]
+then
+    echo "Generating initial conditions for the Sedov blast example..."
+    python makeIC.py
+fi
+
+# Run SWIFT
+../swift -s -t 1 sedov.yml
+
+# Plot the solution
+python plotSolution.py 5

examples/SedovBlast_1D/sedov.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:   5e-2  # The end time of the simulation (in internal units).
+  dt_min:     1e-7  # The minimal time-step size of the simulation (in internal units).
+  dt_max:     1e-4  # The maximal time-step size of the simulation (in internal units).
+
+# Parameters governing the snapshots
+Snapshots:
+  basename:            sedov # Common part of the name of output files
+  time_first:          0.    # Time of the first output (in internal units)
+  delta_time:          1e-2  # 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:  ./sedov.hdf5          # The file to read
+