Added 1D vacuum expansion test.

examples/Vacuum_1D/makeIC.py

+###############################################################################
+# This file is part of SWIFT.
+# Copyright (c) 2018 Bert Vandenbroucke (bert.vandenbroucke@gmail.com)
+#
+# 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/>.
+#
+##############################################################################
+
+# Generates an overdensity within a vacuum to test the vacuum handling
+# capabilities of the code
+
+import numpy as np
+import h5py
+
+fileName = "vacuum.hdf5"
+numPart = 100
+boxSize = 1.
+gamma = 5. / 3.
+
+coords = np.zeros((numPart, 3))
+v = np.zeros((numPart, 3))
+m = np.zeros(numPart)
+h = np.zeros(numPart)
+u = np.zeros(numPart)
+ids = np.arange(numPart, dtype = 'L')
+rho = np.zeros(numPart)
+
+# first set the positions, as we try to do a reasonable volume estimate to
+# set the masses
+for i in range(numPart):
+  # we only generate particles in the range [0.25, 0.75]
+  coords[i,0] = 0.25 + 0.5 * (i + 0.5) / numPart
+  rho[i] = 1.
+  P = 1.
+  u[i] = P / (gamma - 1.) / rho[i]
+  m[i] = rho[i] * 0.5 / numPart
+  # reasonable smoothing length estimate
+  h[i] = 1. / numPart
+
+#File
+file = h5py.File(fileName, 'w')
+
+# Header
+grp = file.create_group("/Header")
+grp.attrs["BoxSize"] = boxSize
+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
+grp.attrs["Dimension"] = 1
+
+#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')
+grp.create_dataset('Density', data=rho, dtype='f')
+
+file.close()

examples/Vacuum_1D/plotSolution.py

+###############################################################################
+# This file is part of SWIFT.
+# Copyright (c) 2018 Bert Vandenbroucke (bert.vandenbroucke@gmail.com)
+#
+# 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 matplotlib
+matplotlib.use("Agg")
+import pylab as pl
+import h5py
+import sys
+
+# Parameters
+gamma = 5. / 3. # Polytropic index
+rhoL = 1.       # Initial density in the non vacuum state
+vL = 0.         # Initial velocity in the non vacuum state
+PL = 1.         # Initial pressure in the non vacuum state
+rhoR = 0.       # Initial vacuum density
+vR = 0.         # Initial vacuum velocity
+PR = 0.         # Initial vacuum pressure
+
+# 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
+}
+pl.rcParams.update(params)
+pl.rc('font',**{'family':'sans-serif','sans-serif':['Times']})
+
+# Read the snapshot index from the command line argument
+snap = int(sys.argv[1])
+
+# Open the file and read the relevant data
+file = h5py.File("vacuum_{0:04d}.hdf5".format(snap), "r")
+x = file["/PartType0/Coordinates"][:,0]
+rho = file["/PartType0/Density"]
+v = file["/PartType0/Velocities"][:,0]
+u = file["/PartType0/InternalEnergy"]
+S = file["/PartType0/Entropy"]
+P = file["/PartType0/Pressure"]
+time = file["/Header"].attrs["Time"][0]
+
+scheme = file["/HydroScheme"].attrs["Scheme"]
+kernel = file["/HydroScheme"].attrs["Kernel function"]
+neighbours = file["/HydroScheme"].attrs["Kernel target N_ngb"][0]
+eta = file["/HydroScheme"].attrs["Kernel eta"][0]
+git = file["Code"].attrs["Git Revision"]
+
+# Get the analytic solution, which is just the solution of the corresponding
+# vacuum Riemann problem evaluated at the correct time
+
+# left state sound speed (and rarefaction wave speed)
+aL = np.sqrt(gamma * PL / rhoL)
+
+# vacuum front speed
+SL = vL + 2. / (gamma - 1.) * aL
+
+# we evaluate the solution centred on 0., and shift to the correct position
+# afterwards
+xa = np.arange(-0.25, 0.25, 0.001)
+rhoa = np.zeros(len(xa))
+va = np.zeros(len(xa))
+Pa = np.zeros(len(xa))
+
+for i in range(len(xa)):
+  dxdt = xa[i] / time
+  if dxdt > vL - aL:
+    if dxdt < SL:
+      # rarefaction regime
+      # factor that appears in both the density and pressure expression
+      fac = 2. / (gamma + 1.) + \
+            (gamma - 1.) / (gamma + 1.) * (vL - dxdt) / aL
+      rhoa[i] = rhoL * fac**(2. / (gamma - 1.))
+      va[i] = 2. / (gamma + 1.) * (aL + 0.5 * (gamma - 1.) * vL + dxdt)
+      Pa[i] = PL * fac**(2. * gamma / (gamma - 1.))
+    else:
+      # vacuum regime
+      rhoa[i] = 0.
+      va[i] = 0.
+      Pa[i] = 0.
+  else:
+    # left state regime
+    rhoa[i] = rhoL
+    va[i] = vL
+    Pa[i] = PL
+
+ua = Pa / (gamma - 1.) / rhoa
+Sa = Pa / rhoa**gamma
+
+# Plot the interesting quantities
+fig, ax = pl.subplots(2, 3)
+
+# Velocity profile
+ax[0][0].plot(x, v, "r.", markersize = 4.)
+ax[0][0].plot(xa + 0.75, va, "k--", alpha = 0.8, linewidth = 1.2)
+ax[0][0].plot(xa + 0.25, -va[::-1], "k--", alpha = 0.8, linewidth = 1.2)
+ax[0][0].set_xlabel("${\\rm{Position}}~x$", labelpad = 0)
+ax[0][0].set_ylabel("${\\rm{Velocity}}~v_x$", labelpad = 0)
+
+# Density profile
+ax[0][1].plot(x, rho, "r.", markersize = 4.)
+ax[0][1].plot(xa + 0.75, rhoa, "k--", alpha = 0.8, linewidth = 1.2)
+ax[0][1].plot(xa + 0.25, rhoa[::-1], "k--", alpha = 0.8, linewidth = 1.2)
+ax[0][1].set_xlabel("${\\rm{Position}}~x$", labelpad = 0)
+ax[0][1].set_ylabel("${\\rm{Density}}~\\rho$", labelpad = 0)
+
+# Pressure profile
+ax[0][2].plot(x, P, "r.", markersize = 4.)
+ax[0][2].plot(xa + 0.75, Pa, "k--", alpha = 0.8, linewidth = 1.2)
+ax[0][2].plot(xa + 0.25, Pa[::-1], "k--", alpha = 0.8, linewidth = 1.2)
+ax[0][2].set_xlabel("${\\rm{Position}}~x$", labelpad = 0)
+ax[0][2].set_ylabel("${\\rm{Pressure}}~P$", labelpad = 0)
+
+# Internal energy profile
+ax[1][0].plot(x, u, "r.", markersize = 4.)
+ax[1][0].plot(xa + 0.75, ua, "k--", alpha = 0.8, linewidth = 1.2)
+ax[1][0].plot(xa + 0.25, ua[::-1], "k--", alpha = 0.8, linewidth = 1.2)
+ax[1][0].set_xlabel("${\\rm{Position}}~x$", labelpad = 0)
+ax[1][0].set_ylabel("${\\rm{Internal~Energy}}~u$", labelpad = 0)
+
+# Entropy profile
+ax[1][1].plot(x, S, "r.", markersize = 4.)
+ax[1][1].plot(xa + 0.75, Sa, "k--", alpha = 0.8, linewidth = 1.2)
+ax[1][1].plot(xa + 0.25, Sa[::-1], "k--", alpha = 0.8, linewidth = 1.2)
+ax[1][1].set_xlabel("${\\rm{Position}}~x$", labelpad = 0)
+ax[1][1].set_ylabel("${\\rm{Entropy}}~S$", labelpad = 0)
+
+# Run information
+ax[1][2].set_frame_on(False)
+ax[1][2].text(-0.49, 0.9,
+  "Vacuum test with $\\gamma={0:.3f}$ in 1D at $t = {1:.2f}$".format(
+    gamma, time), fontsize = 10)
+ax[1][2].text(-0.49, 0.8,
+  "Left:~~ $(P_L, \\rho_L, v_L) = ({0:.3f}, {1:.3f}, {2:.3f})$".format(
+    PL, rhoL, vL), fontsize = 10)
+ax[1][2].text(-0.49, 0.7,
+  "Right: $(P_R, \\rho_R, v_R) = ({0:.3f}, {1:.3f}, {2:.3f})$".format(
+    PR, rhoR, vR), fontsize = 10)
+ax[1][2].plot([-0.49, 0.1], [0.62, 0.62], "k-", lw = 1)
+ax[1][2].text(-0.49, 0.5, "$\\textsc{{Swift}}$ {0}".format(git), fontsize = 10)
+ax[1][2].text(-0.49, 0.4, scheme, fontsize = 10)
+ax[1][2].text(-0.49, 0.3, kernel, fontsize = 10)
+ax[1][2].text(-0.49, 0.2,
+  "${0:.2f}$ neighbours ($\\eta={1:.3f}$)".format(neighbours, eta),
+  fontsize = 10)
+ax[1][2].set_xlim(-0.5, 0.5)
+ax[1][2].set_ylim(0., 1.)
+ax[1][2].set_xticks([])
+ax[1][2].set_yticks([])
+
+pl.tight_layout()
+pl.savefig("Vacuum.png".format(snap))

examples/Vacuum_1D/run.sh

+#!/bin/bash
+
+# Generate the initial conditions if they are not present.
+if [ ! -e vacuum.hdf5 ]
+then
+    echo "Generating initial conditions for the 1D vacuum expansion example..."
+    python makeIC.py
+fi
+
+# Run SWIFT
+../swift -s -t 1 vacuum.yml 2>&1 | tee output.log
+
+# Plot the result
+python plotSolution.py 1

examples/Vacuum_1D/vacuum.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:   0.1   # The end time of the simulation (in internal units).
+  dt_min:     1e-10  # 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:            vacuum # Common part of the name of output files
+  time_first:          0.       # Time of the first output (in internal units)
+  delta_time:          0.1     # 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).
+  CFL_condition:         0.1      # Courant-Friedrich-Levy condition for time integration.
+
+# Parameters related to the initial conditions
+InitialConditions:
+  file_name:  ./vacuum.hdf5       # The file to read
+