Commit 11425964 authored by Matthieu Schaller's avatar Matthieu Schaller
Browse files

Added a 1D Sedov-Taylor blast example

parent dea2e02d
###############################################################################
# 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()
###############################################################################
# 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)
#!/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
# 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
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