Commit 4713e6d4 authored by Matthieu Schaller's avatar Matthieu Schaller
Browse files

Added the 1D Noh problem and solution script

parent 8eb92b67
###############################################################################
# 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 Noh problem 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
fileName = "noh.hdf5"
#---------------------------------------------------
coords = zeros((numPart, 3))
h = zeros(numPart)
vol = 2.
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)
m[:] = rho0 * vol / numPart
u[:] = P0 / (rho0 * (gamma - 1))
v[coords[:,0]<vol/2. ,0] = 1
v[coords[:,0]>vol/2. ,0] = -1
#--------------------------------------------------
#File
file = h5py.File(fileName, 'w')
# Header
grp = file.create_group("/Header")
grp.attrs["BoxSize"] = [vol, vol, vol]
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')
file.close()
# 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: 0.6 # 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-3 # The maximal time-step size of the simulation (in internal units).
# Parameters governing the snapshots
Snapshots:
basename: noh # Common part of the name of output files
time_first: 0. # Time of the first output (in internal units)
delta_time: 5e-2 # Time difference between consecutive outputs (in internal units)
# Parameters governing the conserved quantities statistics
Statistics:
delta_time: 1e-5 # 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.
CFL_condition: 0.1 # Courant-Friedrich-Levy condition for time integration.
# Parameters related to the initial conditions
InitialConditions:
file_name: ./noh.hdf5 # The file to read
###############################################################################
# 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 Noh problem and plots the SPH answer
# Parameters
gas_gamma = 5./3. # Polytropic index
rho0 = 1. # Background density
P0 = 1.e-6 # Background pressure
v0 = 1
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("noh_%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"]
x = sim["/PartType0/Coordinates"][:,0]
v = sim["/PartType0/Velocities"][:,0]
u = sim["/PartType0/InternalEnergy"][:]
S = sim["/PartType0/Entropy"][:]
P = sim["/PartType0/Pressure"][:]
rho = sim["/PartType0/Density"][:]
N = 1000 # Number of points
x_min = -1
x_max = 1
x += x_min
# ---------------------------------------------------------------
# Don't touch anything after this.
# ---------------------------------------------------------------
x_s = np.arange(0, 2., 2./N) - 1.
rho_s = np.ones(N) * rho0
P_s = np.ones(N) * rho0
v_s = np.ones(N) * v
# Shock position
u0 = rho0 * P0 * (gas_gamma-1)
us = 0.5 * (gas_gamma - 1) * v0
rs = us * time
# Post-shock values
rho_s[np.abs(x_s) < rs] = rho0 * (gas_gamma + 1) / (gas_gamma - 1)
P_s[np.abs(x_s) < rs] = 0.5 * rho0 * v0**2 * (gas_gamma + 1)
v_s[np.abs(x_s) < rs] = 0.
# Pre-shock values
rho_s[np.abs(x_s) >= rs] = rho0
P_s[np.abs(x_s) >= rs] = 0
v_s[x_s >= rs] = -v0
v_s[x_s <= -rs] = v0
# 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(x, v, '.', color='r', ms=4.0)
plot(x_s, v_s, '--', color='k', alpha=0.8, lw=1.2)
xlabel("${\\rm{Position}}~x$", labelpad=0)
ylabel("${\\rm{Velocity}}~v_x$", labelpad=-4)
xlim(-0.5, 0.5)
ylim(-1.2, 1.2)
# Density profile --------------------------------
subplot(232)
plot(x, rho, '.', color='r', ms=4.0)
plot(x_s, rho_s, '--', color='k', alpha=0.8, lw=1.2)
xlabel("${\\rm{Position}}~x$", labelpad=0)
ylabel("${\\rm{Density}}~\\rho$", labelpad=0)
xlim(-0.5, 0.5)
ylim(0.95, 4.4)
# Pressure profile --------------------------------
subplot(233)
plot(x, P, '.', color='r', ms=4.0)
plot(x_s, P_s, '--', color='k', alpha=0.8, lw=1.2)
xlabel("${\\rm{Position}}~x$", labelpad=0)
ylabel("${\\rm{Pressure}}~P$", labelpad=0)
xlim(-0.5, 0.5)
ylim(-0.05, 1.8)
# Internal energy profile -------------------------
subplot(234)
plot(x, u, '.', color='r', ms=4.0)
plot(x_s, u_s, '--', color='k', alpha=0.8, lw=1.2)
xlabel("${\\rm{Position}}~x$", labelpad=0)
ylabel("${\\rm{Internal~Energy}}~u$", labelpad=0)
xlim(-0.5, 0.5)
ylim(-0.05, 0.8)
# Entropy profile ---------------------------------
subplot(235)
plot(x, S, '.', color='r', ms=4.0)
plot(x_s, s_s, '--', color='k', alpha=0.8, lw=1.2)
xlabel("${\\rm{Position}}~x$", labelpad=0)
ylabel("${\\rm{Entropy}}~S$", labelpad=-9)
xlim(-0.5, 0.5)
ylim(-0.05, 0.2)
# Information -------------------------------------
subplot(236, frameon=False)
text(-0.49, 0.9, "Noh problem with $\\gamma=%.3f$ in 1D at $t=%.2f$"%(gas_gamma,time), 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("Noh.png", dpi=200)
#!/bin/bash
# Generate the initial conditions if they are not present.
if [ ! -e noh.hdf5 ]
then
echo "Generating initial conditions for the Noh problem..."
python makeIC.py
fi
# Run SWIFT
../swift -s -t 1 noh.yml 2>&1 | tee output.log
# Plot the solution
python plotSolution.py 12
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