Commit 3d3dbda5 authored by Matthieu Schaller's avatar Matthieu Schaller
Browse files

Added a 1D Sod shock test-case to the example suite. Includes a plotting script.

parent 697f3946
###############################################################################
# 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
import random
from numpy import *
# Generates a swift IC file for the Sod Shock in a periodic box
# Parameters
gamma = 5./3. # Gas adiabatic index
numPart_L = 800 # Number of particles in the left state
x_min = -1.
x_max = 1.
rho_L = 1. # Density left state
rho_R = 0.125 # Density right state
v_L = 0. # Velocity left state
v_R = 0. # Velocity right state
P_L = 1. # Pressure left state
P_R = 0.1 # Pressure right state
fileName = "sodShock.hdf5"
#---------------------------------------------------
# Find how many particles we actually have
boxSize = x_max - x_min
numPart_R = int(numPart_L * (rho_R / rho_L))
numPart = numPart_L + numPart_R
# Now get the distances
delta_L = (boxSize/2) / numPart_L
delta_R = (boxSize/2) / numPart_R
offset_L = delta_L / 2
offset_R = delta_R / 2
# Build the arrays
coords = zeros((numPart, 3))
v = zeros((numPart, 3))
ids = linspace(1, numPart, numPart)
m = zeros(numPart)
h = zeros(numPart)
u = zeros(numPart)
# Set the particles on the left
for i in range(numPart_L):
coords[i,0] = x_min + offset_L + i * delta_L
u[i] = P_L / (rho_L * (gamma - 1.))
h[i] = 1.2348 * delta_L
m[i] = boxSize * rho_L / (2. * numPart_L)
# Set the particles on the right
for j in range(numPart_R):
i = numPart_L + j
coords[i,0] = offset_R + j * delta_R
u[i] = P_R / (rho_R * (gamma - 1.))
h[i] = 1.2348 * delta_R
m[i] = boxSize * rho_R / (2. * numPart_R)
# Shift particles
coords[:,0] -= x_min
#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
#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) 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 Sod shock and plots the SPH answer
# Generates the analytical solution for the Sod shock test case
# The script works for a given left (x<0) and right (x>0) state and computes the solution at a later time t.
# 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 points between x_min and x_max.
# This follows the solution given in (Toro, 2009)
# Parameters
gas_gamma = 5./3. # Polytropic index
rho_L = 1. # Density left state
rho_R = 0.125 # Density right state
v_L = 0. # Velocity left state
v_R = 0. # Velocity right state
P_L = 1. # Pressure left state
P_R = 0.1 # Pressure right state
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("sodShock_%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"]
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.
# ---------------------------------------------------------------
c_L = sqrt(gas_gamma * P_L / rho_L) # Speed of the rarefaction wave
c_R = sqrt(gas_gamma * P_R / rho_R) # Speed of the shock front
# Helpful variable
Gama = (gas_gamma - 1.) / (gas_gamma + 1.)
beta = (gas_gamma - 1.) / (2. * gas_gamma)
# Characteristic function and its derivative, following Toro (2009)
def compute_f(P_3, P, c):
u = P_3 / P
if u > 1:
term1 = gas_gamma*((gas_gamma+1.)*u + gas_gamma-1.)
term2 = sqrt(2./term1)
fp = (u - 1.)*c*term2
dfdp = c*term2/P + (u - 1.)*c/term2*(-1./term1**2)*gas_gamma*(gas_gamma+1.)/P
else:
fp = (u**beta - 1.)*(2.*c/(gas_gamma-1.))
dfdp = 2.*c/(gas_gamma-1.)*beta*u**(beta-1.)/P
return (fp, dfdp)
# Solution of the Riemann problem following Toro (2009)
def RiemannProblem(rho_L, P_L, v_L, rho_R, P_R, v_R):
P_new = ((c_L + c_R + (v_L - v_R)*0.5*(gas_gamma-1.))/(c_L / P_L**beta + c_R / P_R**beta))**(1./beta)
P_3 = 0.5*(P_R + P_L)
f_L = 1.
while fabs(P_3 - P_new) > 1e-6:
P_3 = P_new
(f_L, dfdp_L) = compute_f(P_3, P_L, c_L)
(f_R, dfdp_R) = compute_f(P_3, P_R, c_R)
f = f_L + f_R + (v_R - v_L)
df = dfdp_L + dfdp_R
dp = -f/df
prnew = P_3 + dp
v_3 = v_L - f_L
return (P_new, v_3)
# Solve Riemann problem for post-shock region
(P_3, v_3) = RiemannProblem(rho_L, P_L, v_L, rho_R, P_R, v_R)
# Check direction of shocks and wave
shock_R = (P_3 > P_R)
shock_L = (P_3 > P_L)
# Velocity of shock front and and rarefaction wave
if shock_R:
v_right = v_R + c_R**2*(P_3/P_R - 1.)/(gas_gamma*(v_3-v_R))
else:
v_right = c_R + 0.5*(gas_gamma+1.)*v_3 - 0.5*(gas_gamma-1.)*v_R
if shock_L:
v_left = v_L + c_L**2*(P_3/p_L - 1.)/(gas_gamma*(v_3-v_L))
else:
v_left = c_L - 0.5*(gas_gamma+1.)*v_3 + 0.5*(gas_gamma-1.)*v_L
# Compute position of the transitions
x_23 = -fabs(v_left) * time
if shock_L :
x_12 = -fabs(v_left) * time
else:
x_12 = -(c_L - v_L) * time
x_34 = v_3 * time
x_45 = fabs(v_right) * time
if shock_R:
x_56 = fabs(v_right) * time
else:
x_56 = (c_R + v_R) * time
# Prepare arrays
delta_x = (x_max - x_min) / N
x_s = arange(x_min, x_max, delta_x)
rho_s = zeros(N)
P_s = zeros(N)
v_s = zeros(N)
# Compute solution in the different regions
for i in range(N):
if x_s[i] <= x_12:
rho_s[i] = rho_L
P_s[i] = P_L
v_s[i] = v_L
if x_s[i] >= x_12 and x_s[i] < x_23:
if shock_L:
rho_s[i] = rho_L*(Gama + P_3/P_L)/(1. + Gama * P_3/P_L)
P_s[i] = P_3
v_s[i] = v_3
else:
rho_s[i] = rho_L*(Gama * (0. - x_s[i])/(c_L * time) + Gama * v_L/c_L + (1.-Gama))**(2./(gas_gamma-1.))
P_s[i] = P_L*(rho_s[i] / rho_L)**gas_gamma
v_s[i] = (1.-Gama)*(c_L -(0. - x_s[i]) / time) + Gama*v_L
if x_s[i] >= x_23 and x_s[i] < x_34:
if shock_L:
rho_s[i] = rho_L*(Gama + P_3/P_L)/(1+Gama * P_3/p_L)
else:
rho_s[i] = rho_L*(P_3 / P_L)**(1./gas_gamma)
P_s[i] = P_3
v_s[i] = v_3
if x_s[i] >= x_34 and x_s[i] < x_45:
if shock_R:
rho_s[i] = rho_R*(Gama + P_3/P_R)/(1. + Gama * P_3/P_R)
else:
rho_s[i] = rho_R*(P_3 / P_R)**(1./gas_gamma)
P_s[i] = P_3
v_s[i] = v_3
if x_s[i] >= x_45 and x_s[i] < x_56:
if shock_R:
rho_s[i] = rho_R
P_s[i] = P_R
v_s[i] = v_R
else:
rho_s[i] = rho_R*(Gama*(x_s[i])/(c_R*time) - Gama*v_R/c_R + (1.-Gama))**(2./(gas_gamma-1.))
P_s[i] = p_R*(rho_s[i]/rho_R)**gas_gamma
v_s[i] = (1.-Gama)*(-c_R - (-x_s[i])/time) + Gama*v_R
if x_s[i] >= x_56:
rho_s[i] = rho_R
P_s[i] = P_R
v_s[i] = v_R
# 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')
plot(x_s, v_s, '--', color='k', alpha=0.8, lw=1.2)
xlabel("$x$", labelpad=0)
ylabel("$v$", labelpad=0)
xlim(-0.5, 0.5)
ylim(-0.1, 0.95)
# Density profile --------------------------------
subplot(232)
plot(x, rho, '.', color='r')
plot(x_s, rho_s, '--', color='k', alpha=0.8, lw=1.2)
xlabel("$x$", labelpad=0)
ylabel("$\\rho$", labelpad=0)
xlim(-0.5, 0.5)
ylim(0.05, 1.1)
# Pressure profile --------------------------------
subplot(233)
plot(x, P, '.', color='r')
plot(x_s, P_s, '--', color='k', alpha=0.8, lw=1.2)
xlabel("$x$", labelpad=0)
ylabel("$P$", labelpad=0)
xlim(-0.5, 0.5)
ylim(0.01, 1.1)
# Internal energy profile -------------------------
subplot(234)
plot(x, u, '.', color='r')
plot(x_s, u_s, '--', color='k', alpha=0.8, lw=1.2)
xlabel("$x$", labelpad=0)
ylabel("$u$", labelpad=0)
xlim(-0.5, 0.5)
ylim(0.8, 2.2)
# Entropy profile ---------------------------------
subplot(235)
plot(x, S, '.', color='r')
plot(x_s, s_s, '--', color='k', alpha=0.8, lw=1.2)
xlabel("$x$", labelpad=0)
ylabel("$S$", labelpad=0)
xlim(-0.5, 0.5)
ylim(0.8, 3.8)
# Information -------------------------------------
subplot(236, frameon=False)
text(-0.49, 0.9, "Sod shock with $\\gamma=%.3f$ in 1D at $t=%.2f$"%(gas_gamma,time), fontsize=10)
text(-0.49, 0.8, "Left:~~ $(P_L, \\rho_L, v_L) = (%.3f, %.3f, %.3f)$"%(P_L, rho_L, v_L), fontsize=10)
text(-0.49, 0.7, "Right: $(P_R, \\rho_R, v_R) = (%.3f, %.3f, %.3f)$"%(P_R, rho_R, v_R), fontsize=10)
plot([-0.49, 0.1], [0.62, 0.62], 'k-', lw=1)
text(-0.49, 0.5, scheme, fontsize=10)
text(-0.49, 0.4, kernel, fontsize=10)
text(-0.49, 0.3, "$%.2f$ neighbours ($\\eta=%.3f$)"%(neighbours, eta), fontsize=10)
xlim(-0.5, 0.5)
ylim(0, 1)
xticks([])
yticks([])
savefig("SodShock.png", dpi=200)
#!/bin/bash
# Generate the initial conditions if they are not present.
if [ ! -e sodShock.hdf5 ]
then
echo "Generating initial conditions for the 1D SodShock example..."
python makeIC.py
fi
# Run SWIFT
../swift -s -t 1 sodShock.yml
# Plot the result
python plotSolution.py 1
# 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: 0.2 # 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-2 # The maximal time-step size of the simulation (in internal units).
# Parameters governing the snapshots
Snapshots:
basename: sodShock # Common part of the name of output files
time_first: 0. # Time of the first output (in internal units)
delta_time: 0.2 # 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: 0.4 # 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: ./sodShock.hdf5 # The file to read
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