def plot_set1(tsteps, tvec, path):
reader = mgdr.MovingGridDataReader(path)
print("Domain Size: {} ".format(reader._domain_size))
print("Variables available: {}".format(reader._var_names))
Nx, Ny, Nz = reader._domain_size
middle_selection = 0.20 #select middle 25% of domain in x
middle_offset = 0.016
x1 = int(Nx/2 - middle_selection/2*Nx + middle_offset*Nx)
x2 = int(Nx/2 + middle_selection/2*Nx + middle_offset*Nx)
reader.setSubDomain(((x1,0,0),(x2,Ny-1,Nz-1)))
# Get coordinates based on subdomain
x,y,z = reader.readCoordinates()
x_center = np.mean(x[:,0,0])
nx, ny, nz = reader._subdomain_hi-reader._subdomain_lo+1
W = np.zeros(len(tsteps))
t_legend = []
for tind, step in enumerate(tsteps):
#Reading in
reader.setStep(step)
print("reading in Mass Fraction at step {}.".format(step))
YHeavy = np.squeeze(np.array(reader.readData('mass fraction 0')))
plt.figure()
plt.title("t = {} ms".format(step*1e-2))
plt.pcolor(1000*x[:,:,int(Nz/2)],1000*y[:,:,int(Nz/2)],YHeavy[:,:,int(Nz/2)])
plt.xlabel('x [mm]')
plt.ylabel('y [mm]')
ax = plt.gca()
ax.set_aspect('equal')
plt.colorbar()
plt.clim([0,1])
#Format plots
print("Formatting Plots")
for ind in plt.get_fignums():
plt.figure(ind)
plt.tight_layout()
return None
def plot_set1(tsteps, tvec, path):
reader = mgdr.MovingGridDataReader(path)
print("Domain Size: {} ".format(reader._domain_size))
print("Variables available: {}".format(reader._var_names))
Nx, Ny, Nz = reader._domain_size
middle_selection = 0.12 #select middle 25% of domain in x
middle_offset = 0.016
x1 = int(Nx/2 - middle_selection/2*Nx + middle_offset*Nx)
x2 = int(Nx/2 + middle_selection/2*Nx + middle_offset*Nx)
reader.setSubDomain(((x1,0,0),(x2,Ny-1,Nz-1)))
# Get coordinates based on subdomain
x,y,z = reader.readCoordinates()
x_center = np.mean(x[:,0,0])
nx, ny, nz = reader._subdomain_hi-reader._subdomain_lo+1
W = np.zeros(len(tsteps))
t_legend = []
for tind, step in enumerate(tsteps):
#Reading in
reader.setStep(step)
print("reading in Mass Fraction at step {}.".format(step))
YHeavy = np.squeeze(np.array(reader.readData('mass fraction 0')))
print("reading in density at step {}.".format(step))
density = np.squeeze(np.array(reader.readData('density')))
print("reading in pressure at step {}.".format(step))
pressure = np.squeeze(np.array(reader.readData('pressure')))
#Calculating Stats
print("Computing Diffusion Properties")
rho_bar = np.mean(np.mean(density,axis=2),axis=1)
Cp = YHeavy*Cp_Heavy + (1-YHeavy)*Cp_air
Cv = YHeavy*Cv_Heavy + (1-YHeavy)*Cv_air
gamma = Cp/Cv
del Cp, Cv
c = (gamma*pressure/density)**0.5
del gamma
M = (YHeavy/M_Heavy+(1-YHeavy)/M_air)**(-1)
T = M*pressure/(density*Ru)
#Find inner mixing zone (IMZ)
IMZ_thresh = 0.9
XHeavy = M/M_Heavy*YHeavy
XHeavy_bar = np.mean(np.mean(XHeavy,axis=2),axis=1)
IMZ_crit = 4*XHeavy_bar*(1-XHeavy_bar) - IMZ_thresh
for ind in range(len(IMZ_crit)):
if IMZ_crit[ind] >= 0:
IMZ_lo = ind
break
for ind in range(len(IMZ_crit)):
ind2 = nx-ind-1
if IMZ_crit[ind2] >= 0:
IMZ_hi = ind2
break
IMZ_mid = np.argmax(IMZ_crit)
del XHeavy
#Density Spectra
t_legend.append("t = {} ms".format(step*1e-2))
k_rad, rho_spec_rad = fh.radial_spectra(x[:,0,0],y[0,:,0],z[0,0,:],density[IMZ_lo:IMZ_hi+1,:,:])
plt.figure(2)
plt.loglog(k_rad, rho_spec_rad)
plt.xlabel('Radial Wavenumber [m-1]')
plt.ylabel("Density spectra")
#Energy Spectra
velocity = np.squeeze(np.array(reader.readData('velocity')))
u_tilde = np.mean(np.mean(velocity[0,:,:,:]*density,axis=2),axis=1)/np.mean(np.mean(density,axis=2),axis=1)
u_doubleprime = velocity[0,:,:,:]-u_tilde.reshape((nx,1,1))
energy_for_spectra = density*u_doubleprime/(np.reshape(rho_bar,(nx,1,1)))**0.5
k_rad, rhoU_spec_rad = fh.radial_spectra(x[:,0,0],y[0,:,0],z[0,0,:],energy_for_spectra[IMZ_lo:IMZ_hi+1,:,:])
plt.figure(3)
plt.loglog(k_rad, rhoU_spec_rad)
plt.xlabel('Radial Wavenumber [m-1]')
plt.ylabel("Energy Spectra")
#Format plots
print("Formatting Plots")
t_legend.append("-3/2 slope")
for ind in plt.get_fignums():
plt.figure(ind)
plt.loglog(k_rad, 1e2*k_rad**(-1.5),'k--')
plt.legend(t_legend)
plt.tight_layout()
return None
A = 1.06036
B = -0.1561
C = 0.19300
D = -0.47635
E = 1.03587
F = -1.52996
G = 1.76474
H = -3.89411
#calculate some constants
eps_ij = (eps_on_k_air * eps_on_k_Heavy)**0.5
sigma_ij = 0.5 * (sigma_air + sigma_Heavy)
M_ij = 2.0 / (1 / M_air + 1 / M_Heavy)
#Read in a file and plot something
reader = mgdr.MovingGridDataReader(
"/home/jrwest/Research/FloATPy_moving_grid/data/Wong/grid_B")
print("Domain Size: {} ".format(reader._domain_size))
Nx, Ny, Nz = reader._domain_size
middle_selection = 0.12 #select middle 25% of domain in x
middle_offset = 0.016
x1 = int(Nx / 2 - middle_selection / 2 * Nx + middle_offset * Nx)
x2 = int(Nx / 2 + middle_selection / 2 * Nx + middle_offset * Nx)
reader.setSubDomain(((x1, 0, 0), (x2, Ny - 1, Nz - 1)))
#Choose the time steps to use
#tsteps = (0,10,45,80,115,125,135,145,155,165,180) #all steps
#tsteps = (125,145,165,180) #for spectra
#tsteps = (10,45,80,115,125,145,165,180) #use for density reconstruction and anisotropy
#tsteps = (10,125) #for covariances
tsteps = (10, 165)
def plot_set1(tsteps, tvec, path, plot_reshock):
reader = mgdr.MovingGridDataReader(path)
print("Domain Size: {} ".format(reader._domain_size))
print("Variables available: {}".format(reader._var_names))
Nx, Ny, Nz = reader._domain_size
middle_selection = 0.12 #select middle 25% of domain in x
middle_offset = 0.016
x1 = int(Nx / 2 - middle_selection / 2 * Nx + middle_offset * Nx)
x2 = int(Nx / 2 + middle_selection / 2 * Nx + middle_offset * Nx)
reader.setSubDomain(((x1, 0, 0), (x2, Ny - 1, Nz - 1)))
# Get coordinates based on subdomain
x, y, z = reader.readCoordinates()
x_center = np.mean(x[:, 0, 0])
nx, ny, nz = reader._subdomain_hi - reader._subdomain_lo + 1
Ma_t_IMZ = np.zeros(len(tsteps))
At_e_IMZ = np.zeros(len(tsteps))
At_e_centerplane = np.zeros(len(tsteps))
W = np.zeros(len(tsteps))
Theta = np.zeros(len(tsteps))
TKE_int = np.zeros(len(tsteps))
Diss_int = np.zeros(len(tsteps))
Enstrophy_int = np.zeros(len(tsteps))
b11_IMZ = np.zeros(len(tsteps))
for tind, step in enumerate(tsteps):
#Reading in
reader.setStep(step)
print("reading in Mass Fraction at step {}.".format(step))
YHeavy = np.squeeze(np.array(reader.readData('mass fraction 0')))
print("reading in density at step {}.".format(step))
density = np.squeeze(np.array(reader.readData('density')))
print("reading in pressure at step {}.".format(step))
pressure = np.squeeze(np.array(reader.readData('pressure')))
#Calculating Stats
print("Computing Diffusion Properties")
rho_bar = np.mean(np.mean(density, axis=2), axis=1)
Cp = YHeavy * Cp_Heavy + (1 - YHeavy) * Cp_air
Cv = YHeavy * Cv_Heavy + (1 - YHeavy) * Cv_air
gamma = Cp / Cv
del Cp, Cv
c = (gamma * pressure / density)**0.5
del gamma
M = (YHeavy / M_Heavy + (1 - YHeavy) / M_air)**(-1)
T = M * pressure / (density * Ru)
Tij = T / eps_ij
Omega_D = A * Tij**B + C * np.exp(D * Tij) + E * np.exp(
F * Tij) + G * np.exp(H * Tij)
D_binary = (0.0266 / Omega_D) * (T**1.5) / (sigma_ij**2 * pressure *
M_ij**0.5)
del Tij, Omega_D, pressure, T
# Compute Integrated Scalar Dissipation Rate
print("Computing Dissipation")
dx = x[1, 0, 0] - x[0, 0, 0]
dy = y[0, 1, 0] - y[0, 0, 0]
dz = z[0, 0, 1] - z[0, 0, 0]
dYdx = first_der.differentiateSixthOrderFiniteDifference(
YHeavy, dx, 0, None, True, 3, 'C')
dYdy = first_der.differentiateSixthOrderFiniteDifference(
YHeavy, dy, 1, None, True, 3, 'C')
dYdz = first_der.differentiateSixthOrderFiniteDifference(
YHeavy, dz, 2, None, True, 3, 'C')
Diss = D_binary * (dYdx**2 + dYdy**2 + dYdz**2)
Diss_int[tind] = integrate.simps(integrate.simps(integrate.simps(
Diss, z[0, 0, :], axis=2),
y[0, :, 0],
axis=1),
x[:, 0, 0],
axis=0)
del dYdx, dYdy, dYdz, Diss, D_binary
#Find inner mixing zone (IMZ)
IMZ_thresh = 0.9
XHeavy = M / M_Heavy * YHeavy
XHeavy_bar = np.mean(np.mean(XHeavy, axis=2), axis=1)
IMZ_crit = 4 * XHeavy_bar * (1 - XHeavy_bar) - IMZ_thresh
del M
for ind in range(len(IMZ_crit)):
if IMZ_crit[ind] >= 0:
IMZ_lo = ind
break
for ind in range(len(IMZ_crit)):
ind2 = nx - ind - 1
if IMZ_crit[ind2] >= 0:
IMZ_hi = ind2
break
IMZ_mid = np.argmax(IMZ_crit)
# Compute Mixing Width
print("Computing Mixing Width and Mixedness")
integrand = 4 * XHeavy_bar * (1 - XHeavy_bar)
W[tind] = integrate.simps(integrand, x[:, 0, 0])
# Compute Mixedness
integrand = XHeavy * (1 - XHeavy)
integrand = np.mean(np.mean(integrand, axis=2), axis=1)
numer = integrate.simps(integrand, x[:, 0, 0])
denom = W[tind] / 4.0
Theta[tind] = numer / denom
xstar = (x[:, 0, 0] - x[IMZ_mid, 0, 0]) / W[tind]
del XHeavy
#Compute Turbulent Mach Number
print("reading in velocity at step {}.".format(step))
print("Computing Turbulent Mach Number")
velocity = np.squeeze(np.array(reader.readData('velocity')))
u_tilde = np.mean(np.mean(velocity[0, :, :, :] * density, axis=2),
axis=1) / np.mean(np.mean(density, axis=2), axis=1)
v_tilde = np.mean(np.mean(velocity[1, :, :, :] * density, axis=2),
axis=1) / np.mean(np.mean(density, axis=2), axis=1)
w_tilde = np.mean(np.mean(velocity[2, :, :, :] * density, axis=2),
axis=1) / np.mean(np.mean(density, axis=2), axis=1)
u_doubleprime = velocity[0, :, :, :] - u_tilde.reshape((nx, 1, 1))
v_doubleprime = velocity[1, :, :, :] - v_tilde.reshape((nx, 1, 1))
w_doubleprime = velocity[2, :, :, :] - w_tilde.reshape((nx, 1, 1))
del u_tilde, v_tilde, w_tilde
TKE = 0.5 * density * (u_doubleprime**2 + v_doubleprime**2 +
w_doubleprime**2)
# Compute Integrated TKE
TKE_int[tind] = integrate.simps(integrate.simps(integrate.simps(
TKE, z[0, 0, :], axis=2),
y[0, :, 0],
axis=1),
x[:, 0, 0],
axis=0)
#Anisotropy (23 and 24)
R11 = np.mean(np.mean(density * u_doubleprime**2, axis=2),
axis=1) / np.mean(np.mean(density, axis=2), axis=1)
Rkk = np.mean(np.mean(2 * TKE, axis=2), axis=1) / np.mean(
np.mean(density, axis=2), axis=1)
b11 = R11 / Rkk - 1.0 / 3.0
b11_IMZ[tind] = np.mean(b11[IMZ_lo:IMZ_hi + 1])
Ma_t = (((np.mean(np.mean(2 * TKE / density, axis=2), axis=1))**0.5) /
np.mean(np.mean(c, axis=2), axis=1))
Ma_t_IMZ[tind] = np.mean(Ma_t[IMZ_lo:IMZ_hi + 1])
del u_doubleprime, v_doubleprime, w_doubleprime, TKE
#Compute Effective Atwood Number
rho_prime = density - rho_bar.reshape((nx, 1, 1))
At_e = (
(np.mean(np.mean(rho_prime**2, axis=2), axis=1))**0.5) / rho_bar
At_e_IMZ[tind] = np.mean(At_e[IMZ_lo:IMZ_hi + 1])
At_e_centerplane[tind] = At_e[IMZ_mid]
del rho_prime
# Compute Integrated Enstrophy
print("Computing Enstrophy")
Enstrophy = 0
dwdy = first_der.differentiateSixthOrderFiniteDifference(
velocity[2, :, :, :], dy, 1, None, True, 3, 'C')
dvdx = first_der.differentiateSixthOrderFiniteDifference(
velocity[1, :, :, :], dx, 0, None, True, 3, 'C')
Enstrophy += density * (dwdy - dvdx)**2
del dwdy, dvdx
dudz = first_der.differentiateSixthOrderFiniteDifference(
velocity[0, :, :, :], dz, 2, None, True, 3, 'C')
dwdx = first_der.differentiateSixthOrderFiniteDifference(
velocity[2, :, :, :], dx, 0, None, True, 3, 'C')
Enstrophy += density * (dudz - dwdx)**2
del dudz, dwdx
dvdx = first_der.differentiateSixthOrderFiniteDifference(
velocity[1, :, :, :], dx, 0, None, True, 3, 'C')
dudy = first_der.differentiateSixthOrderFiniteDifference(
velocity[0, :, :, :], dy, 1, None, True, 3, 'C')
Enstrophy += density * (dvdx - dudy)**2
del dvdx, dudy, velocity
Enstrophy_int[tind] = integrate.simps(integrate.simps(integrate.simps(
Enstrophy, z[0, 0, :], axis=2),
y[0, :, 0],
axis=1),
x[:, 0, 0],
axis=0)
del Enstrophy, density, YHeavy
print("Plotting")
#Plots
xline = np.array([1.15, 1.15])
plt.figure(1)
plt.plot(tvec * 1000, W * 1000, '-o')
plt.ylabel('W [mm]')
plt.xlabel('time [ms]')
if plot_reshock:
var = W * 1000
yline = np.array([np.min(var), np.max(var)])
plt.plot(xline, yline, 'k--')
plt.figure(2)
plt.plot(tvec * 1000, Theta, '-o')
plt.ylabel('Mixedness [-]')
plt.xlabel('time [ms]')
if plot_reshock:
var = Theta
yline = np.array([np.min(var), np.max(var)])
plt.plot(xline, yline, 'k--')
plt.figure(3)
plt.semilogy(tvec * 1000, TKE_int, '-o')
plt.ylabel('Int. TKE [kg m2 s-2]')
plt.xlabel('time [ms]')
if plot_reshock:
var = TKE_int
yline = np.array([np.min(var), np.max(var)])
plt.plot(xline, yline, 'k--')
plt.figure(4)
plt.semilogy(tvec * 1000, Diss_int, '-o')
plt.ylabel('Int. Dissipation Rate [m3 s-1]')
plt.xlabel('time [ms]')
if plot_reshock:
var = Diss_int
yline = np.array([np.min(var), np.max(var)])
plt.plot(xline, yline, 'k--')
plt.figure(5)
plt.semilogy(tvec * 1000, Enstrophy_int, '-o')
plt.ylabel(r'Int. Enstrophy [kg s-2]')
plt.xlabel('time [ms]')
if plot_reshock:
var = Enstrophy_int
yline = np.array([np.min(var), np.max(var)])
plt.plot(xline, yline, 'k--')
plt.figure(6)
plt.plot(tvec * 1000, Ma_t_IMZ, '-o')
plt.ylabel('Turbulent Ma')
plt.xlabel('time [ms]')
if plot_reshock:
var = Ma_t_IMZ
yline = np.array([np.min(var), np.max(var)])
plt.plot(xline, yline, 'k--')
plt.figure(7)
plt.plot(tvec * 1000, At_e_IMZ, '-o')
plt.ylabel('Effective At')
plt.xlabel('time [ms]')
if plot_reshock:
var = At_e_IMZ
yline = np.array([np.min(var), np.max(var)])
plt.plot(xline, yline, 'k--')
plt.figure(8)
plt.plot(tvec * 1000, b11_IMZ, '-o')
plt.ylabel('b11')
plt.xlabel('time [ms]')
if plot_reshock:
var = b11_IMZ
yline = np.array([np.min(var), np.max(var)])
plt.plot(xline, yline, 'k--')
return None
def plot_set1(tsteps, tvec, path):
reader = mgdr.MovingGridDataReader(path)
print("Domain Size: {} ".format(reader._domain_size))
print("Variables available: {}".format(reader._var_names))
Nx, Ny, Nz = reader._domain_size
middle_selection = 0.12 #select middle 25% of domain in x
middle_offset = 0.016
x1 = int(Nx/2 - middle_selection/2*Nx + middle_offset*Nx)
x2 = int(Nx/2 + middle_selection/2*Nx + middle_offset*Nx)
reader.setSubDomain(((x1,0,0),(x2,Ny-1,Nz-1)))
# Get coordinates based on subdomain
x,y,z = reader.readCoordinates()
x_center = np.mean(x[:,0,0])
nx, ny, nz = reader._subdomain_hi-reader._subdomain_lo+1
W = np.zeros(len(tsteps))
t_legend1 = []
t_legend2 = []
for tind, step in enumerate(tsteps):
#Reading in
reader.setStep(step)
print("reading in Mass Fraction at step {}.".format(step))
YHeavy = np.squeeze(np.array(reader.readData('mass fraction 0')))
print("reading in density at step {}.".format(step))
density = np.squeeze(np.array(reader.readData('density')))
print("reading in pressure at step {}.".format(step))
pressure = np.squeeze(np.array(reader.readData('pressure')))
#Calculating Stats
print("Computing Diffusion Properties")
rho_bar = np.mean(np.mean(density,axis=2),axis=1)
Cp = YHeavy*Cp_Heavy + (1-YHeavy)*Cp_air
Cv = YHeavy*Cv_Heavy + (1-YHeavy)*Cv_air
gamma = Cp/Cv
del Cp, Cv
c = (gamma*pressure/density)**0.5
del gamma
M = (YHeavy/M_Heavy+(1-YHeavy)/M_air)**(-1)
T = M*pressure/(density*Ru)
#Find inner mixing zone (IMZ)
IMZ_thresh = 0.9
XHeavy = M/M_Heavy*YHeavy
XHeavy_bar = np.mean(np.mean(XHeavy,axis=2),axis=1)
IMZ_crit = 4*XHeavy_bar*(1-XHeavy_bar) - IMZ_thresh
for ind in range(len(IMZ_crit)):
if IMZ_crit[ind] >= 0:
IMZ_lo = ind
break
for ind in range(len(IMZ_crit)):
ind2 = nx-ind-1
if IMZ_crit[ind2] >= 0:
IMZ_hi = ind2
break
IMZ_mid = np.argmax(IMZ_crit)
# Compute Mixing Width
print("Computing Mixing Width and Mixedness")
integrand = 4*XHeavy_bar*(1-XHeavy_bar)
W[tind] = integrate.simps(integrand,x[:,0,0])
xstar= (x[:,0,0]-x[IMZ_mid,0,0])/W[tind]
#Mole Fraction Variance
XHeavy_prime = XHeavy-XHeavy_bar.reshape((nx,1,1))
XHeavy_variance = np.mean(np.mean(XHeavy_prime**2,axis=2),axis=1)
if step < 125:
#before reshock
plt.figure(1)
t_legend1.append("t = {} ms".format(step*1e-2))
else:
#after reshock
plt.figure(2)
t_legend2.append("t = {} ms".format(step*1e-2))
plt.plot(xstar,XHeavy_variance**0.5)
plt.xlim([-2,2])
plt.xlabel('x*')
plt.ylabel("X'rms (SF6)")
plt.ylim([0,0.3])
del XHeavy
#Compute Turbulent Mach Number
print("reading in velocity at step {}.".format(step))
print("Computing Turbulent Mach Number")
velocity = np.squeeze(np.array(reader.readData('velocity')))
u_tilde = np.mean(np.mean(velocity[0,:,:,:]*density,axis=2),axis=1)/np.mean(np.mean(density,axis=2),axis=1)
v_tilde = np.mean(np.mean(velocity[1,:,:,:]*density,axis=2),axis=1)/np.mean(np.mean(density,axis=2),axis=1)
w_tilde = np.mean(np.mean(velocity[2,:,:,:]*density,axis=2),axis=1)/np.mean(np.mean(density,axis=2),axis=1)
u_doubleprime = velocity[0,:,:,:]-u_tilde.reshape((nx,1,1))
v_doubleprime = velocity[1,:,:,:]-v_tilde.reshape((nx,1,1))
w_doubleprime = velocity[2,:,:,:]-w_tilde.reshape((nx,1,1))
del u_tilde, v_tilde, w_tilde
TKE = 0.5*density*(u_doubleprime**2+v_doubleprime**2+w_doubleprime**2)
#Anisotropy (23 and 24)
R11 = np.mean(np.mean(density*u_doubleprime**2,axis=2),axis=1)/np.mean(np.mean(density,axis=2),axis=1)
Rkk = np.mean(np.mean(2*TKE,axis=2),axis=1)/np.mean(np.mean(density,axis=2),axis=1)
b11 = R11/Rkk - 1.0/3.0
Ma_t = (((np.mean(np.mean(2*TKE/density,axis=2),axis=1))**0.5)/
np.mean(np.mean(c,axis=2),axis=1))
del u_doubleprime,v_doubleprime,w_doubleprime, TKE
if step < 125:
#before reshock
plt.figure(3)
else:
#after reshock
plt.figure(4)
plt.plot(xstar,b11)
plt.xlabel('x*')
plt.ylabel('b11')
plt.xlim([-1.5,1.5])
plt.ylim([-2.0/3.0,2.0/3.0])
#Compute Effective Atwood Number
rho_prime = density-rho_bar.reshape((nx,1,1))
At_e = ((np.mean(np.mean(rho_prime**2,axis=2),axis=1))**0.5)/rho_bar
# Compute Covariances of Density
M_bar = np.mean(np.mean(M,axis=2),axis=1)
M_prime = M-M_bar.reshape((nx,1,1))
cov_rho_M = np.mean(np.mean(rho_prime*M_prime,axis=2),axis=1)/(rho_bar*M_bar)
p_bar = np.mean(np.mean(pressure,axis=2),axis=1)
p_prime = pressure-p_bar.reshape((nx,1,1))
cov_rho_p = np.mean(np.mean(rho_prime*p_prime,axis=2),axis=1)/(rho_bar*p_bar)
Tinv_bar = np.mean(np.mean(1.0/T,axis=2),axis=1)
Tinv_prime = 1.0/T-Tinv_bar.reshape((nx,1,1))
cov_rho_Tinv = np.mean(np.mean(rho_prime*Tinv_prime,axis=2),axis=1)/(rho_bar*Tinv_bar)
del rho_prime, M, M_prime, T, Tinv_prime, p_prime
if (step == 80) or (step == 135):
plt.figure(step)
plt.plot(xstar,cov_rho_p)
plt.plot(xstar,cov_rho_M)
plt.plot(xstar,cov_rho_Tinv)
plt.xlabel('x*')
plt.xlim([-2.0,2.0])
plt.ylim([0,0.25])
plt.legend(['rho-p','rho-M','rho-1/T'])
plt.ylabel('Density Covariance')
plt.title("t = {} ms".format(step*1e-2))
#Density Reconstruction
rho_Heavy = np.mean(density[0,:,:])
rho_air = np.mean(density[-1,:,:])
rho_recon_bar = (rho_Heavy-rho_air)*XHeavy_bar+rho_air
if step < 125:
#before reshock
plt.figure(5)
else:
#after reshock
plt.figure(6)
plt.plot(xstar,rho_recon_bar/rho_bar)
plt.xlim([-2.0,2.0])
plt.xlabel('x*')
plt.ylabel('rho / incompressible rho')
del density, YHeavy
#Format plots
print("Formatting Plots")
for ind in range(1,7):
plt.figure(ind)
if ind%2 == 1:
plt.legend(t_legend1)
else:
plt.legend(t_legend2)
for ind in plt.get_fignums():
plt.figure(ind)
plt.tight_layout()
return None