def testFirstDirection(self):
"""
Test the first derivatives in the first direction.
"""
x = numpy.empty([1, 100])
x[0, :] = numpy.linspace(0, 2*numpy.pi, 100)
dx = x[0, 1] - x[0, 0]
y = numpy.sin(x)
y_prime_exact = numpy.cos(x)
y_prime_2 = first_der.differentiateSecondOrderFiniteDifference(y, dx, 0, 0, True, 1, 'C')
y_prime_4 = first_der.differentiateFourthOrderFiniteDifference(y, dx, 0, 0, True, 1, 'C')
y_prime_6 = first_der.differentiateSixthOrderFiniteDifference(y, dx, 0, 0, True, 1, 'C')
error_2 = numpy.linalg.norm(y_prime_exact[0, :] - y_prime_2[:])
error_4 = numpy.linalg.norm(y_prime_exact[0, :] - y_prime_4[:])
error_6 = numpy.linalg.norm(y_prime_exact[0, :] - y_prime_6[:])
self.assertLess(error_2, 1.0e-2, "Incorrect derivative in first direction for second order finite difference!")
self.assertLess(error_4, 1.0e-5, "Incorrect derivative in first direction for fourth order finite difference!")
self.assertLess(error_6, 1.0e-7, "Incorrect derivative in first direction for sixth order finite difference!")
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
# 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)
del TKE
# Compute Integrated Scalar Dissipation Rate
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