I = I0
flx_tolerance *= 2
f = lambda b: b * L - (1 - L / extrap_len) * np.tan(b * L)
# info: add a small epsilon to the left bound to avoid
# failure of root-finding algorithm
BG = brentq(
lambda b: b * L - (1 - L / extrap_len) * np.tan(b * L),
.50000001 * np.pi / L, np.pi / L)
diffsol_ref = lambda x: np.sin(BG * x) / x
# integration of sin(x)/x yields 'sine integral func'
# anorm, _ = sici(BG * L)
# integration of (sin(BG*r)/r) r**2 dr yields
anorm = (np.sin(BG * L) - BG * L * np.cos(BG * L)) / BG**2
Dktol, Dftol = 2e-3, 2e-2
# r = geomprogr_mesh(N=I, L=L, ratio=0.95)
r = equivolume_mesh(I, 0, L, geo)
lg.info('Reference critical length (L) is %.6f cm' % L)
lg.info('Extrapolation distance (zeta*D) is %.3f cm' % extrap_len)
xs_media, media = set_media(materials[m], L, m)
data = input_data(xs_media,
media,
r,
geo,
LBC=LBC,
RBC=0,
per_unit_angle=True)
# *** WARNING ***
# The extrapolation length is a quite large w.r.t. to the problem
# width in these problems. Therefore, the numerical solution can be
lg.info("*** UD2O-H2Ox-1-0-x ***")
materials = change_H2O(materials)
# --------------------------------------------------------------------------
# Problem 25
m, geo = 'UD2O', 'slab'
case = "%s-H2O(1)-1-0-%s" % (m, get_geoid(geo))
I0 = 180 # to get 5 significative digits, i.e. error below 1 pcm.
L0, L1, L = 9.214139, 1.830563, Lc[case]
LBC = RBC = 0
I1 = I0
I = I1 + I0
widths_of_buffers = [L1, L + L0, 2 * L]
xs_media, media = set_media(materials, widths_of_buffers,
['H2O', m, 'H2O'])
r = equivolume_mesh(I1, 0, widths_of_buffers[0], geo)
for i in range(2):
Lb, Le = widths_of_buffers[i], widths_of_buffers[i + 1]
Ix = I0 if i % 2 == 0 else I1
r = np.append(r, equivolume_mesh(Ix, Lb, Le, geo)[1:])
data = input_data(xs_media, media, r, geo, LBC=LBC, RBC=RBC)
slvr_opts = solver_options(iitmax=5,
oitmax=5,
ritmax=200,
CMFD=True,
pCMFD=False,
Anderson_depth='auto')
filename = os.path.join(odir, case + "_LBC%dRBC%d_I%d" % (LBC, RBC, I))
flx, k = run_calc_with_RM_its(data, slvr_opts, filename)
np.testing.assert_allclose(k,
import logging as lg
lg.info("*** Sood's test suite ***")
lg.info("*** 1G heterogeneous isotropic scattering ***")
lg.info("*** Ux-H2Ox-1-0-x ***")
# --------------------------------------------------------------------------
# Problem 16
m, geo, nks = 'Ub', 'sphere', 4
case = "%s-H2O(1)-1-0-%s" % (m, get_geoid(geo))
L0, L1, L = 6.12745, 3.063725, Lc[case]
LBC, RBC = 2, 0
I1 = I0 = 20 # to get error on k less than 10 pcm
I = I1 + I0
xs_media, media = set_media(materials, [L0, L], [m, 'H2O'])
r = equivolume_mesh(I0, 0, L0, geo)
r = np.append(r, equivolume_mesh(I1, L0, L, geo)[1:])
data = input_data(xs_media, media, r, geo, LBC=LBC, RBC=RBC,
per_unit_angle=True)
slvr_opts = solver_options(iitmax=5, oitmax=5, ritmax=200, CMFD=True,
pCMFD=False, Anderson_depth='auto',
ks=np.full(I, nks))
filename = os.path.join(odir, case + "_LBC%dRBC%d_I%d" %
(LBC, RBC, I))
flx, k = run_calc_with_RM_its(data, slvr_opts, filename)
np.testing.assert_allclose(k, 1.0, atol=1.e-4, err_msg=case +
": criticality not verified")
# Problem 18
m = 'Uc'
geometry_type, LBC=2, RBC=2)
# ks is needed anyway when validating the input solver options
k, flx = solve_cpm1D(Homog2GSlab_data, solver_options(ks=np.full(I, 0)))
flxinf = np.dot(np.linalg.inv(np.diag(st) - ss[:,:,0]), chi)
kinf = np.dot(nsf, flxinf) # 1.07838136
flxinf *= np.linalg.norm(flx[:, 0]) / np.linalg.norm(flxinf)
np.testing.assert_allclose(flx, np.tile(flxinf, (I, 1)).T,
err_msg="flx-inf not verified")
np.testing.assert_allclose(k, kinf, atol=1.e-7,
err_msg="k-inf not verified")
# solve the MC2011 problem
lg.info("Solve the MC2011 problem by CPM in the " + geometry_type)
# L *= 2; media = [['HM', L]]
I = 100 # number of cells in the spatial mesh
r = equivolume_mesh(I, 0, L, geometry_type)
# r = geomprogr_mesh(I, 0, L, ratio=1.005)
# warning: remind that the solution in half slab use white reflection
# at the center, introducing some error!
Homog2GSlab_data = input_data(xs_media, media, r,
geometry_type, LBC=0, RBC=2)
# ks is needed anyway when validating the input solver options
k, flx = solve_cpm1D(Homog2GSlab_data,
solver_options(ks=np.full(I, 0)), vrbs=False)
kref = 0.744417
np.testing.assert_allclose(k, kref, atol=1.e-3,
err_msg="ref k of MC2011 not verified")
lg.info("k verified up to about three significant digits")
lg.info("Reference k from S16 is %.6f" % kref)
lg.info("*** PUx-H2Ox-1-0-x ***")
# --------------------------------------------------------------------------
# Problem 3
m, geo = 'PUa', 'slab'
LBC, RBC = 0, 0
case = "%s-H2O(1)-1-0-%s" % (m, get_geoid(geo))
L0, L1, L = 1.47840, 3.063725, Lc[case]
I0 = 80 # nb. of cells in the fuel
I1 = I0 * 2
I = I0 + I1
widths_of_buffers = [2 * L0, 2 * L0 + L1]
xs_media, media = set_media(materials, widths_of_buffers, [m, 'H2O'])
r = equivolume_mesh(I0, 0, widths_of_buffers[0], geo)
r = np.append(r, equivolume_mesh(I1, *widths_of_buffers, geo)[1:])
data = input_data(xs_media, media, r, geo, LBC=LBC, RBC=RBC)
slvr_opts = solver_options(iitmax=5,
oitmax=5,
ritmax=200,
CMFD=True,
pCMFD=False,
Anderson_depth='auto')
filename = os.path.join(odir, case + "_LBC%dRBC%d_I%d" % (LBC, RBC, I))
flx, k = run_calc_with_RM_its(data, slvr_opts, filename)
np.testing.assert_allclose(k,
1.0,
atol=1.e-5,
err_msg=case + ": criticality not verified")