#
# 3. Root System fluxes
#
t3 = timer.time()
kr = np.array(list(map(lambda t: rs_Kr[int(t) - 1],
type))) # convert from 'per type' to 'per segment'
kz = np.array(list(map(lambda t: rs_Kz[int(t) - 1], type)))
soil_p2 = lambda x, y, z: soil_p(x, y, z, inf.psi, soil[-1].lowerDepth
) # J/kg
if dirichlet == False: # Neumann
Q, b = xylem_flux.linear_system(seg, nodes, radius, kr, kz, rho, g,
soil_p2)
Q, b = xylem_flux.bc_neumann(Q, b, np.array([0]),
np.array([pot_trans]))
x = LA.spsolve(Q, b) # direct
eff_trans = xylem_flux.axial_flux0(
x, seg, nodes, kz, rho, g) # verify that eff_trans == pot_trans
print(
"using neumann ( Effective Transpiration = " + str(eff_trans) +
" m^3 s^-1)", "top potential", x[0])
if dirichlet or (x[0] < top_pot):
Q, b = xylem_flux.linear_system(seg, nodes, radius, kr, kz, rho, g,
soil_p2)
dirichlet = True
Q, b = xylem_flux.bc_dirichlet(Q, b, np.array([0]),
np.array([top_pot]))
x = LA.spsolve(Q, b) # direct
eff_trans = xylem_flux.axial_flux0(x, seg, nodes, kz, rho, g)
kz = np.array(list(map(lambda t: rs_Kz[int(t) - 1], type)))
#
# 3. Root System fluxes
#
t3 = timer.time()
# print("3 . Xylem fluxes")
# age dependency
#kr = kr * (10*time_ + 1)
#kz = kz / (10*time_ + 1)
soil_p2 = lambda x, y, z: soil_p(x, y, z, inf.psi, soil[-1].lowerDepth
) # J/kg
if dirichlet == False: # Neumann
Q, b = xylem_flux.linear_system(seg, nodes, radius, kr, kz, rho, g,
soil_p2)
Q, b = xylem_flux.bc_neumann(Q, b, np.array([0]), pot_trans, seg,
nodes)
x = LA.spsolve(Q, b) # direct
eff_trans = xylem_flux.axial_flux0(
x, seg, nodes, kz, rho, g) # verify that eff_trans == pot_trans
print(
"using neumann ( Effective Transpiration = " + str(eff_trans) +
" m^3 s^-1)", "top potential", x[0])
if dirichlet or (x[0] < top_pot):
Q, b = xylem_flux.linear_system(seg, nodes, radius, kr, kz, rho, g,
soil_p2)
dirichlet = True
Q, b = xylem_flux.bc_dirichlet(Q, b, np.array([0]),
np.array([top_pot]))
x = LA.spsolve(Q, b) # direct
eff_trans = xylem_flux.axial_flux0(x, seg, nodes, kz, rho, g)
# from constant to per segment
kr_ = [kr] * 2 * (nnz - 1)
kz_ = [kz] * 2 * (nnz - 1)
a_ = [a] * 2 * (nnz - 1)
# call back function for soil potential
soil = lambda x, y, z: p_s
# calculate fluxes within the root system
Q, b = xylem_flux.linear_system(seg, nodes, a_, kr_, kz_, rho, g, soil) #
# Q, b = xylem_flux.bc_dirichlet(Q, b, np.array([0,nnz-1]), np.array([p0,pL]))
Q, b = xylem_flux.bc_dirichlet(Q, b, np.array([0]),
np.array([p0])) # dirichlet top
Q, b = xylem_flux.bc_neumann(Q, b, [nnz - 1], [0]) # neumann tip
# plt.spy(Q)
# plt.show()
start = timeit.default_timer()
x = LA.spsolve(Q, b, use_umfpack=True) # direct
stop = timeit.default_timer()
# print ("linear system solved in", stop - start, " s")
# plot results
plt.plot(list(map(toHead, x)), z_, "r*")
plt.plot(pr, za_)
plt.xlabel("Xylem pressure (cm)")
plt.ylabel("Depth (m)")
plt.show()