1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
|
#!/usr/bin/env python3
import matplotlib.pyplot as plt
import numpy as np
import bisect
with open('./1D_top.txt', "r") as data:
xch, ych, zch = np.loadtxt(data, delimiter=' ', unpack=True)
# Fit with polyfit
m, c = np.polyfit(ych, zch, 1)
print('gradient =', m, 'intercept =', c)
slope = abs(m) # slope at top boundary
target_flow = 2.0 # imposed discharge
with open('../topography/top_boundary.xyz', "r") as topo:
xin, yin, zin = np.loadtxt(topo, delimiter=' ', unpack=True)
# array index and co-ordinates are related by:
# index = (co-ord - 0.25)*2
xregion = xin[280:301]
zregion = zin[280:301]
xregion_west = xin[100:281]
zregion_west = zin[100:281]
xregion_east = xin[300:408]
zregion_east = zin[300:408]
#print(zregion)
zmin = zregion.min() # minimum height
zmax = zregion[-1]-0.01 # overtopping height
zmax_west = zmax
zmax_east = zmax
zmin_west = zregion_west.min()
zmin_east = zregion_east.min()
print(zmin_east)
numH = 50 # number of height intervals
n_co_chan = 0.035 # Manning's coefficient for inland water
n_co_west = 0.040 # Manning's coefficient for general surface
n_co_east = 0.040 # Manning's coefficient for general surface
def conveyance(numH, n_co, xregion, zregion, zmin, zmax):
p_i = [] # wetted perimeter
A_i = [] # area
r_h = [] # hydraulic radius
h_i = [] # list of heights
K_i = [] # conveyance
Q_i = [] # discharge
x_sub = [[] for i in range(numH)] # list of x values in subregion
z_sub = [[] for i in range(numH)] # list of z values in subregion
for i in range(numH):
h_i.append(zmin + (i+1)*(zmax-zmin)/numH)
#print(zregion[zregion < h_i[i]])
booleanArray = zregion < h_i[i]
#print(booleanArray[i])
x_sub[i] += list(xregion[booleanArray])
z_sub[i] += list(zregion[booleanArray])
for interval in range(len(xregion)-1):
if booleanArray[interval+1] != booleanArray[interval]:
x_extra = xregion[interval] + (h_i[i]-zregion[interval])*(xregion[interval+1]-xregion[interval])/(zregion[interval+1]-zregion[interval])
bisect.insort(x_sub[i], x_extra) # add intercept value
ind_x = x_sub[i].index(x_extra)
z_sub[i].insert(ind_x, h_i[i]) # add height value
#print(z_sub[i])
dp = 0
dA = 0
eps = 1e-06
for j in range(len(x_sub[i])-1):
if abs(z_sub[i][j+1] - h_i[i]) > eps or abs(z_sub[i][j] - h_i[i]) > eps:
dp += np.hypot(x_sub[i][j+1] - x_sub[i][j],
abs(z_sub[i][j+1] - z_sub[i][j]))
#print(dp)
# calculate area using trapezium rule
dA += (h_i[i] - (z_sub[i][j+1] + z_sub[i][j])/2)*(x_sub[i][j+1] - x_sub[i][j])
#print('Area =', dA)
p_i.append(dp)
A_i.append(dA)
r_h.append(A_i[i]/p_i[i]) # ratio of area and wetted perimeter
#print('hydraulic radius =', r_h[i])
K_i.append(A_i[i]*(1/n_co)*r_h[i]**(2/3)) # conveyance
Q_i.append(K_i[i]*slope**0.5) # discharge
return p_i, A_i, r_h, h_i, K_i, Q_i
#print(h_i)
def plot_region(xdata, labelx,
ydata1, labely1,
ydata2, labely2,
ydata3, labely3, titlep):
plt.xlabel(labelx)
plt.ylabel(labely1)
plt.title(titlep)
plt.plot(xdata, ydata1)
plt.show()
plt.xlabel(labelx)
plt.ylabel(labely2)
plt.title(titlep)
plt.plot(xdata, ydata2)
plt.show()
plt.xlabel(labelx)
plt.ylabel(labely3)
plt.title(titlep)
plt.plot(xdata, ydata3)
plt.show()
p_i, A_i, r_h, h_i, K_i, Q_i = conveyance(
numH, n_co_chan, xregion, zregion,zmin, zmax)
plot_region(h_i-zmin, 'maximum depth / m',
r_h, 'hydraulic radius / m',
K_i, r'conveyance / $m^3/s$',
Q_i, r'discharge / $m^3/s$', 'main channel flow')
p_i_west, A_i_west, r_h_west, h_i_west, K_i_west, Q_i_west = conveyance(
numH, n_co_west, xregion_west, zregion_west, zmin_west, zmax_west)
plot_region(h_i_west-zmin_west, 'maximum depth / m',
r_h_west, 'hydraulic radius / m',
K_i_west, r'conveyance / $m^3/s$',
Q_i_west, r'discharge / $m^3/s$', 'west overland flow')
p_i_east, A_i_east, r_h_east, h_i_east, K_i_east, Q_i_east = conveyance(
numH, n_co_east, xregion_east, zregion_east, zmin_east, zmax_east)
plot_region(h_i_east-zmin_east, 'maximum depth / m',
r_h_east, 'hydraulic radius / m',
K_i_east, r'conveyance / $m^3/s$',
Q_i_east, r'discharge / $m^3/s$', 'east overland flow')
target_flow_west = target_flow - Q_i[-1] - Q_i_east[-1]
# calculate velocity: note dependence on hydraulic radius
velocity_channel = Q_i[-1]/A_i[-1]
velocity_east = Q_i_east[-1]/A_i_east[-1]
print(target_flow_west)
# find insertion point for target flow value
ind_q = bisect.bisect(Q_i_west, target_flow_west)
print(ind_q)
# find height at target flow by linear interpolation
h_extra = h_i_west[ind_q-1] + (h_i_west[ind_q]-h_i_west[ind_q-1])*(target_flow_west-Q_i_west[ind_q-1])/(Q_i_west[ind_q]-Q_i_west[ind_q-1])
print(h_i_west[ind_q-1], h_extra, h_i_west[ind_q])
# find area at target flow by linear interpolation
A_extra = A_i_west[ind_q-1] + (h_extra-h_i_west[ind_q-1])*(A_i_west[ind_q]-A_i_west[ind_q-1])/(h_i_west[ind_q]-h_i_west[ind_q-1])
print(r_h_west[ind_q-1], r_h_west[ind_q])
velocity_west = target_flow_west/A_extra
print(velocity_channel, velocity_east, velocity_west)
dX = (xin[0]+xin[-1])/len(xin) # cell size
print('dX =', dX)
csa = np.zeros(len(xin)) # cross-sectional area
csa_west = 0
csa_chan = 0
csa_east = 0
for index, xitem in enumerate(xin):
if xitem < xin[280]:
csa[index] = max(0, (h_extra - zin[index])*dX)
csa_west += csa[index]
elif xitem < xin[301]:
csa[index] = max(0, (zmax - zin[index])*dX)
csa_chan += csa[index]
else:
csa[index] = max(0, (zmax_east - zin[index])*dX)
csa_east += csa[index]
#print('csa_west = {} csa_chan = {} csa_east = {}'.format(csa_west, csa_chan, csa_east))
#print('A_i_west = {} A_i = {} A_i_east = {}'.format(A_extra, A_i[-1], A_i_east[-1]))
def save_bc():
with open('BCTop.txt', 'w') as f:
f.write('{:6} {:>2} {:>2} {:>10}\n'.format('#x', 'c', 'q', 'h'))
for ind_z, (xitem, zitem) in enumerate(zip(xin, zin)):
if csa[ind_z] == 0:
# wall boundary condition
f.write('{:6.2f} {:>2}\n'.format(xitem, 2))
elif xitem < xin[280]:
# imposed discharge on western side
f.write('{:6.2f} {:>2} {:10.6f} {:9.6f}\n'.format(
xitem, 5,
-csa[ind_z]*target_flow_west/csa_west,
h_extra-zitem))
elif xitem < xin[301]:
# imposed discharge within channel
f.write('{:6.2f} {:>2} {:10.6f} {:9.6f}\n'.format(
xitem, 5,
-csa[ind_z]*Q_i[-1]/csa_chan,
zmax-zitem))
else:
# imposed discharge on eastern side
f.write('{:6.2f} {:>2} {:10.6f} {:9.6f}\n'.format(
xitem, 5,
-csa[ind_z]*Q_i_east[-1]/csa_west,
zmax_east-zitem))
save_bc()
|
