source: anuga_work/development/anuga_1d/dry_dam_sudi.py @ 5587

Last change on this file since 5587 was 5587, checked in by steve, 14 years ago

Added in minimum height

File size: 4.3 KB
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1import os
2from math import sqrt, pi
3from shallow_water_domain import *
4from Numeric import allclose, array, zeros, ones, Float, take, sqrt
5from config import g, epsilon
6
7def analytical_sol(C,t):
8   
9    #t  = 0.0     # time (s)
10    g  = 9.81    # gravity (m/s^2)
11    h1 = 10.0    # depth upstream (m)
12    h0 = 0.0     # depth downstream (m)
13    L = 2000.0   # length of stream/domain (m)
14    n = len(C)    # number of cells
15
16    u = zeros(n,Float)
17    h = zeros(n,Float)
18    x = C-3*L/4.0
19   
20
21    for i in range(n):
22        # Calculate Analytical Solution at time t > 0
23        u3 = 2.0/3.0*(sqrt(g*h1)+x[i]/t) 
24        h3 = 4.0/(9.0*g)*(sqrt(g*h1)-x[i]/(2.0*t))*(sqrt(g*h1)-x[i]/(2.0*t))
25        u3_ = 2.0/3.0*((x[i]+L/2.0)/t-sqrt(g*h1))
26        h3_ = 1.0/(9.0*g)*((x[i]+L/2.0)/t+2*sqrt(g*h1))*((x[i]+L/2.0)/t+2*sqrt(g*h1))
27
28        if ( x[i] <= -1*L/2.0+2*(-sqrt(g*h1)*t)):
29            u[i] = 0.0
30            h[i] = h0
31        elif ( x[i] <= -1*L/2.0-(-sqrt(g*h1)*t)):
32            u[i] = u3_
33            h[i] = h3_
34
35        elif ( x[i] <= -t*sqrt(g*h1) ):
36            u[i] = 0.0 
37            h[i] = h1
38        elif ( x[i] <= 2.0*t*sqrt(g*h1) ):
39            u[i] = u3
40            h[i] = h3
41        else:
42            u[i] = 0.0 
43            h[i] = h0
44
45    return h , u*h
46
47#def newLinePlot(title='Simple Plot'):
48#   import Gnuplot
49#    gg = Gnuplot.Gnuplot(persist=0)
50#    gg.terminal(postscript)
51#    gg.title(title)
52#    gg('set data style linespoints')
53#    gg.xlabel('x')
54#    gg.ylabel('y')
55#    return gg
56
57#def linePlot(gg,x1,y1,x2,y2):
58#    import Gnuplot
59#    plot1 = Gnuplot.PlotItems.Data(x1.flat,y1.flat,with="linespoints")
60#    plot2 = Gnuplot.PlotItems.Data(x2.flat,y2.flat, with="lines 3")
61#    g.plot(plot1,plot2)
62
63
64
65print "TEST 1D-SOLUTION III -- DRY BED"
66
67L = 2000.0     # Length of channel (m)
68N = 800        # Number of computational cells
69cell_len = L/N # Origin = 0.0
70
71points = zeros(N+1,Float)
72for i in range(N+1):
73    points[i] = i*cell_len
74
75domain = Domain(points)
76
77def stage(x):
78    h1 = 10.0
79    h0 = 0.0
80    y = zeros(len(x),Float)
81    for i in range(len(x)):
82        if x[i]<=L/4.0:
83            y[i] = h0
84        elif x[i]<=3*L/4.0:
85            y[i] = h1
86        else:
87            y[i] = h0
88    return y
89
90
91import time
92
93finaltime = 20.0
94yieldstep = 1.0
95L = 2000.0     # Length of channel (m)
96number_of_cells = [200]#,200,500,1000,2000,5000,10000,20000]
97h_error = zeros(len(number_of_cells),Float)
98uh_error = zeros(len(number_of_cells),Float)
99k = 0
100for i in range(len(number_of_cells)):
101    N = int(number_of_cells[i])
102    print "Evaluating domain with %d cells" %N
103    cell_len = L/N # Origin = 0.0
104    points = zeros(N+1,Float)
105    for j in range(N+1):
106        points[j] = j*cell_len
107       
108    domain = Domain(points)
109   
110    domain.set_quantity('stage', stage)
111    domain.set_boundary({'exterior': Reflective_boundary(domain)})
112    domain.default_order = 2
113    domain.default_time_order = 2
114    domain.cfl = 1.0
115    domain.limiter = "minmod"
116
117    t0 = time.time()
118
119    for t in domain.evolve(yieldstep = yieldstep, finaltime = finaltime):
120        domain.write_time()
121
122    N = float(N)
123    StageC = domain.quantities['stage'].centroid_values
124    XmomC = domain.quantities['xmomentum'].centroid_values
125    C = domain.centroids
126    h, uh = analytical_sol(C,domain.time)
127    h_error[k] = 1.0/(N)*sum(abs(h-StageC))
128    uh_error[k] = 1.0/(N)*sum(abs(uh-XmomC))
129    print "h_error %.10f" %(h_error[k])
130    print "uh_error %.10f"% (uh_error[k])
131    k = k+1
132    print 'That took %.2f seconds' %(time.time()-t0)
133    X = domain.vertices
134    StageQ = domain.quantities['stage'].vertex_values
135    XmomQ = domain.quantities['xmomentum'].vertex_values
136    h, uh = analytical_sol(X.flat,domain.time)
137    x = X.flat
138   
139    from pylab import plot,title,xlabel,ylabel,legend,savefig,show,hold,subplot
140    print 'test 2'
141    hold(False)
142    print 'test 3'
143    plot1 = subplot(211)
144    print 'test 4'
145    plot(x,h,x,StageQ.flat)
146    print 'test 5'
147    plot1.set_ylim([-1,11])
148    xlabel('Position')
149    ylabel('Stage')
150    legend(('Analytical Solution', 'Numerical Solution'),
151           'upper right', shadow=True)
152    plot2 = subplot(212)
153    plot(x,uh,x,XmomQ.flat)
154    plot2.set_ylim([-35,35])
155   
156    xlabel('Position')
157    ylabel('Xmomentum')
158   
159    file = "dry_bed_"
160    file += str(number_of_cells[i])
161    file += ".eps"
162    #savefig(file)
163    show()
164   
165print "Error in height", h_error
166print "Error in xmom", uh_error
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