# source:anuga_work/development/anuga_1d/dry_dam_sudi.py@7818

Last change on this file since 7818 was 5844, checked in by steve, 16 years ago

Updating domain etc to take conserved, evolved and other quantitiies

File size: 4.2 KB
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1import os
2from math import sqrt, pi
3from shallow_water_vel_domain import *
4from Numeric import allclose, array, zeros, ones, Float, take, sqrt
5from config import g, epsilon
6
7
8h1 = 10.0
9h0 = 0.0
10
11def analytical_sol(C,t):
12
13    #t  = 0.0     # time (s)
14    # gravity (m/s^2)
15    #h1 = 10.0    # depth upstream (m)
16    #h0 = 0.0     # depth downstream (m)
17    L = 2000.0   # length of stream/domain (m)
18    n = len(C)    # number of cells
19
20    u = zeros(n,Float)
21    h = zeros(n,Float)
22    x = C-3*L/4.0
23
24
25    for i in range(n):
26        # Calculate Analytical Solution at time t > 0
27        u3 = 2.0/3.0*(sqrt(g*h1)+x[i]/t)
28        h3 = 4.0/(9.0*g)*(sqrt(g*h1)-x[i]/(2.0*t))*(sqrt(g*h1)-x[i]/(2.0*t))
29        u3_ = 2.0/3.0*((x[i]+L/2.0)/t-sqrt(g*h1))
30        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))
31
32        if ( x[i] <= -1*L/2.0+2*(-sqrt(g*h1)*t)):
33            u[i] = 0.0
34            h[i] = h0
35        elif ( x[i] <= -1*L/2.0-(-sqrt(g*h1)*t)):
36            u[i] = u3_
37            h[i] = h3_
38
39        elif ( x[i] <= -t*sqrt(g*h1) ):
40            u[i] = 0.0
41            h[i] = h1
42        elif ( x[i] <= 2.0*t*sqrt(g*h1) ):
43            u[i] = u3
44            h[i] = h3
45        else:
46            u[i] = 0.0
47            h[i] = h0
48
49    return h , u*h, u
50
51#def newLinePlot(title='Simple Plot'):
52#   import Gnuplot
53#    gg = Gnuplot.Gnuplot(persist=0)
54#    gg.terminal(postscript)
55#    gg.title(title)
56#    gg('set data style linespoints')
57#    gg.xlabel('x')
58#    gg.ylabel('y')
59#    return gg
60
61#def linePlot(gg,x1,y1,x2,y2):
62#    import Gnuplot
63#    plot1 = Gnuplot.PlotItems.Data(x1.flat,y1.flat,with="linespoints")
64#    plot2 = Gnuplot.PlotItems.Data(x2.flat,y2.flat, with="lines 3")
65#    g.plot(plot1,plot2)
66
67
68
69print "TEST 1D-SOLUTION III -- DRY BED"
70
71def stage(x):
72    y = zeros(len(x),Float)
73    for i in range(len(x)):
74        if x[i]<=L/4.0:
75            y[i] = h0
76        elif x[i]<=3*L/4.0:
77            y[i] = h1
78        else:
79            y[i] = h0
80    return y
81
82
83import time
84
85finaltime = 10.0
86yieldstep = finaltime
87L = 2000.0     # Length of channel (m)
88number_of_cells = [810]#,200,500,1000,2000,5000,10000,20000]
89h_error = zeros(len(number_of_cells),Float)
90uh_error = zeros(len(number_of_cells),Float)
91k = 0
92for i in range(len(number_of_cells)):
93    N = int(number_of_cells[i])
94    print "Evaluating domain with %d cells" %N
95    cell_len = L/N # Origin = 0.0
96    points = zeros(N+1,Float)
97    for j in range(N+1):
98        points[j] = j*cell_len
99
100    domain = Domain(points)
101
102    domain.set_quantity('stage', stage)
103    domain.set_boundary({'exterior': Reflective_boundary(domain)})
104    domain.order = 2
105    domain.set_timestepping_method('rk2')
106    domain.set_CFL(1.0)
107    domain.set_limiter("vanleer")
108    #domain.h0=0.0001
109
110    t0 = time.time()
111
112    for t in domain.evolve(yieldstep = yieldstep, finaltime = finaltime):
113        domain.write_time()
114
115    N = float(N)
116    StageC = domain.quantities['stage'].centroid_values
117    XmomC = domain.quantities['xmomentum'].centroid_values
118    C = domain.centroids
119    h, uh, u = analytical_sol(C,domain.time)
120    h_error[k] = 1.0/(N)*sum(abs(h-StageC))
121    uh_error[k] = 1.0/(N)*sum(abs(uh-XmomC))
122    print "h_error %.10f" %(h_error[k])
123    print "uh_error %.10f"% (uh_error[k])
124    k = k+1
125    print 'That took %.2f seconds' %(time.time()-t0)
126    X = domain.vertices
127    StageQ = domain.quantities['stage'].vertex_values
128    XmomQ = domain.quantities['xmomentum'].vertex_values
129    velQ = domain.quantities['velocity'].vertex_values
130
131    h, uh, u = analytical_sol(X.flat,domain.time)
132    x = X.flat
133
134    from pylab import plot,title,xlabel,ylabel,legend,savefig,show,hold,subplot
135    print 'test 2'
136    hold(False)
137    print 'test 3'
138    plot1 = subplot(211)
139    print 'test 4'
140    plot(x,h,x,StageQ.flat)
141    print 'test 5'
142    plot1.set_ylim([-1,11])
143    xlabel('Position')
144    ylabel('Stage')
145    legend(('Analytical Solution', 'Numerical Solution'),
146           'upper right', shadow=True)
147    plot2 = subplot(212)
148    plot(x,u,x,velQ.flat)
149    plot2.set_ylim([-35,35])
150
151    xlabel('Position')
152    ylabel('Velocity')
153
154    file = "dry_bed_"
155    file += str(number_of_cells[i])
156    file += ".eps"
157    #savefig(file)
158    show()
159
160print "Error in height", h_error
161print "Error in xmom", uh_error
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