source: anuga_work/development/anuga_1d/dry_dam_vel.py @ 5845

import os
from math import sqrt, pi
from shallow_water_vel_domain import *
from Numeric import allclose, array, zeros, ones, Float, take, sqrt
from config import g, epsilon


h1 = 10.0
h0 = 0.0

def analytical_sol(C,t):
    
    #t  = 0.0     # time (s)
    # gravity (m/s^2)
    #h1 = 10.0    # depth upstream (m)
    #h0 = 0.0     # depth downstream (m)
    L = 2000.0   # length of stream/domain (m)
    n = len(C)    # number of cells

    u = zeros(n,Float)
    h = zeros(n,Float)
    x = C-3*L/4.0
    

    for i in range(n):
        # Calculate Analytical Solution at time t > 0
        u3 = 2.0/3.0*(sqrt(g*h1)+x[i]/t) 
        h3 = 4.0/(9.0*g)*(sqrt(g*h1)-x[i]/(2.0*t))*(sqrt(g*h1)-x[i]/(2.0*t))
        u3_ = 2.0/3.0*((x[i]+L/2.0)/t-sqrt(g*h1))
        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))

        if ( x[i] <= -1*L/2.0+2*(-sqrt(g*h1)*t)):
            u[i] = 0.0
            h[i] = h0
        elif ( x[i] <= -1*L/2.0-(-sqrt(g*h1)*t)):
            u[i] = u3_
            h[i] = h3_

        elif ( x[i] <= -t*sqrt(g*h1) ):
            u[i] = 0.0 
            h[i] = h1 
        elif ( x[i] <= 2.0*t*sqrt(g*h1) ):
            u[i] = u3 
            h[i] = h3 
        else:
            u[i] = 0.0 
            h[i] = h0 

    return h , u*h, u

print "TEST 1D-SOLUTION III -- DRY BED"

def stage(x):
    y = zeros(len(x),Float)
    for i in range(len(x)):
        if x[i]<=L/4.0:
            y[i] = h0
        elif x[i]<=3*L/4.0:
            y[i] = h1
        else:
            y[i] = h0
    return y


import time

finaltime = 10.0
yieldstep = finaltime
L = 2000.0     # Length of channel (m)
number_of_cells = [800]#,200,500,1000,2000,5000,10000,20000]
h_error = zeros(len(number_of_cells),Float)
uh_error = zeros(len(number_of_cells),Float)
u_error = zeros(len(number_of_cells),Float)
k = 0
for i in range(len(number_of_cells)):
    N = int(number_of_cells[i])
    print "Evaluating domain with %d cells" %N
    cell_len = L/N # Origin = 0.0
    points = zeros(N+1,Float)
    for j in range(N+1):
        points[j] = j*cell_len
        
    domain = Domain(points)
    
    domain.set_quantity('stage', stage)
    domain.set_boundary({'exterior': Reflective_boundary(domain)})
    domain.order = 2
    domain.set_timestepping_method('rk2')
    domain.set_CFL(1.0)
    domain.set_limiter("vanleer")
    #domain.h0=0.0001

    t0 = time.time()

    for t in domain.evolve(yieldstep = yieldstep, finaltime = finaltime):
        domain.write_time()

    N = float(N)
    StageC = domain.quantities['stage'].centroid_values
    XmomC = domain.quantities['xmomentum'].centroid_values
    u_C = domain.quantities['velocity'].centroid_values
    C = domain.centroids
    h, uh, u = analytical_sol(C,domain.time)
    h_error[k] = 1.0/(N)*sum(abs(h-StageC))
    uh_error[k] = 1.0/(N)*sum(abs(uh-XmomC))
    u_error[k] = 1.0/(N)*sum(abs(u-u_C))
    print "h_error %.10f" %(h_error[k])
    print "uh_error %.10f"% (uh_error[k])
    print "u_error %.10f"% (u_error[k])
    k = k+1
    print 'That took %.2f seconds' %(time.time()-t0)
    X = domain.vertices
    StageQ = domain.quantities['stage'].vertex_values
    XmomQ = domain.quantities['xmomentum'].vertex_values
    velQ = domain.quantities['velocity'].vertex_values
    
    h, uh, u = analytical_sol(X.flat,domain.time)
    x = X.flat
    
    from pylab import plot,title,xlabel,ylabel,legend,savefig,show,hold,subplot
    print 'test 2'
    hold(False)
    print 'test 3'
    plot1 = subplot(211)
    print 'test 4'
    plot(x,h,x,StageQ.flat)
    print 'test 5'
    plot1.set_ylim([-1,11])
    xlabel('Position')
    ylabel('Stage')
    legend(('Analytical Solution', 'Numerical Solution'),
           'upper right', shadow=True)
    plot2 = subplot(212)
    plot(x,u,x,velQ.flat)
    plot2.set_ylim([-35,35])
    
    xlabel('Position')
    ylabel('Velocity')
   
    file = "dry_bed_"
    file += str(number_of_cells[i])
    file += ".eps"
    #savefig(file)
    show()
    
print "Error in height", h_error
print "Error in xmom", uh_error