source: branches/Numeric_anuga_validation/convergence_study/tilted.py

"""Simple water flow example using ANUGA

Will Powers example of a simple sinusoidal wave which showed diffusive effects of
thefirst order and standard second order method. Problem resolved if "rk2" timestepping
and higher beta = 2 limiter used. Also new edge limiter with rk2 resolves problem 
"""

#------------------------------------------------------------------------------
# Import necessary modules
#------------------------------------------------------------------------------

import sys
from anuga.abstract_2d_finite_volumes.mesh_factory import rectangular_cross
from anuga.shallow_water import Domain
from anuga.shallow_water import Reflective_boundary
from anuga.shallow_water import Dirichlet_boundary
from anuga.shallow_water import Time_boundary
from anuga.shallow_water import Transmissive_boundary
from anuga.shallow_water import Transmissive_Momentum_Set_Stage_boundary
from anuga.shallow_water.data_manager import start_screen_catcher, copy_code_files

from math import cos
from Numeric import zeros, Float
from time import localtime, strftime, gmtime
from os import sep



#-------------------------------------------------------------------------------
# Copy scripts to time stamped output directory and capture screen
# output to file
#-------------------------------------------------------------------------------
model_name = 'tilted'

time = strftime('%Y%m%d_%H%M%S',localtime())
output_dir = model_name + '_'+time
output_file = model_name
copy_code_files(output_dir,__file__)
#start_screen_catcher(output_dir+sep)

#------------------------------------------------------------------------------
# Setup domain
#------------------------------------------------------------------------------
dx = 6.0*0.01
dy = dx
L = 600*0.01
W = 10*dx

# structured mesh
points, vertices, boundary = rectangular_cross(int(L/dx), int(W/dy), L, W, (0.0, -W/2))

domain = Domain(points, vertices, boundary) 

domain.set_name(output_file)                
domain.set_datadir(output_dir)  

#------------------------------------------------------------------------------
# Setup Algorithm
#------------------------------------------------------------------------------
domain.set_timestepping_method('rk2')
domain.set_default_order(2)

print domain.get_timestepping_method()

domain.use_edge_limiter = True
domain.tight_slope_limiters = True

domain.CFL = 1.0

domain.beta_w      = 0.6
domain.beta_w_dry  = 0.0
domain.beta_uh     = 0.6
domain.beta_uh_dry = 0.0
domain.beta_vh     = 0.6
domain.beta_vh_dry = 0.0


interactive_visualisation = True


#------------------------------------------------------------------------------
# Setup initial conditions
#------------------------------------------------------------------------------
domain.set_quantity('elevation',0.0)
domain.set_quantity('friction', 0.00)
domain.set_quantity('stage', lambda x,y : 14.0*0.01 + x/(600.0*0.01)*14.0*0.01 )            

#-----------------------------------------------------------------------------
# Setup boundary conditions
#------------------------------------------------------------------------------
from math import sin, pi, exp
Br = Reflective_boundary(domain)      # Solid reflective wall

# Associate boundary tags with boundary objects
domain.set_boundary({'left': Br, 'right': Br, 'top': Br, 'bottom': Br})


#===============================================================================
if interactive_visualisation:
    from anuga.visualiser import RealtimeVisualiser
    vis = RealtimeVisualiser(domain)
    vis.render_quantity_height("stage", zScale =1, dynamic=True)
    vis.colour_height_quantity('stage', (1.0, 0.5, 0.5))
    vis.start()
#===============================================================================


#------------------------------------------------------------------------------
# Evolve system through time
#------------------------------------------------------------------------------

for t in domain.evolve(yieldstep = 0.5, finaltime = 60.0):
    domain.write_time()
    if interactive_visualisation:
        vis.update()

if interactive_visualisation:
    vis.evolveFinished()