"""Simple example of shallow water wave equation using Pyvolution

Water driven by linear slope and Dirichlet boundary

"""

######################
# Module imports 
#
from mesh_factory import rectangular
from shallow_water import Domain, Reflective_boundary, Dirichlet_boundary,\
     Constant_height, Time_boundary, Transmissive_boundary
from Numeric import array

#Create basic mesh
points, vertices, boundary = rectangular(10, 10)

#Create shallow water domain
domain = Domain(points, vertices, boundary)
domain.smooth = False
domain.visualise = True
domain.store = True
domain.filename = 'bedslope'
domain.default_order=2

#######################
#Bed-slope and friction
domain.set_quantity('elevation', lambda x,y: -x/3)
domain.set_quantity('friction', 0.1)


######################
# Boundary conditions
from math import sin, pi
Br = Reflective_boundary(domain)
Bt = Transmissive_boundary(domain)
Bd = Dirichlet_boundary([0.2,0.,0.])
Bw = Time_boundary(domain=domain,
                   f=lambda t: [(0.1*sin(t*2*pi)), 0.0, 0.0])

domain.set_boundary({'left': Bd, 'right': Br, 'top': Br, 'bottom': Br})


######################
#Initial condition
h = 0.05
elevation = domain.quantities['elevation'].vertex_values
domain.set_quantity('stage', elevation + h)

domain.check_integrity()

  
######################
#Evolution
for t in domain.evolve(yieldstep = 0.01, finaltime = 5.0):
    domain.write_time()