| 1 | """Example of shallow water wave equation. |
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| 2 | |
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| 3 | Specific methods pertaining to the 2D shallow water equation |
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| 4 | are imported from shallow_water |
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| 5 | for use with the generic finite volume framework |
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| 6 | |
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| 7 | Conserved quantities are h, uh and vh stored as elements 0, 1 and 2 in the |
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| 8 | numerical vector named conserved_quantities. |
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| 9 | """ |
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| 10 | |
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| 11 | #------------------------------------------------------------------------------ |
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| 12 | # Import necessary modules |
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| 13 | #------------------------------------------------------------------------------ |
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| 14 | from anuga.abstract_2d_finite_volumes.mesh_factory import rectangular_cross |
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| 15 | from anuga.shallow_water import Domain |
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| 16 | from anuga.shallow_water.shallow_water_domain import Reflective_boundary |
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| 17 | from anuga.shallow_water.shallow_water_domain import Dirichlet_boundary |
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| 18 | |
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| 19 | |
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| 20 | #------------------------------------------------------------------------------ |
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| 21 | # Setup computational domain |
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| 22 | #------------------------------------------------------------------------------ |
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| 23 | length = 40. |
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| 24 | width = 5. |
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| 25 | |
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| 26 | #dx = dy = 1 # Resolution: Length of subdivisions on both axes |
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| 27 | #dx = dy = .5 # Resolution: Length of subdivisions on both axes |
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| 28 | dx = dy = .1 # Resolution: Length of subdivisions on both axes |
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| 29 | |
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| 30 | points, vertices, boundary = rectangular_cross(int(length/dx), int(width/dy), |
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| 31 | len1=length, len2=width) |
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| 32 | domain = Domain(points, vertices, boundary) |
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| 33 | domain.set_name('culvert_example') # Output name |
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| 34 | print 'Size', len(domain) |
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| 35 | |
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| 36 | #------------------------------------------------------------------------------ |
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| 37 | # Setup initial conditions |
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| 38 | #------------------------------------------------------------------------------ |
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| 39 | |
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| 40 | def topography(x, y): |
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| 41 | """Set up a weir |
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| 42 | |
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| 43 | A culvert will connect either side |
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| 44 | """ |
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| 45 | |
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| 46 | z = -x/10 |
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| 47 | |
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| 48 | N = len(x) |
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| 49 | for i in range(N): |
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| 50 | |
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| 51 | # Weir from 10 to 12 m |
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| 52 | if 10 < x[i] < 12: |
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| 53 | z[i] += 0.4 - 0.05*y[i] |
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| 54 | |
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| 55 | # Constriction |
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| 56 | #if 27 < x[i] < 29 and y[i] > 3: |
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| 57 | # z[i] += 2 |
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| 58 | |
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| 59 | # Pole |
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| 60 | #if (x[i] - 34)**2 + (y[i] - 2)**2 < 0.4**2: |
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| 61 | # z[i] += 2 |
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| 62 | |
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| 63 | return z |
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| 64 | |
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| 65 | |
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| 66 | domain.set_quantity('elevation', topography) # Use function for elevation |
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| 67 | domain.set_quantity('friction', 0.01) # Constant friction |
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| 68 | domain.set_quantity('stage', |
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| 69 | expression='elevation') # Dry initial condition |
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| 70 | |
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| 71 | |
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| 72 | |
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| 73 | |
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| 74 | #------------------------------------------------------------------------------ |
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| 75 | # Setup specialised forcing terms |
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| 76 | #------------------------------------------------------------------------------ |
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| 77 | |
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| 78 | class Inflow: |
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| 79 | """Class Inflow - general 'rain and drain' forcing term. |
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| 80 | |
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| 81 | Useful for implementing flows in and out of the domain. |
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| 82 | |
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| 83 | Inflow(center, radius, flow) |
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| 84 | |
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| 85 | center [m]: Coordinates at center of flow point |
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| 86 | radius [m]: Size of circular area |
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| 87 | flow [m/s]: Rate of change of quantity over the specified area. |
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| 88 | This parameter can be either a constant or a function of time. |
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| 89 | Positive values indicate inflow, |
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| 90 | negative values indicate outflow. |
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| 91 | |
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| 92 | Examples |
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| 93 | |
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| 94 | Inflow((0.7, 0.4), 0.07, -0.2) # Constant drain at 0.2 m/s. |
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| 95 | # This corresponds to a flow of |
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| 96 | # 0.07**2*pi*0.2 = 0.00314 m^3/s |
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| 97 | |
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| 98 | Inflow((0.5, 0.5), 0.001, lambda t: min(4*t, 5)) # Tap turning up to |
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| 99 | # a maximum inflow of |
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| 100 | # 5 m/s over the |
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| 101 | # specified area |
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| 102 | """ |
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| 103 | |
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| 104 | # FIXME (OLE): Add a polygon as an alternative. |
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| 105 | # FIXME (OLE): Generalise to all quantities |
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| 106 | # FIXME (OLE): |
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| 107 | |
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| 108 | def __init__(self, |
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| 109 | domain, |
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| 110 | center=None, radius=None, |
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| 111 | flow=0.0, |
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| 112 | quantity_name = 'stage'): |
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| 113 | |
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| 114 | from anuga.utilities.numerical_tools import ensure_numeric |
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| 115 | |
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| 116 | if center is not None and radius is not None: |
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| 117 | assert len(center) == 2 |
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| 118 | else: |
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| 119 | msg = 'Both center and radius must be specified' |
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| 120 | raise Exception, msg |
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| 121 | |
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| 122 | self.domain = domain |
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| 123 | self.center = ensure_numeric(center) |
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| 124 | self.radius = radius |
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| 125 | self.flow = flow |
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| 126 | |
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| 127 | self.quantity = domain.quantities[quantity_name].explicit_update |
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| 128 | |
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| 129 | # Determine indices in flow area |
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| 130 | N = len(domain) |
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| 131 | self.indices = [] |
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| 132 | coordinates = domain.get_centroid_coordinates() |
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| 133 | for k in range(N): |
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| 134 | x, y = coordinates[k,:] # Centroid |
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| 135 | if ((x-center[0])**2+(y-center[1])**2) < radius**2: |
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| 136 | self.indices.append(k) |
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| 137 | |
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| 138 | |
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| 139 | def __call__(self, domain): |
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| 140 | |
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| 141 | # Update inflow |
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| 142 | if callable(self.flow): |
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| 143 | flow = self.flow(domain.get_time()) |
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| 144 | else: |
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| 145 | flow = self.flow |
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| 146 | |
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| 147 | for k in self.indices: |
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| 148 | self.quantity[k] += flow |
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| 149 | |
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| 150 | |
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| 151 | class Culvert_flow: |
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| 152 | """Culvert flow - transfer water from one hole to another |
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| 153 | """ |
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| 154 | |
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| 155 | def __init__(self, |
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| 156 | domain, |
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| 157 | center0=None, radius0=None, |
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| 158 | center1=None, radius1=None, |
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| 159 | transfer_flow=None): |
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| 160 | |
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| 161 | from Numeric import sqrt, sum |
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| 162 | |
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| 163 | self.openings = [] |
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| 164 | self.openings.append(Inflow(domain, |
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| 165 | center=center0, |
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| 166 | radius=radius0, |
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| 167 | flow=None)) |
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| 168 | |
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| 169 | self.openings.append(Inflow(domain, |
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| 170 | center=center1, |
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| 171 | radius=radius1, |
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| 172 | flow=None)) |
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| 173 | |
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| 174 | # Compute distance between opening centers. I assume there are only two. |
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| 175 | self.distance = sqrt(sum( (self.openings[0].center - self.openings[1].center)**2 )) |
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| 176 | print 'Distance between openings is', self.distance |
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| 177 | |
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| 178 | |
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| 179 | def __call__(self, domain): |
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| 180 | from anuga.utilities.numerical_tools import mean |
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| 181 | |
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| 182 | |
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| 183 | # Get average water depths at each opening |
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| 184 | for opening in self.openings: |
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| 185 | stage = domain.quantities['stage'].get_values(location='centroids', |
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| 186 | indices=opening.indices) |
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| 187 | elevation = domain.quantities['elevation'].get_values(location='centroids', |
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| 188 | indices=opening.indices) |
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| 189 | |
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| 190 | # Store current avg depth with opening object |
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| 191 | opening.depth = mean(stage-elevation) |
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| 192 | # print 'Depth', opening.depth |
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| 193 | |
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| 194 | |
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| 195 | # Here's a simple transfer function hardwired into this Culvert class: |
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| 196 | # Let flow rate depend on difference in depth |
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| 197 | # Flow is instantaneous for now but one might use |
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| 198 | # the precomputed distance between the two openings |
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| 199 | # to somehow introduce a delay. |
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| 200 | |
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| 201 | delta_h = self.openings[0].depth - self.openings[1].depth |
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| 202 | flow_rate = 0.5*9.81*delta_h**2 # Just an example of flow rate |
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| 203 | flow_rate /= (self.openings[0].radius + self.openings[1].radius)/2 # |
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| 204 | |
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| 205 | if delta_h > 0: |
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| 206 | # Opening 0 has the greatest depth. |
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| 207 | # Flow will go from opening 0 to opening 1 |
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| 208 | |
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| 209 | self.openings[0].flow = -flow_rate |
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| 210 | self.openings[1].flow = flow_rate |
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| 211 | else: |
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| 212 | # Opening 1 has the greatest depth. |
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| 213 | # Flow will go from opening 1 to opening 0 |
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| 214 | |
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| 215 | self.openings[0].flow = flow_rate |
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| 216 | self.openings[1].flow = -flow_rate |
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| 217 | |
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| 218 | |
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| 219 | # Execute flow term for each opening |
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| 220 | for opening in self.openings: |
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| 221 | opening(domain) |
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| 222 | |
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| 223 | |
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| 224 | |
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| 225 | #sink = Inflow(domain, center=[0.7, 0.4], radius=0.0707, flow = 0.0) |
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| 226 | #tap = Inflow(domain, center=(0.5, 0.5), radius=0.0316, |
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| 227 | # flow=lambda t: min(4*t, 5)) # Tap turning up |
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| 228 | #domain.forcing_terms.append(tap) |
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| 229 | #domain.forcing_terms.append(sink) |
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| 230 | |
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| 231 | culvert = Culvert_flow(domain, |
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| 232 | center0=[5.0, 2.5], radius0=0.3, |
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| 233 | center1=[20., 2.5], radius1=0.3, |
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| 234 | transfer_flow=None) # Hardwired for now |
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| 235 | |
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| 236 | domain.forcing_terms.append(culvert) |
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| 237 | |
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| 238 | #------------------------------------------------------------------------------ |
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| 239 | # Setup boundary conditions |
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| 240 | #------------------------------------------------------------------------------ |
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| 241 | Bi = Dirichlet_boundary([0.4, 0, 0]) # Inflow |
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| 242 | Br = Reflective_boundary(domain) # Solid reflective wall |
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| 243 | Bo = Dirichlet_boundary([-5, 0, 0]) # Outflow |
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| 244 | |
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| 245 | domain.set_boundary({'left': Bi, 'right': Bo, 'top': Br, 'bottom': Br}) |
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| 246 | |
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| 247 | |
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| 248 | #------------------------------------------------------------------------------ |
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| 249 | # Evolve system through time |
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| 250 | #------------------------------------------------------------------------------ |
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| 251 | for t in domain.evolve(yieldstep = 0.01, finaltime = 15): |
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| 252 | domain.write_time() |
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| 253 | |
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| 254 | #if domain.get_time() >= 4 and tap.flow != 0.0: |
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| 255 | # print 'Turning tap off' |
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| 256 | # tap.flow = 0.0 |
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| 257 | |
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| 258 | #if domain.get_time() >= 3 and sink.flow < 0.0: |
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| 259 | # print 'Turning drain on' |
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| 260 | # sink.flow = -0.8 |
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| 261 | |
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