[5827] | 1 | """Class Domain - |
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| 2 | 1D interval domains for finite-volume computations of |
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| 3 | the shallow water wave equation. |
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| 4 | |
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| 5 | This module contains a specialisation of class Domain from module domain.py |
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| 6 | consisting of methods specific to the Shallow Water Wave Equation |
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| 7 | |
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| 8 | |
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| 9 | U_t + E_x = S |
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| 10 | |
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| 11 | where |
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| 12 | |
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| 13 | U = [w, uh] |
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| 14 | E = [uh, u^2h + gh^2/2] |
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| 15 | S represents source terms forcing the system |
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| 16 | (e.g. gravity, friction, wind stress, ...) |
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| 17 | |
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| 18 | and _t, _x, _y denote the derivative with respect to t, x and y respectiely. |
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| 19 | |
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| 20 | The quantities are |
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| 21 | |
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| 22 | symbol variable name explanation |
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| 23 | x x horizontal distance from origin [m] |
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| 24 | z elevation elevation of bed on which flow is modelled [m] |
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| 25 | h height water height above z [m] |
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| 26 | w stage absolute water level, w = z+h [m] |
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| 27 | u speed in the x direction [m/s] |
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| 28 | uh xmomentum momentum in the x direction [m^2/s] |
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| 29 | |
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| 30 | eta mannings friction coefficient [to appear] |
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| 31 | nu wind stress coefficient [to appear] |
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| 32 | |
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| 33 | The conserved quantities are w, uh |
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| 34 | |
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| 35 | For details see e.g. |
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| 36 | Christopher Zoppou and Stephen Roberts, |
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| 37 | Catastrophic Collapse of Water Supply Reservoirs in Urban Areas, |
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| 38 | Journal of Hydraulic Engineering, vol. 127, No. 7 July 1999 |
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| 39 | |
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| 40 | |
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| 41 | John Jakeman, Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
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| 42 | Geoscience Australia, 2006 |
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| 43 | """ |
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| 44 | |
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| 45 | |
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| 46 | from domain import * |
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| 47 | Generic_Domain = Domain #Rename |
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| 48 | |
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| 49 | #Shallow water domain |
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| 50 | class Domain(Generic_Domain): |
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| 51 | |
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| 52 | def __init__(self, coordinates, boundary = None, tagged_elements = None): |
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| 53 | |
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| 54 | conserved_quantities = ['stage', 'xmomentum'] |
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[5832] | 55 | evolved_quantities = ['stage', 'xmomentum', 'elevation', 'height', 'velocity'] |
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| 56 | other_quantities = ['friction'] |
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| 57 | Generic_Domain.__init__(self, |
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| 58 | coordinates = coordinates, |
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| 59 | boundary = boundary, |
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| 60 | conserved_quantities = conserved_quantities, |
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| 61 | evolved_quantities = evolved_quantities, |
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| 62 | other_quantities = other_quantities, |
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| 63 | tagged_elements = tagged_elements) |
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[5827] | 64 | |
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| 65 | from config import minimum_allowed_height, g, h0 |
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| 66 | self.minimum_allowed_height = minimum_allowed_height |
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| 67 | self.g = g |
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| 68 | self.h0 = h0 |
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| 69 | |
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| 70 | #forcing terms not included in 1d domain ?WHy? |
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| 71 | self.forcing_terms.append(gravity) |
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| 72 | #self.forcing_terms.append(manning_friction) |
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| 73 | #print "\nI have Removed forcing terms line 64 1dsw" |
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| 74 | |
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| 75 | |
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| 76 | #Stored output |
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| 77 | self.store = True |
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| 78 | self.format = 'sww' |
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| 79 | self.smooth = True |
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| 80 | |
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| 81 | |
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| 82 | #Reduction operation for get_vertex_values |
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| 83 | from util import mean |
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| 84 | self.reduction = mean |
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| 85 | #self.reduction = min #Looks better near steep slopes |
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| 86 | |
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[5832] | 87 | self.set_quantities_to_be_stored(['stage','xmomentum']) |
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[5827] | 88 | |
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| 89 | self.__doc__ = 'shallow_water_domain' |
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| 90 | |
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[5832] | 91 | self.check_integrity() |
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[5827] | 92 | |
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[5832] | 93 | |
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[5827] | 94 | def set_quantities_to_be_stored(self, q): |
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| 95 | """Specify which quantities will be stored in the sww file. |
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| 96 | |
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| 97 | q must be either: |
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| 98 | - the name of a quantity |
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| 99 | - a list of quantity names |
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| 100 | - None |
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| 101 | |
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| 102 | In the two first cases, the named quantities will be stored at each |
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| 103 | yieldstep |
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| 104 | (This is in addition to the quantities elevation and friction) |
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| 105 | If q is None, storage will be switched off altogether. |
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| 106 | """ |
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| 107 | |
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| 108 | |
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| 109 | if q is None: |
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| 110 | self.quantities_to_be_stored = [] |
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| 111 | self.store = False |
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| 112 | return |
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| 113 | |
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| 114 | if isinstance(q, basestring): |
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| 115 | q = [q] # Turn argument into a list |
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| 116 | |
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| 117 | #Check correcness |
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| 118 | for quantity_name in q: |
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| 119 | msg = 'Quantity %s is not a valid conserved quantity' %quantity_name |
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| 120 | assert quantity_name in self.conserved_quantities, msg |
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| 121 | |
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| 122 | self.quantities_to_be_stored = q |
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| 123 | |
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| 124 | |
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[5832] | 125 | def check_integrity(self): |
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[5827] | 126 | |
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| 127 | #Check that we are solving the shallow water wave equation |
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| 128 | |
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| 129 | msg = 'First conserved quantity must be "stage"' |
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| 130 | assert self.conserved_quantities[0] == 'stage', msg |
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| 131 | msg = 'Second conserved quantity must be "xmomentum"' |
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| 132 | assert self.conserved_quantities[1] == 'xmomentum', msg |
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| 133 | |
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[5832] | 134 | msg = 'First evolved quantity must be "stage"' |
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| 135 | assert self.evolved_quantities[0] == 'stage', msg |
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| 136 | msg = 'Second evolved quantity must be "xmomentum"' |
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| 137 | assert self.evolved_quantities[1] == 'xmomentum', msg |
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| 138 | msg = 'Third evolved quantity must be "elevation"' |
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| 139 | assert self.evolved_quantities[2] == 'elevation', msg |
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| 140 | msg = 'Fourth evolved quantity must be "height"' |
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| 141 | assert self.evolved_quantities[3] == 'height', msg |
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| 142 | msg = 'Fifth evolved quantity must be "velocity"' |
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| 143 | assert self.evolved_quantities[4] == 'velocity', msg |
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| 144 | |
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| 145 | Generic_Domain.check_integrity(self) |
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| 146 | |
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[5827] | 147 | def extrapolate_second_order_sw(self): |
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| 148 | #Call correct module function |
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| 149 | #(either from this module or C-extension) |
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| 150 | extrapolate_second_order_sw(self) |
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| 151 | |
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| 152 | def compute_fluxes(self): |
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| 153 | #Call correct module function |
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| 154 | #(either from this module or C-extension) |
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| 155 | compute_fluxes_C_wellbalanced(self) |
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| 156 | |
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| 157 | def compute_timestep(self): |
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| 158 | #Call correct module function |
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| 159 | compute_timestep(self) |
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| 160 | |
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| 161 | def distribute_to_vertices_and_edges(self): |
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| 162 | #Call correct module function |
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| 163 | #(either from this module or C-extension) |
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| 164 | distribute_to_vertices_and_edges(self) |
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| 165 | |
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| 166 | def evolve(self, yieldstep = None, finaltime = None, duration = None, |
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| 167 | skip_initial_step = False): |
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| 168 | """Specialisation of basic evolve method from parent class |
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| 169 | """ |
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| 170 | |
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| 171 | #Call check integrity here rather than from user scripts |
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| 172 | #self.check_integrity() |
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| 173 | |
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| 174 | #msg = 'Parameter beta_h must be in the interval [0, 1)' |
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| 175 | #assert 0 <= self.beta_h < 1.0, msg |
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| 176 | #msg = 'Parameter beta_w must be in the interval [0, 1)' |
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| 177 | #assert 0 <= self.beta_w < 1.0, msg |
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| 178 | |
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| 179 | |
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| 180 | #Initial update of vertex and edge values before any storage |
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| 181 | #and or visualisation |
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| 182 | |
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| 183 | #self.distribute_to_vertices_and_edges ????????????????????????????????? |
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| 184 | |
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| 185 | #Initialise real time viz if requested |
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| 186 | #if self.visualise is True and self.time == 0.0: |
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| 187 | # if self.visualiser is None: |
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| 188 | # self.initialise_visualiser() |
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| 189 | # |
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| 190 | # self.visualiser.update_timer() |
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| 191 | # self.visualiser.setup_all() |
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| 192 | |
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| 193 | #Store model data, e.g. for visualisation |
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| 194 | #if self.store is True and self.time == 0.0: |
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| 195 | # self.initialise_storage() |
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| 196 | # #print 'Storing results in ' + self.writer.filename |
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| 197 | #else: |
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| 198 | # pass |
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| 199 | # #print 'Results will not be stored.' |
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| 200 | # #print 'To store results set domain.store = True' |
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| 201 | # #FIXME: Diagnostic output should be controlled by |
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| 202 | # # a 'verbose' flag living in domain (or in a parent class) |
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| 203 | |
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| 204 | #Call basic machinery from parent class |
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| 205 | for t in Generic_Domain.evolve(self, yieldstep, finaltime,duration, |
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| 206 | skip_initial_step): |
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| 207 | #Real time viz |
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| 208 | # if self.visualise is True: |
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| 209 | # self.visualiser.update_all() |
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| 210 | # self.visualiser.update_timer() |
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| 211 | |
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| 212 | |
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| 213 | #Store model data, e.g. for subsequent visualisation |
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| 214 | # if self.store is True: |
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| 215 | # self.store_timestep(self.quantities_to_be_stored) |
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| 216 | |
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| 217 | #FIXME: Could maybe be taken from specified list |
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| 218 | #of 'store every step' quantities |
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| 219 | |
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| 220 | #Pass control on to outer loop for more specific actions |
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| 221 | yield(t) |
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| 222 | |
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| 223 | def initialise_storage(self): |
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| 224 | """Create and initialise self.writer object for storing data. |
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| 225 | Also, save x and bed elevation |
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| 226 | """ |
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| 227 | |
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| 228 | import data_manager |
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| 229 | |
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| 230 | #Initialise writer |
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| 231 | self.writer = data_manager.get_dataobject(self, mode = 'w') |
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| 232 | |
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| 233 | #Store vertices and connectivity |
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| 234 | self.writer.store_connectivity() |
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| 235 | |
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| 236 | |
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| 237 | def store_timestep(self, name): |
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| 238 | """Store named quantity and time. |
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| 239 | |
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| 240 | Precondition: |
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| 241 | self.write has been initialised |
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| 242 | """ |
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| 243 | self.writer.store_timestep(name) |
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| 244 | |
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| 245 | |
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| 246 | #=============== End of Shallow Water Domain =============================== |
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| 247 | |
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| 248 | #Rotation of momentum vector |
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| 249 | def rotate(q, normal, direction = 1): |
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| 250 | """Rotate the momentum component q (q[1], q[2]) |
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| 251 | from x,y coordinates to coordinates based on normal vector. |
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| 252 | |
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| 253 | If direction is negative the rotation is inverted. |
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| 254 | |
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| 255 | Input vector is preserved |
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| 256 | |
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| 257 | This function is specific to the shallow water wave equation |
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| 258 | """ |
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| 259 | |
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| 260 | from Numeric import zeros, Float |
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| 261 | |
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| 262 | assert len(q) == 3,\ |
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| 263 | 'Vector of conserved quantities must have length 3'\ |
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| 264 | 'for 2D shallow water equation' |
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| 265 | |
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| 266 | try: |
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| 267 | l = len(normal) |
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| 268 | except: |
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| 269 | raise 'Normal vector must be an Numeric array' |
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| 270 | |
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| 271 | assert l == 2, 'Normal vector must have 2 components' |
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| 272 | |
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| 273 | |
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| 274 | n1 = normal[0] |
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| 275 | n2 = normal[1] |
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| 276 | |
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| 277 | r = zeros(len(q), Float) #Rotated quantities |
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| 278 | r[0] = q[0] #First quantity, height, is not rotated |
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| 279 | |
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| 280 | if direction == -1: |
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| 281 | n2 = -n2 |
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| 282 | |
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| 283 | |
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| 284 | r[1] = n1*q[1] + n2*q[2] |
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| 285 | r[2] = -n2*q[1] + n1*q[2] |
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| 286 | |
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| 287 | return r |
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| 288 | |
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| 289 | |
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| 290 | def flux_function(normal, ql, qr, zl, zr): |
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| 291 | """Compute fluxes between volumes for the shallow water wave equation |
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| 292 | cast in terms of w = h+z using the 'central scheme' as described in |
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| 293 | |
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| 294 | Kurganov, Noelle, Petrova. 'Semidiscrete Central-Upwind Schemes For |
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| 295 | Hyperbolic Conservation Laws and Hamilton-Jacobi Equations'. |
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| 296 | Siam J. Sci. Comput. Vol. 23, No. 3, pp. 707-740. |
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| 297 | |
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| 298 | The implemented formula is given in equation (3.15) on page 714 |
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| 299 | |
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| 300 | Conserved quantities w, uh, are stored as elements 0 and 1 |
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| 301 | in the numerical vectors ql an qr. |
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| 302 | |
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| 303 | Bed elevations zl and zr. |
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| 304 | """ |
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| 305 | |
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| 306 | from config import g, epsilon, h0 |
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| 307 | from math import sqrt |
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| 308 | from Numeric import array |
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| 309 | |
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| 310 | #print 'ql',ql |
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| 311 | |
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| 312 | #Align momentums with x-axis |
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| 313 | #q_left = rotate(ql, normal, direction = 1) |
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| 314 | #q_right = rotate(qr, normal, direction = 1) |
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| 315 | q_left = ql |
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| 316 | q_left[1] = q_left[1]*normal |
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| 317 | q_right = qr |
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| 318 | q_right[1] = q_right[1]*normal |
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| 319 | |
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| 320 | #z = (zl+zr)/2 #Take average of field values |
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| 321 | z = 0.5*(zl+zr) #Take average of field values |
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| 322 | |
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| 323 | w_left = q_left[0] #w=h+z |
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| 324 | h_left = w_left-z |
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| 325 | uh_left = q_left[1] |
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| 326 | |
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| 327 | if h_left < epsilon: |
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| 328 | u_left = 0.0 #Could have been negative |
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| 329 | h_left = 0.0 |
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| 330 | else: |
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| 331 | u_left = uh_left/(h_left + h0/h_left) |
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| 332 | |
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| 333 | |
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| 334 | uh_left = u_left*h_left |
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| 335 | |
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| 336 | |
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| 337 | w_right = q_right[0] #w=h+z |
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| 338 | h_right = w_right-z |
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| 339 | uh_right = q_right[1] |
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| 340 | |
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| 341 | if h_right < epsilon: |
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| 342 | u_right = 0.0 #Could have been negative |
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| 343 | h_right = 0.0 |
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| 344 | else: |
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| 345 | u_right = uh_right/(h_right + h0/h_right) |
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| 346 | |
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| 347 | uh_right = u_right*h_right |
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| 348 | |
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| 349 | |
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| 350 | #We have got h and u at vertex, then the following is the calculation of fluxes!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 351 | soundspeed_left = sqrt(g*h_left) |
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| 352 | soundspeed_right = sqrt(g*h_right) |
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| 353 | |
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| 354 | #Maximal wave speed |
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| 355 | s_max = max(u_left+soundspeed_left, u_right+soundspeed_right, 0) |
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| 356 | |
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| 357 | #Minimal wave speed |
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| 358 | s_min = min(u_left-soundspeed_left, u_right-soundspeed_right, 0) |
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| 359 | |
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| 360 | #Flux computation |
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| 361 | flux_left = array([u_left*h_left, |
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| 362 | u_left*uh_left + 0.5*g*h_left*h_left]) |
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| 363 | flux_right = array([u_right*h_right, |
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| 364 | u_right*uh_right + 0.5*g*h_right*h_right]) |
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| 365 | |
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| 366 | denom = s_max-s_min |
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| 367 | if denom == 0.0: |
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| 368 | edgeflux = array([0.0, 0.0]) |
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| 369 | max_speed = 0.0 |
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| 370 | else: |
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| 371 | edgeflux = (s_max*flux_left - s_min*flux_right)/denom |
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| 372 | edgeflux += s_max*s_min*(q_right-q_left)/denom |
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| 373 | |
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| 374 | edgeflux[1] = edgeflux[1]*normal |
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| 375 | |
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| 376 | max_speed = max(abs(s_max), abs(s_min)) |
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| 377 | |
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| 378 | return edgeflux, max_speed |
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| 379 | # |
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| 380 | def compute_fluxes(domain): |
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| 381 | """ |
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| 382 | Compute all fluxes and the timestep suitable for all volumes |
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| 383 | in domain. |
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| 384 | |
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| 385 | Compute total flux for each conserved quantity using "flux_function" |
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| 386 | |
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| 387 | Fluxes across each edge are scaled by edgelengths and summed up |
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| 388 | Resulting flux is then scaled by area and stored in |
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| 389 | explicit_update for each of the three conserved quantities |
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| 390 | stage, xmomentum and ymomentum |
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| 391 | |
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| 392 | The maximal allowable speed computed by the flux_function for each volume |
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| 393 | is converted to a timestep that must not be exceeded. The minimum of |
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| 394 | those is computed as the next overall timestep. |
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| 395 | |
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| 396 | Post conditions: |
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| 397 | domain.explicit_update is reset to computed flux values |
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| 398 | domain.timestep is set to the largest step satisfying all volumes. |
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| 399 | |
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| 400 | """ |
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| 401 | |
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| 402 | import sys |
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| 403 | from Numeric import zeros, Float |
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| 404 | |
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| 405 | |
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| 406 | domain.distribute_to_vertices_and_edges() |
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| 407 | domain.update_boundary() |
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| 408 | |
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| 409 | N = domain.number_of_elements |
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| 410 | Stage = domain.quantities['stage'] |
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| 411 | Xmom = domain.quantities['xmomentum'] |
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| 412 | Bed = domain.quantities['elevation'] |
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| 413 | |
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| 414 | stage = Stage.vertex_values |
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| 415 | xmom = Xmom.vertex_values |
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| 416 | bed = Bed.vertex_values |
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| 417 | |
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| 418 | stage_bdry = Stage.boundary_values |
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| 419 | xmom_bdry = Xmom.boundary_values |
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| 420 | |
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| 421 | |
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| 422 | |
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| 423 | flux = zeros(2, Float) #Work array for summing up fluxes |
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| 424 | ql = zeros(2, Float) |
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| 425 | qr = zeros(2, Float) |
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| 426 | |
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| 427 | #Loop |
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| 428 | timestep = float(sys.maxint) |
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| 429 | enter = True |
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| 430 | for k in range(N): |
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| 431 | |
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| 432 | flux[:] = 0. #Reset work array |
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| 433 | #for i in range(3): |
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| 434 | for i in range(2): |
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| 435 | #Quantities inside volume facing neighbour i |
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| 436 | #ql[0] = stage[k, i] |
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| 437 | #ql[1] = xmom[k, i] |
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| 438 | ql = [stage[k, i], xmom[k, i]] |
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| 439 | zl = bed[k, i] |
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| 440 | |
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| 441 | #Quantities at neighbour on nearest face |
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| 442 | n = domain.neighbours[k,i] |
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| 443 | if n < 0: |
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| 444 | m = -n-1 #Convert negative flag to index |
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| 445 | qr[0] = stage_bdry[m] |
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| 446 | qr[1] = xmom_bdry[m] |
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| 447 | zr = zl #Extend bed elevation to boundary |
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| 448 | else: |
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| 449 | #m = domain.neighbour_edges[k,i] |
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| 450 | m = domain.neighbour_vertices[k,i] |
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| 451 | #qr = [stage[n, m], xmom[n, m], ymom[n, m]] |
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| 452 | qr[0] = stage[n, m] |
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| 453 | qr[1] = xmom[n, m] |
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| 454 | zr = bed[n, m] |
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| 455 | |
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| 456 | |
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| 457 | #Outward pointing normal vector |
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| 458 | normal = domain.normals[k, i] |
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| 459 | |
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| 460 | #Flux computation using provided function |
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| 461 | |
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| 462 | edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
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| 463 | |
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| 464 | #print 'edgeflux', edgeflux |
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| 465 | |
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| 466 | # THIS IS THE LINE TO DEAL WITH LEFT AND RIGHT FLUXES |
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| 467 | # flux = edgefluxleft - edgefluxright |
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| 468 | flux -= edgeflux #* domain.edgelengths[k,i] |
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| 469 | #Update optimal_timestep |
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| 470 | try: |
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| 471 | #timestep = min(timestep, 0.5*domain.radii[k]/max_speed) |
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| 472 | timestep = min(timestep, domain.cfl*0.5*domain.areas[k]/max_speed) |
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| 473 | except ZeroDivisionError: |
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| 474 | pass |
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| 475 | |
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| 476 | #Normalise by area and store for when all conserved |
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| 477 | #quantities get updated |
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| 478 | flux /= domain.areas[k] |
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| 479 | |
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| 480 | Stage.explicit_update[k] = flux[0] |
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| 481 | Xmom.explicit_update[k] = flux[1] |
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| 482 | #Ymom.explicit_update[k] = flux[2] |
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| 483 | #print "flux cell",k,flux[0] |
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| 484 | |
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| 485 | domain.flux_timestep = timestep |
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| 486 | #print domain.quantities['stage'].centroid_values |
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| 487 | # |
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| 488 | def compute_timestep(domain): |
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| 489 | import sys |
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| 490 | from Numeric import zeros, Float |
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| 491 | |
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| 492 | N = domain.number_of_elements |
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| 493 | |
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| 494 | #Shortcuts |
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| 495 | Stage = domain.quantities['stage'] |
---|
| 496 | Xmom = domain.quantities['xmomentum'] |
---|
| 497 | Bed = domain.quantities['elevation'] |
---|
| 498 | |
---|
| 499 | stage = Stage.vertex_values |
---|
| 500 | xmom = Xmom.vertex_values |
---|
| 501 | bed = Bed.vertex_values |
---|
| 502 | |
---|
| 503 | stage_bdry = Stage.boundary_values |
---|
| 504 | xmom_bdry = Xmom.boundary_values |
---|
| 505 | |
---|
| 506 | flux = zeros(2, Float) #Work array for summing up fluxes |
---|
| 507 | ql = zeros(2, Float) |
---|
| 508 | qr = zeros(2, Float) |
---|
| 509 | |
---|
| 510 | #Loop |
---|
| 511 | timestep = float(sys.maxint) |
---|
| 512 | enter = True |
---|
| 513 | for k in range(N): |
---|
| 514 | |
---|
| 515 | flux[:] = 0. #Reset work array |
---|
| 516 | for i in range(2): |
---|
| 517 | #Quantities inside volume facing neighbour i |
---|
| 518 | ql = [stage[k, i], xmom[k, i]] |
---|
| 519 | zl = bed[k, i] |
---|
| 520 | |
---|
| 521 | #Quantities at neighbour on nearest face |
---|
| 522 | n = domain.neighbours[k,i] |
---|
| 523 | if n < 0: |
---|
| 524 | m = -n-1 #Convert negative flag to index |
---|
| 525 | qr[0] = stage_bdry[m] |
---|
| 526 | qr[1] = xmom_bdry[m] |
---|
| 527 | zr = zl #Extend bed elevation to boundary |
---|
| 528 | else: |
---|
| 529 | #m = domain.neighbour_edges[k,i] |
---|
| 530 | m = domain.neighbour_vertices[k,i] |
---|
| 531 | qr[0] = stage[n, m] |
---|
| 532 | qr[1] = xmom[n, m] |
---|
| 533 | zr = bed[n, m] |
---|
| 534 | |
---|
| 535 | |
---|
| 536 | #Outward pointing normal vector |
---|
| 537 | normal = domain.normals[k, i] |
---|
| 538 | |
---|
| 539 | edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
---|
| 540 | |
---|
| 541 | #Update optimal_timestep |
---|
| 542 | try: |
---|
| 543 | timestep = min(timestep, domain.cfl*0.5*domain.areas[k]/max_speed) |
---|
| 544 | except ZeroDivisionError: |
---|
| 545 | pass |
---|
| 546 | |
---|
| 547 | domain.timestep = timestep |
---|
| 548 | |
---|
| 549 | # Compute flux definition |
---|
| 550 | def compute_fluxes_C_long(domain): |
---|
| 551 | from Numeric import zeros, Float |
---|
| 552 | import sys |
---|
| 553 | |
---|
| 554 | |
---|
| 555 | timestep = float(sys.maxint) |
---|
| 556 | #print 'timestep=',timestep |
---|
| 557 | #print 'The type of timestep is',type(timestep) |
---|
| 558 | |
---|
| 559 | epsilon = domain.epsilon |
---|
| 560 | #print 'epsilon=',epsilon |
---|
| 561 | #print 'The type of epsilon is',type(epsilon) |
---|
| 562 | |
---|
| 563 | g = domain.g |
---|
| 564 | #print 'g=',g |
---|
| 565 | #print 'The type of g is',type(g) |
---|
| 566 | |
---|
| 567 | neighbours = domain.neighbours |
---|
| 568 | #print 'neighbours=',neighbours |
---|
| 569 | #print 'The type of neighbours is',type(neighbours) |
---|
| 570 | |
---|
| 571 | neighbour_vertices = domain.neighbour_vertices |
---|
| 572 | #print 'neighbour_vertices=',neighbour_vertices |
---|
| 573 | #print 'The type of neighbour_vertices is',type(neighbour_vertices) |
---|
| 574 | |
---|
| 575 | normals = domain.normals |
---|
| 576 | #print 'normals=',normals |
---|
| 577 | #print 'The type of normals is',type(normals) |
---|
| 578 | |
---|
| 579 | areas = domain.areas |
---|
| 580 | #print 'areas=',areas |
---|
| 581 | #print 'The type of areas is',type(areas) |
---|
| 582 | |
---|
| 583 | stage_edge_values = domain.quantities['stage'].vertex_values |
---|
| 584 | #print 'stage_edge_values=',stage_edge_values |
---|
| 585 | #print 'The type of stage_edge_values is',type(stage_edge_values) |
---|
| 586 | |
---|
| 587 | xmom_edge_values = domain.quantities['xmomentum'].vertex_values |
---|
| 588 | #print 'xmom_edge_values=',xmom_edge_values |
---|
| 589 | #print 'The type of xmom_edge_values is',type(xmom_edge_values) |
---|
| 590 | |
---|
| 591 | bed_edge_values = domain.quantities['elevation'].vertex_values |
---|
| 592 | #print 'bed_edge_values=',bed_edge_values |
---|
| 593 | #print 'The type of bed_edge_values is',type(bed_edge_values) |
---|
| 594 | |
---|
| 595 | stage_boundary_values = domain.quantities['stage'].boundary_values |
---|
| 596 | #print 'stage_boundary_values=',stage_boundary_values |
---|
| 597 | #print 'The type of stage_boundary_values is',type(stage_boundary_values) |
---|
| 598 | |
---|
| 599 | xmom_boundary_values = domain.quantities['xmomentum'].boundary_values |
---|
| 600 | #print 'xmom_boundary_values=',xmom_boundary_values |
---|
| 601 | #print 'The type of xmom_boundary_values is',type(xmom_boundary_values) |
---|
| 602 | |
---|
| 603 | stage_explicit_update = domain.quantities['stage'].explicit_update |
---|
| 604 | #print 'stage_explicit_update=',stage_explicit_update |
---|
| 605 | #print 'The type of stage_explicit_update is',type(stage_explicit_update) |
---|
| 606 | |
---|
| 607 | xmom_explicit_update = domain.quantities['xmomentum'].explicit_update |
---|
| 608 | #print 'xmom_explicit_update=',xmom_explicit_update |
---|
| 609 | #print 'The type of xmom_explicit_update is',type(xmom_explicit_update) |
---|
| 610 | |
---|
| 611 | number_of_elements = len(stage_edge_values) |
---|
| 612 | #print 'number_of_elements=',number_of_elements |
---|
| 613 | #print 'The type of number_of_elements is',type(number_of_elements) |
---|
| 614 | |
---|
| 615 | max_speed_array = domain.max_speed_array |
---|
| 616 | #print 'max_speed_array=',max_speed_array |
---|
| 617 | #print 'The type of max_speed_array is',type(max_speed_array) |
---|
| 618 | |
---|
| 619 | |
---|
| 620 | from comp_flux_ext import compute_fluxes_ext |
---|
| 621 | |
---|
| 622 | domain.flux_timestep = compute_fluxes_ext(timestep, |
---|
| 623 | epsilon, |
---|
| 624 | g, |
---|
| 625 | neighbours, |
---|
| 626 | neighbour_vertices, |
---|
| 627 | normals, |
---|
| 628 | areas, |
---|
| 629 | stage_edge_values, |
---|
| 630 | xmom_edge_values, |
---|
| 631 | bed_edge_values, |
---|
| 632 | stage_boundary_values, |
---|
| 633 | xmom_boundary_values, |
---|
| 634 | stage_explicit_update, |
---|
| 635 | xmom_explicit_update, |
---|
| 636 | number_of_elements, |
---|
| 637 | max_speed_array) |
---|
| 638 | |
---|
| 639 | |
---|
| 640 | # Compute flux definition |
---|
| 641 | def compute_fluxes_C_short(domain): |
---|
| 642 | from Numeric import zeros, Float |
---|
| 643 | import sys |
---|
| 644 | |
---|
| 645 | |
---|
| 646 | timestep = float(sys.maxint) |
---|
| 647 | |
---|
| 648 | stage = domain.quantities['stage'] |
---|
| 649 | xmom = domain.quantities['xmomentum'] |
---|
| 650 | bed = domain.quantities['elevation'] |
---|
| 651 | |
---|
| 652 | |
---|
| 653 | from comp_flux_ext import compute_fluxes_ext_short |
---|
| 654 | |
---|
| 655 | domain.flux_timestep = compute_fluxes_ext_short(timestep,domain,stage,xmom,bed) |
---|
| 656 | |
---|
| 657 | |
---|
| 658 | |
---|
| 659 | # ################################### |
---|
| 660 | def compute_fluxes_C_wellbalanced(domain): |
---|
| 661 | #from Numeric import zeros, Float |
---|
| 662 | #import sys |
---|
| 663 | |
---|
| 664 | |
---|
| 665 | #timestep = float(sys.maxint) |
---|
| 666 | #epsilon = domain.epsilon |
---|
| 667 | #g = domain.g |
---|
| 668 | #neighbours = domain.neighbours |
---|
| 669 | #neighbour_vertices = domain.neighbour_vertices |
---|
| 670 | #normals = domain.normals |
---|
| 671 | #areas = domain.areas |
---|
| 672 | #stage_edge_values = domain.quantities['stage'].vertex_values |
---|
| 673 | #xmom_edge_values = domain.quantities['xmomentum'].vertex_values |
---|
| 674 | #bed_edge_values = domain.quantities['elevation'].vertex_values |
---|
| 675 | #stage_boundary_values = domain.quantities['stage'].boundary_values |
---|
| 676 | #xmom_boundary_values = domain.quantities['xmomentum'].boundary_values |
---|
| 677 | #stage_explicit_update = domain.quantities['stage'].explicit_update |
---|
| 678 | #xmom_explicit_update = domain.quantities['xmomentum'].explicit_update |
---|
| 679 | #number_of_elements = len(stage_edge_values) |
---|
| 680 | #max_speed_array = domain.max_speed_array |
---|
| 681 | |
---|
| 682 | import sys |
---|
| 683 | from Numeric import zeros, Float |
---|
| 684 | |
---|
| 685 | N = domain.number_of_elements |
---|
| 686 | timestep = float(sys.maxint) |
---|
| 687 | epsilon = domain.epsilon |
---|
| 688 | g = domain.g |
---|
| 689 | neighbours = domain.neighbours |
---|
| 690 | neighbour_vertices = domain.neighbour_vertices |
---|
| 691 | normals = domain.normals |
---|
| 692 | areas = domain.areas |
---|
| 693 | |
---|
| 694 | Stage = domain.quantities['stage'] |
---|
| 695 | Xmom = domain.quantities['xmomentum'] |
---|
| 696 | Bed = domain.quantities['elevation'] |
---|
| 697 | |
---|
| 698 | stage_boundary_values = Stage.boundary_values |
---|
| 699 | xmom_boundary_values = Xmom.boundary_values |
---|
| 700 | stage_explicit_update = Stage.explicit_update |
---|
| 701 | xmom_explicit_update = Xmom.explicit_update |
---|
| 702 | max_speed_array = domain.max_speed_array |
---|
| 703 | |
---|
| 704 | domain.distribute_to_vertices_and_edges() |
---|
| 705 | domain.update_boundary() |
---|
| 706 | stage_V = Stage.vertex_values |
---|
| 707 | xmom_V = Xmom.vertex_values |
---|
| 708 | bed_V = Bed.vertex_values |
---|
| 709 | #h_V = Height.vertex_values |
---|
| 710 | #u_V = Velocity.vertex_values |
---|
| 711 | |
---|
| 712 | number_of_elements = len(stage_V) |
---|
| 713 | |
---|
| 714 | #flux = zeros(2, Float) #Work array for summing up fluxes |
---|
| 715 | #ql = zeros(2, Float) |
---|
| 716 | #qr = zeros(2, Float) |
---|
| 717 | |
---|
| 718 | from comp_flux_ext_wellbalanced import compute_fluxes_ext_wellbalanced #from comp_flux_ext import compute_fluxes_ext |
---|
| 719 | |
---|
| 720 | domain.flux_timestep = compute_fluxes_ext_wellbalanced(timestep, |
---|
| 721 | epsilon, |
---|
| 722 | g, |
---|
| 723 | neighbours, |
---|
| 724 | neighbour_vertices, |
---|
| 725 | normals, |
---|
| 726 | areas, |
---|
| 727 | stage_V, |
---|
| 728 | xmom_V, |
---|
| 729 | bed_V, |
---|
| 730 | stage_boundary_values, |
---|
| 731 | xmom_boundary_values, |
---|
| 732 | stage_explicit_update, |
---|
| 733 | xmom_explicit_update, |
---|
| 734 | number_of_elements, |
---|
| 735 | max_speed_array) |
---|
| 736 | |
---|
| 737 | # ################################### |
---|
| 738 | |
---|
| 739 | |
---|
| 740 | |
---|
| 741 | |
---|
| 742 | |
---|
| 743 | |
---|
| 744 | # Module functions for gradient limiting (distribute_to_vertices_and_edges) |
---|
| 745 | |
---|
| 746 | def distribute_to_vertices_and_edges(domain): |
---|
| 747 | """Distribution from centroids to vertices specific to the |
---|
| 748 | shallow water wave |
---|
| 749 | equation. |
---|
| 750 | |
---|
| 751 | It will ensure that h (w-z) is always non-negative even in the |
---|
| 752 | presence of steep bed-slopes by taking a weighted average between shallow |
---|
| 753 | and deep cases. |
---|
| 754 | |
---|
| 755 | In addition, all conserved quantities get distributed as per either a |
---|
| 756 | constant (order==1) or a piecewise linear function (order==2). |
---|
| 757 | |
---|
| 758 | FIXME: more explanation about removal of artificial variability etc |
---|
| 759 | |
---|
| 760 | Precondition: |
---|
| 761 | All quantities defined at centroids and bed elevation defined at |
---|
| 762 | vertices. |
---|
| 763 | |
---|
| 764 | Postcondition |
---|
| 765 | Conserved quantities defined at vertices |
---|
| 766 | |
---|
| 767 | """ |
---|
| 768 | |
---|
| 769 | #from config import optimised_gradient_limiter |
---|
| 770 | |
---|
| 771 | #Remove very thin layers of water |
---|
| 772 | #protect_against_infinitesimal_and_negative_heights(domain) |
---|
| 773 | |
---|
| 774 | import sys |
---|
| 775 | from Numeric import zeros, Float |
---|
| 776 | from config import epsilon, h0 |
---|
| 777 | |
---|
| 778 | N = domain.number_of_elements |
---|
| 779 | |
---|
| 780 | #Shortcuts |
---|
| 781 | Stage = domain.quantities['stage'] |
---|
| 782 | Xmom = domain.quantities['xmomentum'] |
---|
| 783 | Bed = domain.quantities['elevation'] |
---|
| 784 | Height = domain.quantities['height'] |
---|
| 785 | Velocity = domain.quantities['velocity'] |
---|
| 786 | |
---|
| 787 | #Arrays |
---|
| 788 | w_C = Stage.centroid_values |
---|
| 789 | uh_C = Xmom.centroid_values |
---|
| 790 | z_C = Bed.centroid_values |
---|
| 791 | h_C = Height.centroid_values |
---|
| 792 | u_C = Velocity.centroid_values |
---|
| 793 | |
---|
| 794 | #print id(h_C) |
---|
| 795 | for i in range(N): |
---|
| 796 | h_C[i] = w_C[i] - z_C[i] |
---|
| 797 | if h_C[i] <= 0.0: |
---|
| 798 | #print 'h_C[%d]= %15.5e\n' % (i,h_C[i]) |
---|
| 799 | h_C[i] = 1.0e-15 |
---|
| 800 | w_C[i] = z_C[i] |
---|
| 801 | uh_C[i] = 0.0 |
---|
| 802 | |
---|
| 803 | |
---|
| 804 | ## for i in range(len(h_C)): |
---|
| 805 | ## if h_C[i] < epsilon: |
---|
| 806 | ## u_C[i] = 0.0 #Could have been negative |
---|
| 807 | ## h_C[i] = 0.0 |
---|
| 808 | ## else: |
---|
| 809 | |
---|
| 810 | u_C[:] = uh_C/(h_C + h0/h_C) |
---|
| 811 | |
---|
| 812 | for name in [ 'velocity', 'stage' ]: |
---|
| 813 | Q = domain.quantities[name] |
---|
| 814 | if domain.order == 1: |
---|
| 815 | Q.extrapolate_first_order() |
---|
| 816 | elif domain.order == 2: |
---|
| 817 | #print "add extrapolate second order to shallow water" |
---|
| 818 | #if name != 'height': |
---|
| 819 | Q.extrapolate_second_order() |
---|
| 820 | #Q.limit() |
---|
| 821 | else: |
---|
| 822 | raise 'Unknown order' |
---|
| 823 | |
---|
| 824 | stage_V = domain.quantities['stage'].vertex_values |
---|
| 825 | bed_V = domain.quantities['elevation'].vertex_values |
---|
| 826 | h_V = domain.quantities['height'].vertex_values |
---|
| 827 | u_V = domain.quantities['velocity'].vertex_values |
---|
| 828 | xmom_V = domain.quantities['xmomentum'].vertex_values |
---|
| 829 | |
---|
| 830 | h_V[:] = stage_V - bed_V |
---|
| 831 | for i in range(len(h_C)): |
---|
| 832 | for j in range(2): |
---|
| 833 | if h_V[i,j] < 0.0 : |
---|
| 834 | print 'h_V[%d,%d] = %f \n' % (i,j,h_V[i,j]) |
---|
| 835 | dh = h_V[i,j] |
---|
| 836 | h_V[i,j] = 0.0 |
---|
| 837 | stage_V[i,j] = bed_V[i,j] |
---|
| 838 | h_V[i,(j+1)%2] = h_V[i,(j+1)%2] + dh |
---|
| 839 | stage_V[i,(j+1)%2] = stage_V[i,(j+1)%2] + dh |
---|
| 840 | |
---|
| 841 | xmom_V[:] = u_V * h_V |
---|
| 842 | |
---|
| 843 | return |
---|
| 844 | # |
---|
| 845 | |
---|
| 846 | |
---|
| 847 | |
---|
| 848 | |
---|
| 849 | |
---|
| 850 | |
---|
| 851 | |
---|
| 852 | # |
---|
| 853 | def protect_against_infinitesimal_and_negative_heights(domain): |
---|
| 854 | """Protect against infinitesimal heights and associated high velocities |
---|
| 855 | """ |
---|
| 856 | |
---|
| 857 | #Shortcuts |
---|
| 858 | wc = domain.quantities['stage'].centroid_values |
---|
| 859 | zc = domain.quantities['elevation'].centroid_values |
---|
| 860 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
| 861 | # ymomc = domain.quantities['ymomentum'].centroid_values |
---|
| 862 | hc = wc - zc #Water depths at centroids |
---|
| 863 | |
---|
| 864 | zv = domain.quantities['elevation'].vertex_values |
---|
| 865 | wv = domain.quantities['stage'].vertex_values |
---|
| 866 | hv = wv-zv |
---|
| 867 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
| 868 | #remove the above two lines and corresponding code below |
---|
| 869 | |
---|
| 870 | #Update |
---|
| 871 | for k in range(domain.number_of_elements): |
---|
| 872 | |
---|
| 873 | if hc[k] < domain.minimum_allowed_height: |
---|
| 874 | #Control stage |
---|
| 875 | if hc[k] < domain.epsilon: |
---|
| 876 | wc[k] = zc[k] # Contain 'lost mass' error |
---|
| 877 | wv[k,0] = zv[k,0] |
---|
| 878 | wv[k,1] = zv[k,1] |
---|
| 879 | |
---|
| 880 | xmomc[k] = 0.0 |
---|
| 881 | |
---|
| 882 | #N = domain.number_of_elements |
---|
| 883 | #if (k == 0) | (k==N-1): |
---|
| 884 | # wc[k] = zc[k] # Contain 'lost mass' error |
---|
| 885 | # wv[k,0] = zv[k,0] |
---|
| 886 | # wv[k,1] = zv[k,1] |
---|
| 887 | |
---|
| 888 | def h_limiter(domain): |
---|
| 889 | """Limit slopes for each volume to eliminate artificial variance |
---|
| 890 | introduced by e.g. second order extrapolator |
---|
| 891 | |
---|
| 892 | limit on h = w-z |
---|
| 893 | |
---|
| 894 | This limiter depends on two quantities (w,z) so it resides within |
---|
| 895 | this module rather than within quantity.py |
---|
| 896 | """ |
---|
| 897 | |
---|
| 898 | from Numeric import zeros, Float |
---|
| 899 | |
---|
| 900 | N = domain.number_of_elements |
---|
| 901 | beta_h = domain.beta_h |
---|
| 902 | |
---|
| 903 | #Shortcuts |
---|
| 904 | wc = domain.quantities['stage'].centroid_values |
---|
| 905 | zc = domain.quantities['elevation'].centroid_values |
---|
| 906 | hc = wc - zc |
---|
| 907 | |
---|
| 908 | wv = domain.quantities['stage'].vertex_values |
---|
| 909 | zv = domain.quantities['elevation'].vertex_values |
---|
| 910 | hv = wv-zv |
---|
| 911 | |
---|
| 912 | hvbar = zeros(hv.shape, Float) #h-limited values |
---|
| 913 | |
---|
| 914 | #Find min and max of this and neighbour's centroid values |
---|
| 915 | hmax = zeros(hc.shape, Float) |
---|
| 916 | hmin = zeros(hc.shape, Float) |
---|
| 917 | |
---|
| 918 | for k in range(N): |
---|
| 919 | hmax[k] = hmin[k] = hc[k] |
---|
| 920 | #for i in range(3): |
---|
| 921 | for i in range(2): |
---|
| 922 | n = domain.neighbours[k,i] |
---|
| 923 | if n >= 0: |
---|
| 924 | hn = hc[n] #Neighbour's centroid value |
---|
| 925 | |
---|
| 926 | hmin[k] = min(hmin[k], hn) |
---|
| 927 | hmax[k] = max(hmax[k], hn) |
---|
| 928 | |
---|
| 929 | |
---|
| 930 | #Diffences between centroids and maxima/minima |
---|
| 931 | dhmax = hmax - hc |
---|
| 932 | dhmin = hmin - hc |
---|
| 933 | |
---|
| 934 | #Deltas between vertex and centroid values |
---|
| 935 | dh = zeros(hv.shape, Float) |
---|
| 936 | #for i in range(3): |
---|
| 937 | for i in range(2): |
---|
| 938 | dh[:,i] = hv[:,i] - hc |
---|
| 939 | |
---|
| 940 | #Phi limiter |
---|
| 941 | for k in range(N): |
---|
| 942 | |
---|
| 943 | #Find the gradient limiter (phi) across vertices |
---|
| 944 | phi = 1.0 |
---|
| 945 | #for i in range(3): |
---|
| 946 | for i in range(2): |
---|
| 947 | r = 1.0 |
---|
| 948 | if (dh[k,i] > 0): r = dhmax[k]/dh[k,i] |
---|
| 949 | if (dh[k,i] < 0): r = dhmin[k]/dh[k,i] |
---|
| 950 | |
---|
| 951 | phi = min( min(r*beta_h, 1), phi ) |
---|
| 952 | |
---|
| 953 | #Then update using phi limiter |
---|
| 954 | #for i in range(3): |
---|
| 955 | for i in range(2): |
---|
| 956 | hvbar[k,i] = hc[k] + phi*dh[k,i] |
---|
| 957 | |
---|
| 958 | return hvbar |
---|
| 959 | |
---|
| 960 | def balance_deep_and_shallow(domain): |
---|
| 961 | """Compute linear combination between stage as computed by |
---|
| 962 | gradient-limiters limiting using w, and stage computed by |
---|
| 963 | gradient-limiters limiting using h (h-limiter). |
---|
| 964 | The former takes precedence when heights are large compared to the |
---|
| 965 | bed slope while the latter takes precedence when heights are |
---|
| 966 | relatively small. Anything in between is computed as a balanced |
---|
| 967 | linear combination in order to avoid numerical disturbances which |
---|
| 968 | would otherwise appear as a result of hard switching between |
---|
| 969 | modes. |
---|
| 970 | |
---|
| 971 | The h-limiter is always applied irrespective of the order. |
---|
| 972 | """ |
---|
| 973 | |
---|
| 974 | #Shortcuts |
---|
| 975 | wc = domain.quantities['stage'].centroid_values |
---|
| 976 | zc = domain.quantities['elevation'].centroid_values |
---|
| 977 | hc = wc - zc |
---|
| 978 | |
---|
| 979 | wv = domain.quantities['stage'].vertex_values |
---|
| 980 | zv = domain.quantities['elevation'].vertex_values |
---|
| 981 | hv = wv-zv |
---|
| 982 | |
---|
| 983 | #Limit h |
---|
| 984 | hvbar = h_limiter(domain) |
---|
| 985 | |
---|
| 986 | for k in range(domain.number_of_elements): |
---|
| 987 | #Compute maximal variation in bed elevation |
---|
| 988 | # This quantitiy is |
---|
| 989 | # dz = max_i abs(z_i - z_c) |
---|
| 990 | # and it is independent of dimension |
---|
| 991 | # In the 1d case zc = (z0+z1)/2 |
---|
| 992 | # In the 2d case zc = (z0+z1+z2)/3 |
---|
| 993 | |
---|
| 994 | dz = max(abs(zv[k,0]-zc[k]), |
---|
| 995 | abs(zv[k,1]-zc[k]))#, |
---|
| 996 | # abs(zv[k,2]-zc[k])) |
---|
| 997 | |
---|
| 998 | |
---|
| 999 | hmin = min( hv[k,:] ) |
---|
| 1000 | |
---|
| 1001 | #Create alpha in [0,1], where alpha==0 means using the h-limited |
---|
| 1002 | #stage and alpha==1 means using the w-limited stage as |
---|
| 1003 | #computed by the gradient limiter (both 1st or 2nd order) |
---|
| 1004 | |
---|
| 1005 | #If hmin > dz/2 then alpha = 1 and the bed will have no effect |
---|
| 1006 | #If hmin < 0 then alpha = 0 reverting to constant height above bed. |
---|
| 1007 | |
---|
| 1008 | if dz > 0.0: |
---|
| 1009 | alpha = max( min( 2*hmin/dz, 1.0), 0.0 ) |
---|
| 1010 | else: |
---|
| 1011 | #Flat bed |
---|
| 1012 | alpha = 1.0 |
---|
| 1013 | |
---|
| 1014 | alpha = 0.0 |
---|
| 1015 | #Let |
---|
| 1016 | # |
---|
| 1017 | # wvi be the w-limited stage (wvi = zvi + hvi) |
---|
| 1018 | # wvi- be the h-limited state (wvi- = zvi + hvi-) |
---|
| 1019 | # |
---|
| 1020 | # |
---|
| 1021 | #where i=0,1,2 denotes the vertex ids |
---|
| 1022 | # |
---|
| 1023 | #Weighted balance between w-limited and h-limited stage is |
---|
| 1024 | # |
---|
| 1025 | # wvi := (1-alpha)*(zvi+hvi-) + alpha*(zvi+hvi) |
---|
| 1026 | # |
---|
| 1027 | #It follows that the updated wvi is |
---|
| 1028 | # wvi := zvi + (1-alpha)*hvi- + alpha*hvi |
---|
| 1029 | # |
---|
| 1030 | # Momentum is balanced between constant and limited |
---|
| 1031 | |
---|
| 1032 | |
---|
| 1033 | #for i in range(3): |
---|
| 1034 | # wv[k,i] = zv[k,i] + hvbar[k,i] |
---|
| 1035 | |
---|
| 1036 | #return |
---|
| 1037 | |
---|
| 1038 | if alpha < 1: |
---|
| 1039 | |
---|
| 1040 | #for i in range(3): |
---|
| 1041 | for i in range(2): |
---|
| 1042 | wv[k,i] = zv[k,i] + (1.0-alpha)*hvbar[k,i] + alpha*hv[k,i] |
---|
| 1043 | |
---|
| 1044 | #Momentums at centroids |
---|
| 1045 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
| 1046 | # ymomc = domain.quantities['ymomentum'].centroid_values |
---|
| 1047 | |
---|
| 1048 | #Momentums at vertices |
---|
| 1049 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
| 1050 | # ymomv = domain.quantities['ymomentum'].vertex_values |
---|
| 1051 | |
---|
| 1052 | # Update momentum as a linear combination of |
---|
| 1053 | # xmomc and ymomc (shallow) and momentum |
---|
| 1054 | # from extrapolator xmomv and ymomv (deep). |
---|
| 1055 | xmomv[k,:] = (1.0-alpha)*xmomc[k] + alpha*xmomv[k,:] |
---|
| 1056 | # ymomv[k,:] = (1-alpha)*ymomc[k] + alpha*ymomv[k,:] |
---|
| 1057 | |
---|
| 1058 | |
---|
| 1059 | ############################################### |
---|
| 1060 | #Boundaries - specific to the shallow water wave equation |
---|
| 1061 | class Reflective_boundary(Boundary): |
---|
| 1062 | """Reflective boundary returns same conserved quantities as |
---|
| 1063 | those present in its neighbour volume but reflected. |
---|
| 1064 | |
---|
| 1065 | This class is specific to the shallow water equation as it |
---|
| 1066 | works with the momentum quantities assumed to be the second |
---|
| 1067 | and third conserved quantities. |
---|
| 1068 | """ |
---|
| 1069 | |
---|
| 1070 | def __init__(self, domain = None): |
---|
| 1071 | Boundary.__init__(self) |
---|
| 1072 | |
---|
| 1073 | if domain is None: |
---|
| 1074 | msg = 'Domain must be specified for reflective boundary' |
---|
| 1075 | raise msg |
---|
| 1076 | |
---|
| 1077 | #Handy shorthands |
---|
[5832] | 1078 | self.normals = domain.normals |
---|
| 1079 | self.stage = domain.quantities['stage'].vertex_values |
---|
| 1080 | self.xmom = domain.quantities['xmomentum'].vertex_values |
---|
| 1081 | self.bed = domain.quantities['elevation'].vertex_values |
---|
| 1082 | self.height = domain.quantities['height'].vertex_values |
---|
| 1083 | self.velocity = domain.quantities['velocity'].vertex_values |
---|
[5827] | 1084 | |
---|
| 1085 | from Numeric import zeros, Float |
---|
| 1086 | #self.conserved_quantities = zeros(3, Float) |
---|
[5832] | 1087 | self.evolved_quantities = zeros(5, Float) |
---|
[5827] | 1088 | |
---|
| 1089 | def __repr__(self): |
---|
| 1090 | return 'Reflective_boundary' |
---|
| 1091 | |
---|
| 1092 | |
---|
| 1093 | def evaluate(self, vol_id, edge_id): |
---|
| 1094 | """Reflective boundaries reverses the outward momentum |
---|
| 1095 | of the volume they serve. |
---|
| 1096 | """ |
---|
| 1097 | |
---|
[5832] | 1098 | q = self.evolved_quantities |
---|
[5827] | 1099 | q[0] = self.stage[vol_id, edge_id] |
---|
[5832] | 1100 | q[1] = -self.xmom[vol_id, edge_id] |
---|
| 1101 | q[2] = self.bed[vol_id, edge_id] |
---|
| 1102 | q[3] = self.height[vol_id, edge_id] |
---|
| 1103 | q[1] = -self.velocity[vol_id, edge_id] |
---|
[5827] | 1104 | |
---|
| 1105 | |
---|
| 1106 | return q |
---|
| 1107 | |
---|
| 1108 | class Dirichlet_boundary(Boundary): |
---|
| 1109 | """Dirichlet boundary returns constant values for the |
---|
| 1110 | conserved quantities |
---|
| 1111 | """ |
---|
| 1112 | |
---|
| 1113 | |
---|
[5832] | 1114 | def __init__(self, evolved_quantities=None): |
---|
[5827] | 1115 | Boundary.__init__(self) |
---|
| 1116 | |
---|
[5832] | 1117 | if evolved_quantities is None: |
---|
[5827] | 1118 | msg = 'Must specify one value for each conserved quantity' |
---|
| 1119 | raise msg |
---|
| 1120 | |
---|
| 1121 | from Numeric import array, Float |
---|
[5832] | 1122 | self.evolved_quantities=array(evolved_quantities).astype(Float) |
---|
[5827] | 1123 | |
---|
| 1124 | def __repr__(self): |
---|
| 1125 | return 'Dirichlet boundary (%s)' %self.conserved_quantities |
---|
| 1126 | |
---|
| 1127 | def evaluate(self, vol_id=None, edge_id=None): |
---|
[5832] | 1128 | return self.evolved_quantities |
---|
[5827] | 1129 | |
---|
| 1130 | |
---|
| 1131 | ######################### |
---|
| 1132 | #Standard forcing terms: |
---|
| 1133 | # |
---|
| 1134 | def gravity(domain): |
---|
| 1135 | """Apply gravitational pull in the presence of bed slope |
---|
| 1136 | """ |
---|
| 1137 | |
---|
| 1138 | from util import gradient |
---|
| 1139 | from Numeric import zeros, Float, array, sum |
---|
| 1140 | |
---|
| 1141 | xmom = domain.quantities['xmomentum'].explicit_update |
---|
| 1142 | stage = domain.quantities['stage'].explicit_update |
---|
| 1143 | # ymom = domain.quantities['ymomentum'].explicit_update |
---|
| 1144 | |
---|
| 1145 | Stage = domain.quantities['stage'] |
---|
| 1146 | Elevation = domain.quantities['elevation'] |
---|
| 1147 | #h = Stage.edge_values - Elevation.edge_values |
---|
| 1148 | h = Stage.vertex_values - Elevation.vertex_values |
---|
| 1149 | b = Elevation.vertex_values |
---|
| 1150 | w = Stage.vertex_values |
---|
| 1151 | |
---|
| 1152 | x = domain.get_vertex_coordinates() |
---|
| 1153 | g = domain.g |
---|
| 1154 | |
---|
| 1155 | for k in range(domain.number_of_elements): |
---|
| 1156 | # avg_h = sum( h[k,:] )/3 |
---|
| 1157 | avg_h = sum( h[k,:] )/2 |
---|
| 1158 | |
---|
| 1159 | #Compute bed slope |
---|
| 1160 | #x0, y0, x1, y1, x2, y2 = x[k,:] |
---|
| 1161 | x0, x1 = x[k,:] |
---|
| 1162 | #z0, z1, z2 = v[k,:] |
---|
| 1163 | b0, b1 = b[k,:] |
---|
| 1164 | |
---|
| 1165 | w0, w1 = w[k,:] |
---|
| 1166 | wx = gradient(x0, x1, w0, w1) |
---|
| 1167 | |
---|
| 1168 | #zx, zy = gradient(x0, y0, x1, y1, x2, y2, z0, z1, z2) |
---|
| 1169 | bx = gradient(x0, x1, b0, b1) |
---|
| 1170 | |
---|
| 1171 | #Update momentum (explicit update is reset to source values) |
---|
| 1172 | xmom[k] += -g*bx*avg_h |
---|
| 1173 | #xmom[k] = -g*bx*avg_h |
---|
| 1174 | #stage[k] = 0.0 |
---|
| 1175 | |
---|
| 1176 | |
---|
| 1177 | def manning_friction(domain): |
---|
| 1178 | """Apply (Manning) friction to water momentum |
---|
| 1179 | """ |
---|
| 1180 | |
---|
| 1181 | from math import sqrt |
---|
| 1182 | |
---|
| 1183 | w = domain.quantities['stage'].centroid_values |
---|
| 1184 | z = domain.quantities['elevation'].centroid_values |
---|
| 1185 | h = w-z |
---|
| 1186 | |
---|
| 1187 | uh = domain.quantities['xmomentum'].centroid_values |
---|
| 1188 | #vh = domain.quantities['ymomentum'].centroid_values |
---|
| 1189 | eta = domain.quantities['friction'].centroid_values |
---|
| 1190 | |
---|
| 1191 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
---|
| 1192 | #ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
---|
| 1193 | |
---|
| 1194 | N = domain.number_of_elements |
---|
| 1195 | eps = domain.minimum_allowed_height |
---|
| 1196 | g = domain.g |
---|
| 1197 | |
---|
| 1198 | for k in range(N): |
---|
| 1199 | if eta[k] >= eps: |
---|
| 1200 | if h[k] >= eps: |
---|
| 1201 | #S = -g * eta[k]**2 * sqrt((uh[k]**2 + vh[k]**2)) |
---|
| 1202 | S = -g * eta[k]**2 * uh[k] |
---|
| 1203 | S /= h[k]**(7.0/3) |
---|
| 1204 | |
---|
| 1205 | #Update momentum |
---|
| 1206 | xmom_update[k] += S*uh[k] |
---|
| 1207 | #ymom_update[k] += S*vh[k] |
---|
| 1208 | |
---|
| 1209 | def linear_friction(domain): |
---|
| 1210 | """Apply linear friction to water momentum |
---|
| 1211 | |
---|
| 1212 | Assumes quantity: 'linear_friction' to be present |
---|
| 1213 | """ |
---|
| 1214 | |
---|
| 1215 | from math import sqrt |
---|
| 1216 | |
---|
| 1217 | w = domain.quantities['stage'].centroid_values |
---|
| 1218 | z = domain.quantities['elevation'].centroid_values |
---|
| 1219 | h = w-z |
---|
| 1220 | |
---|
| 1221 | uh = domain.quantities['xmomentum'].centroid_values |
---|
| 1222 | # vh = domain.quantities['ymomentum'].centroid_values |
---|
| 1223 | tau = domain.quantities['linear_friction'].centroid_values |
---|
| 1224 | |
---|
| 1225 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
---|
| 1226 | # ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
---|
| 1227 | |
---|
| 1228 | N = domain.number_of_elements |
---|
| 1229 | eps = domain.minimum_allowed_height |
---|
| 1230 | g = domain.g #Not necessary? Why was this added? |
---|
| 1231 | |
---|
| 1232 | for k in range(N): |
---|
| 1233 | if tau[k] >= eps: |
---|
| 1234 | if h[k] >= eps: |
---|
| 1235 | S = -tau[k]/h[k] |
---|
| 1236 | |
---|
| 1237 | #Update momentum |
---|
| 1238 | xmom_update[k] += S*uh[k] |
---|
| 1239 | # ymom_update[k] += S*vh[k] |
---|
| 1240 | |
---|
| 1241 | |
---|
| 1242 | |
---|
| 1243 | def check_forcefield(f): |
---|
| 1244 | """Check that f is either |
---|
| 1245 | 1: a callable object f(t,x,y), where x and y are vectors |
---|
| 1246 | and that it returns an array or a list of same length |
---|
| 1247 | as x and y |
---|
| 1248 | 2: a scalar |
---|
| 1249 | """ |
---|
| 1250 | |
---|
| 1251 | from Numeric import ones, Float, array |
---|
| 1252 | |
---|
| 1253 | |
---|
| 1254 | if callable(f): |
---|
| 1255 | #N = 3 |
---|
| 1256 | N = 2 |
---|
| 1257 | #x = ones(3, Float) |
---|
| 1258 | #y = ones(3, Float) |
---|
| 1259 | x = ones(2, Float) |
---|
| 1260 | #y = ones(2, Float) |
---|
| 1261 | |
---|
| 1262 | try: |
---|
| 1263 | #q = f(1.0, x=x, y=y) |
---|
| 1264 | q = f(1.0, x=x) |
---|
| 1265 | except Exception, e: |
---|
| 1266 | msg = 'Function %s could not be executed:\n%s' %(f, e) |
---|
| 1267 | #FIXME: Reconsider this semantics |
---|
| 1268 | raise msg |
---|
| 1269 | |
---|
| 1270 | try: |
---|
| 1271 | q = array(q).astype(Float) |
---|
| 1272 | except: |
---|
| 1273 | msg = 'Return value from vector function %s could ' %f |
---|
| 1274 | msg += 'not be converted into a Numeric array of floats.\n' |
---|
| 1275 | msg += 'Specified function should return either list or array.' |
---|
| 1276 | raise msg |
---|
| 1277 | |
---|
| 1278 | #Is this really what we want? |
---|
| 1279 | msg = 'Return vector from function %s ' %f |
---|
| 1280 | msg += 'must have same lenght as input vectors' |
---|
| 1281 | assert len(q) == N, msg |
---|
| 1282 | |
---|
| 1283 | else: |
---|
| 1284 | try: |
---|
| 1285 | f = float(f) |
---|
| 1286 | except: |
---|
| 1287 | msg = 'Force field %s must be either a scalar' %f |
---|
| 1288 | msg += ' or a vector function' |
---|
| 1289 | raise msg |
---|
| 1290 | return f |
---|
| 1291 | |
---|
| 1292 | class Wind_stress: |
---|
| 1293 | """Apply wind stress to water momentum in terms of |
---|
| 1294 | wind speed [m/s] and wind direction [degrees] |
---|
| 1295 | """ |
---|
| 1296 | |
---|
| 1297 | def __init__(self, *args, **kwargs): |
---|
| 1298 | """Initialise windfield from wind speed s [m/s] |
---|
| 1299 | and wind direction phi [degrees] |
---|
| 1300 | |
---|
| 1301 | Inputs v and phi can be either scalars or Python functions, e.g. |
---|
| 1302 | |
---|
| 1303 | W = Wind_stress(10, 178) |
---|
| 1304 | |
---|
| 1305 | #FIXME - 'normal' degrees are assumed for now, i.e. the |
---|
| 1306 | vector (1,0) has zero degrees. |
---|
| 1307 | We may need to convert from 'compass' degrees later on and also |
---|
| 1308 | map from True north to grid north. |
---|
| 1309 | |
---|
| 1310 | Arguments can also be Python functions of t,x,y as in |
---|
| 1311 | |
---|
| 1312 | def speed(t,x,y): |
---|
| 1313 | ... |
---|
| 1314 | return s |
---|
| 1315 | |
---|
| 1316 | def angle(t,x,y): |
---|
| 1317 | ... |
---|
| 1318 | return phi |
---|
| 1319 | |
---|
| 1320 | where x and y are vectors. |
---|
| 1321 | |
---|
| 1322 | and then pass the functions in |
---|
| 1323 | |
---|
| 1324 | W = Wind_stress(speed, angle) |
---|
| 1325 | |
---|
| 1326 | The instantiated object W can be appended to the list of |
---|
| 1327 | forcing_terms as in |
---|
| 1328 | |
---|
| 1329 | Alternatively, one vector valued function for (speed, angle) |
---|
| 1330 | can be applied, providing both quantities simultaneously. |
---|
| 1331 | As in |
---|
| 1332 | W = Wind_stress(F), where returns (speed, angle) for each t. |
---|
| 1333 | |
---|
| 1334 | domain.forcing_terms.append(W) |
---|
| 1335 | """ |
---|
| 1336 | |
---|
| 1337 | from config import rho_a, rho_w, eta_w |
---|
| 1338 | from Numeric import array, Float |
---|
| 1339 | |
---|
| 1340 | if len(args) == 2: |
---|
| 1341 | s = args[0] |
---|
| 1342 | phi = args[1] |
---|
| 1343 | elif len(args) == 1: |
---|
| 1344 | #Assume vector function returning (s, phi)(t,x,y) |
---|
| 1345 | vector_function = args[0] |
---|
| 1346 | #s = lambda t,x,y: vector_function(t,x=x,y=y)[0] |
---|
| 1347 | #phi = lambda t,x,y: vector_function(t,x=x,y=y)[1] |
---|
| 1348 | s = lambda t,x: vector_function(t,x=x)[0] |
---|
| 1349 | phi = lambda t,x: vector_function(t,x=x)[1] |
---|
| 1350 | else: |
---|
| 1351 | #Assume info is in 2 keyword arguments |
---|
| 1352 | |
---|
| 1353 | if len(kwargs) == 2: |
---|
| 1354 | s = kwargs['s'] |
---|
| 1355 | phi = kwargs['phi'] |
---|
| 1356 | else: |
---|
| 1357 | raise 'Assumes two keyword arguments: s=..., phi=....' |
---|
| 1358 | |
---|
| 1359 | print 'phi', phi |
---|
| 1360 | self.speed = check_forcefield(s) |
---|
| 1361 | self.phi = check_forcefield(phi) |
---|
| 1362 | |
---|
| 1363 | self.const = eta_w*rho_a/rho_w |
---|
| 1364 | |
---|
| 1365 | |
---|
| 1366 | def __call__(self, domain): |
---|
| 1367 | """Evaluate windfield based on values found in domain |
---|
| 1368 | """ |
---|
| 1369 | |
---|
| 1370 | from math import pi, cos, sin, sqrt |
---|
| 1371 | from Numeric import Float, ones, ArrayType |
---|
| 1372 | |
---|
| 1373 | xmom_update = domain.quantities['xmomentum'].explicit_update |
---|
| 1374 | #ymom_update = domain.quantities['ymomentum'].explicit_update |
---|
| 1375 | |
---|
| 1376 | N = domain.number_of_elements |
---|
| 1377 | t = domain.time |
---|
| 1378 | |
---|
| 1379 | if callable(self.speed): |
---|
| 1380 | xc = domain.get_centroid_coordinates() |
---|
| 1381 | #s_vec = self.speed(t, xc[:,0], xc[:,1]) |
---|
| 1382 | s_vec = self.speed(t, xc) |
---|
| 1383 | else: |
---|
| 1384 | #Assume s is a scalar |
---|
| 1385 | |
---|
| 1386 | try: |
---|
| 1387 | s_vec = self.speed * ones(N, Float) |
---|
| 1388 | except: |
---|
| 1389 | msg = 'Speed must be either callable or a scalar: %s' %self.s |
---|
| 1390 | raise msg |
---|
| 1391 | |
---|
| 1392 | |
---|
| 1393 | if callable(self.phi): |
---|
| 1394 | xc = domain.get_centroid_coordinates() |
---|
| 1395 | #phi_vec = self.phi(t, xc[:,0], xc[:,1]) |
---|
| 1396 | phi_vec = self.phi(t, xc) |
---|
| 1397 | else: |
---|
| 1398 | #Assume phi is a scalar |
---|
| 1399 | |
---|
| 1400 | try: |
---|
| 1401 | phi_vec = self.phi * ones(N, Float) |
---|
| 1402 | except: |
---|
| 1403 | msg = 'Angle must be either callable or a scalar: %s' %self.phi |
---|
| 1404 | raise msg |
---|
| 1405 | |
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| 1406 | #assign_windfield_values(xmom_update, ymom_update, |
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| 1407 | # s_vec, phi_vec, self.const) |
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| 1408 | assign_windfield_values(xmom_update, s_vec, phi_vec, self.const) |
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| 1409 | |
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| 1410 | |
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| 1411 | #def assign_windfield_values(xmom_update, ymom_update, |
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| 1412 | # s_vec, phi_vec, const): |
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| 1413 | def assign_windfield_values(xmom_update, s_vec, phi_vec, const): |
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| 1414 | """Python version of assigning wind field to update vectors. |
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| 1415 | A c version also exists (for speed) |
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| 1416 | """ |
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| 1417 | from math import pi, cos, sin, sqrt |
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| 1418 | |
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| 1419 | N = len(s_vec) |
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| 1420 | for k in range(N): |
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| 1421 | s = s_vec[k] |
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| 1422 | phi = phi_vec[k] |
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| 1423 | |
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| 1424 | #Convert to radians |
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| 1425 | phi = phi*pi/180 |
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| 1426 | |
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| 1427 | #Compute velocity vector (u, v) |
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| 1428 | u = s*cos(phi) |
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| 1429 | v = s*sin(phi) |
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| 1430 | |
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| 1431 | #Compute wind stress |
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| 1432 | #S = const * sqrt(u**2 + v**2) |
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| 1433 | S = const * u |
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| 1434 | xmom_update[k] += S*u |
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| 1435 | #ymom_update[k] += S*v |
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