[4032] | 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 | #from domain import * |
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| 46 | from domain_adjust 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 | geo_reference = None): |
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| 54 | |
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| 55 | conserved_quantities = ['stage', 'xmomentum','height'] |
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| 56 | other_quantities = ['elevation', 'friction']#, 'height'] |
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| 57 | Generic_Domain.__init__(self, coordinates, boundary, |
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| 58 | conserved_quantities, other_quantities, |
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| 59 | tagged_elements, geo_reference) |
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| 60 | |
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| 61 | from config import minimum_allowed_height, g |
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| 62 | self.minimum_allowed_height = minimum_allowed_height |
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| 63 | self.g = g |
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| 64 | |
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| 65 | #forcing terms not included in 1d domain ?WHy? |
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| 66 | self.forcing_terms.append(gravity) |
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| 67 | #self.forcing_terms.append(manning_friction) |
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| 68 | #print "\nI have Removed forcing terms line 64 1dsw" |
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| 69 | |
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| 70 | #Realtime visualisation |
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| 71 | self.visualiser = None |
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| 72 | self.visualise = False |
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| 73 | self.visualise_color_stage = False |
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| 74 | self.visualise_stage_range = 1.0 |
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| 75 | self.visualise_timer = True |
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| 76 | self.visualise_range_z = None |
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| 77 | |
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| 78 | #Stored output |
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| 79 | self.store = True |
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| 80 | self.format = 'sww' |
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| 81 | self.smooth = True |
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| 82 | |
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| 83 | #Evolve parametrs |
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| 84 | self.cfl = 1.0 |
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| 85 | |
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| 86 | #Reduction operation for get_vertex_values |
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| 87 | from util import mean |
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| 88 | self.reduction = mean |
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| 89 | #self.reduction = min #Looks better near steep slopes |
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| 90 | |
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| 91 | self.quantities_to_be_stored = ['stage','xmomentum'] |
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| 92 | |
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| 93 | |
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| 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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| 125 | def initialise_visualiser(self,scale_z=1.0,rect=None): |
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| 126 | #Realtime visualisation |
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| 127 | if self.visualiser is None: |
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| 128 | from realtime_visualisation_new import Visualiser |
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| 129 | self.visualiser = Visualiser(self,scale_z,rect) |
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| 130 | self.visualiser.setup['elevation']=True |
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| 131 | self.visualiser.updating['stage']=True |
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| 132 | self.visualise = True |
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| 133 | if self.visualise_color_stage == True: |
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| 134 | self.visualiser.coloring['stage'] = True |
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| 135 | self.visualiser.qcolor['stage'] = (0.0, 0.0, 0.8) |
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| 136 | print 'initialise visualiser' |
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| 137 | print self.visualiser.setup |
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| 138 | print self.visualiser.updating |
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| 139 | |
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| 140 | def check_integrity(self): |
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| 141 | Generic_Domain.check_integrity(self) |
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| 142 | #Check that we are solving the shallow water wave equation |
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| 143 | |
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| 144 | msg = 'First conserved quantity must be "stage"' |
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| 145 | assert self.conserved_quantities[0] == 'stage', msg |
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| 146 | msg = 'Second conserved quantity must be "xmomentum"' |
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| 147 | assert self.conserved_quantities[1] == 'xmomentum', msg |
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| 148 | |
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| 149 | def extrapolate_second_order_sw(self): |
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| 150 | #Call correct module function |
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| 151 | #(either from this module or C-extension) |
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| 152 | extrapolate_second_order_sw(self) |
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| 153 | |
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| 154 | def compute_fluxes(self): |
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| 155 | #Call correct module function |
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| 156 | #(either from this module or C-extension) |
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| 157 | compute_fluxes(self) |
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| 158 | |
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| 159 | def compute_timestep(self): |
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| 160 | #Call correct module function |
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| 161 | compute_timestep(self) |
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| 162 | |
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| 163 | def distribute_to_vertices_and_edges(self): |
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| 164 | #Call correct module function |
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| 165 | #(either from this module or C-extension) |
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| 166 | distribute_to_vertices_and_edges(self) |
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| 167 | |
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| 168 | |
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| 169 | def distribute_stage_to_height(self): |
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| 170 | #Call correct module function |
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| 171 | #(either from this module or C-extension) |
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| 172 | distribute_stage_to_height(self) |
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| 173 | |
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| 174 | |
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| 175 | def classify_wet_dry_cells(self): |
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| 176 | #Call correct module function |
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| 177 | classify_wet_dry_cells(self) |
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| 178 | |
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| 179 | def set_initial_conserved_quanitites(self): |
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| 180 | #Call correct module function |
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| 181 | set_initial_conserved_quanitites(self) |
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| 182 | |
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| 183 | |
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| 184 | def adjust_partially_submerged_cells(self): |
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| 185 | #Call correct module function |
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| 186 | adjust_partially_submerged_cells(self) |
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| 187 | |
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| 188 | def pre_update(self): |
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| 189 | #Call correct module function |
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| 190 | pre_update(self) |
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| 191 | |
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| 192 | def post_update(self): |
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| 193 | #Call correct module function |
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| 194 | post_update(self) |
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| 195 | |
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| 196 | def evolve(self, yieldstep = None, finaltime = None, |
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| 197 | skip_initial_step = False): |
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| 198 | """Specialisation of basic evolve method from parent class |
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| 199 | """ |
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| 200 | |
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| 201 | #Call check integrity here rather than from user scripts |
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| 202 | #self.check_integrity() |
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| 203 | |
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| 204 | #msg = 'Parameter beta_h must be in the interval [0, 1)' |
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| 205 | #assert 0 <= self.beta_h < 1.0, msg |
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| 206 | #msg = 'Parameter beta_w must be in the interval [0, 1)' |
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| 207 | #assert 0 <= self.beta_w < 1.0, msg |
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| 208 | |
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| 209 | |
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| 210 | #Initial update of vertex and edge values before any storage |
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| 211 | #and or visualisation |
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| 212 | |
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| 213 | print "will not work if stage not set at vertices" |
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| 214 | self.set_initial_conserved_quanitites() |
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| 215 | |
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| 216 | self.distribute_to_vertices_and_edges() |
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| 217 | |
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| 218 | self.distribute_stage_to_height() |
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| 219 | |
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| 220 | #Initialise real time viz if requested |
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| 221 | #if self.visualise is True and self.time == 0.0: |
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| 222 | # if self.visualiser is None: |
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| 223 | # self.initialise_visualiser() |
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| 224 | # |
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| 225 | # self.visualiser.update_timer() |
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| 226 | # self.visualiser.setup_all() |
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| 227 | |
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| 228 | #Store model data, e.g. for visualisation |
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| 229 | #if self.store is True and self.time == 0.0: |
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| 230 | # self.initialise_storage() |
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| 231 | # #print 'Storing results in ' + self.writer.filename |
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| 232 | #else: |
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| 233 | # pass |
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| 234 | # #print 'Results will not be stored.' |
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| 235 | # #print 'To store results set domain.store = True' |
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| 236 | # #FIXME: Diagnostic output should be controlled by |
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| 237 | # # a 'verbose' flag living in domain (or in a parent class) |
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| 238 | |
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| 239 | #Call basic machinery from parent class |
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| 240 | for t in Generic_Domain.evolve(self, yieldstep, finaltime, |
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| 241 | skip_initial_step): |
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| 242 | #Real time viz |
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| 243 | # if self.visualise is True: |
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| 244 | # self.visualiser.update_all() |
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| 245 | # self.visualiser.update_timer() |
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| 246 | |
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| 247 | |
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| 248 | #Store model data, e.g. for subsequent visualisation |
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| 249 | # if self.store is True: |
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| 250 | # self.store_timestep(self.quantities_to_be_stored) |
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| 251 | |
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| 252 | #FIXME: Could maybe be taken from specified list |
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| 253 | #of 'store every step' quantities |
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| 254 | |
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| 255 | #Pass control on to outer loop for more specific actions |
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| 256 | yield(t) |
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| 257 | |
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| 258 | def initialise_storage(self): |
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| 259 | """Create and initialise self.writer object for storing data. |
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| 260 | Also, save x and bed elevation |
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| 261 | """ |
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| 262 | |
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| 263 | import data_manager |
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| 264 | |
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| 265 | #Initialise writer |
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| 266 | self.writer = data_manager.get_dataobject(self, mode = 'w') |
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| 267 | |
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| 268 | #Store vertices and connectivity |
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| 269 | self.writer.store_connectivity() |
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| 270 | |
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| 271 | |
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| 272 | def store_timestep(self, name): |
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| 273 | """Store named quantity and time. |
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| 274 | |
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| 275 | Precondition: |
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| 276 | self.write has been initialised |
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| 277 | """ |
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| 278 | self.writer.store_timestep(name) |
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| 279 | |
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| 280 | |
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| 281 | #=============== End of Shallow Water Domain =============================== |
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| 282 | |
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| 283 | #Rotation of momentum vector |
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| 284 | def rotate(q, normal, direction = 1): |
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| 285 | """Rotate the momentum component q (q[1], q[2]) |
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| 286 | from x,y coordinates to coordinates based on normal vector. |
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| 287 | |
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| 288 | If direction is negative the rotation is inverted. |
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| 289 | |
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| 290 | Input vector is preserved |
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| 291 | |
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| 292 | This function is specific to the shallow water wave equation |
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| 293 | """ |
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| 294 | |
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| 295 | from Numeric import zeros, Float |
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| 296 | |
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| 297 | assert len(q) == 3,\ |
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| 298 | 'Vector of conserved quantities must have length 3'\ |
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| 299 | 'for 2D shallow water equation' |
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| 300 | |
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| 301 | try: |
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| 302 | l = len(normal) |
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| 303 | except: |
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| 304 | raise 'Normal vector must be an Numeric array' |
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| 305 | |
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| 306 | assert l == 2, 'Normal vector must have 2 components' |
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| 307 | |
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| 308 | |
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| 309 | n1 = normal[0] |
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| 310 | n2 = normal[1] |
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| 311 | |
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| 312 | r = zeros(len(q), Float) #Rotated quantities |
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| 313 | r[0] = q[0] #First quantity, height, is not rotated |
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| 314 | |
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| 315 | if direction == -1: |
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| 316 | n2 = -n2 |
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| 317 | |
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| 318 | |
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| 319 | r[1] = n1*q[1] + n2*q[2] |
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| 320 | r[2] = -n2*q[1] + n1*q[2] |
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| 321 | |
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| 322 | return r |
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| 323 | |
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| 324 | def flux_function(normal, ql, qr, zl, zr): |
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| 325 | """Compute fluxes between volumes for the shallow water wave equation |
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| 326 | cast in terms of w = h+z using the 'central scheme' as described in |
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| 327 | |
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| 328 | Kurganov, Noelle, Petrova. 'Semidiscrete Central-Upwind Schemes For |
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| 329 | Hyperbolic Conservation Laws and Hamilton-Jacobi Equations'. |
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| 330 | Siam J. Sci. Comput. Vol. 23, No. 3, pp. 707-740. |
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| 331 | |
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| 332 | The implemented formula is given in equation (3.15) on page 714 |
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| 333 | |
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| 334 | Conserved quantities w, uh, are stored as elements 0 and 1 |
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| 335 | in the numerical vectors ql an qr. |
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| 336 | |
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| 337 | Bed elevations zl and zr. |
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| 338 | """ |
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| 339 | |
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| 340 | from config import g, epsilon |
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| 341 | from math import sqrt |
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| 342 | from Numeric import array |
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| 343 | |
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| 344 | #print 'ql',ql |
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| 345 | #print 'qr', qr |
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| 346 | |
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| 347 | #Align momentums with x-axis |
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| 348 | #q_left = rotate(ql, normal, direction = 1) |
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| 349 | #q_right = rotate(qr, normal, direction = 1) |
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| 350 | q_left = ql |
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| 351 | q_left[1] = q_left[1]*normal |
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| 352 | q_right = qr |
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| 353 | q_right[1] = q_right[1]*normal |
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| 354 | |
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| 355 | #z = (zl+zr)/2 #Take average of field values |
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| 356 | z = 0.5*(zl+zr) #Take average of field values |
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| 357 | |
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| 358 | h_left = q_left[0] #w=h+z |
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| 359 | w_left = h_left+z |
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| 360 | uh_left = q_left[1] |
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| 361 | |
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| 362 | if h_left < epsilon: |
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| 363 | u_left = 0.0 #Could have been negative |
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| 364 | h_left = 0.0 |
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| 365 | else: |
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| 366 | u_left = uh_left/h_left |
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| 367 | |
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| 368 | |
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| 369 | h_right = q_right[0] #w=h+z |
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| 370 | w_right = h_right+z |
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| 371 | uh_right = q_right[1] |
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| 372 | |
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| 373 | |
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| 374 | if h_right < epsilon: |
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| 375 | u_right = 0.0 #Could have been negative |
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| 376 | h_right = 0.0 |
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| 377 | else: |
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| 378 | u_right = uh_right/h_right |
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| 379 | |
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| 380 | #vh_left = q_left[2] |
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| 381 | #vh_right = q_right[2] |
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| 382 | |
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| 383 | #print "uright %f ulef %f"%(u_right,u_left) |
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| 384 | |
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| 385 | soundspeed_left = sqrt(g*h_left) |
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| 386 | soundspeed_right = sqrt(g*h_right) |
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| 387 | |
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| 388 | #Maximal wave speed |
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| 389 | s_max = max(u_left+soundspeed_left, u_right+soundspeed_right, 0) |
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| 390 | |
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| 391 | #Minimal wave speed |
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| 392 | s_min = min(u_left-soundspeed_left, u_right-soundspeed_right, 0) |
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| 393 | |
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| 394 | #Flux computation |
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| 395 | |
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| 396 | #flux_left = array([u_left*h_left, |
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| 397 | # u_left*uh_left + 0.5*g*h_left**2]) |
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| 398 | #flux_right = array([u_right*h_right, |
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| 399 | # u_right*uh_right + 0.5*g*h_right**2]) |
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| 400 | flux_left = array([u_left*h_left, |
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| 401 | u_left*uh_left + 0.5*g*h_left*h_left]) |
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| 402 | flux_right = array([u_right*h_right, |
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| 403 | u_right*uh_right + 0.5*g*h_right*h_right]) |
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| 404 | |
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| 405 | denom = s_max-s_min |
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| 406 | if denom == 0.0: |
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| 407 | edgeflux = array([0.0, 0.0]) |
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| 408 | max_speed = 0.0 |
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| 409 | else: |
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| 410 | edgeflux = (s_max*flux_left - s_min*flux_right)/denom |
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| 411 | edgeflux += s_max*s_min*(q_right-q_left)/denom |
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| 412 | |
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| 413 | edgeflux[1] = edgeflux[1]*normal |
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| 414 | |
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| 415 | max_speed = max(abs(s_max), abs(s_min)) |
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| 416 | |
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| 417 | return edgeflux, max_speed |
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| 418 | |
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| 419 | |
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| 420 | def flux_function_split(normal, ql, qr, zl, zr): |
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| 421 | from config import g, epsilon |
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| 422 | from math import sqrt |
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| 423 | from Numeric import array |
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| 424 | |
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| 425 | #print 'ql',ql |
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| 426 | |
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| 427 | #Align momentums with x-axis |
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| 428 | #q_left = rotate(ql, normal, direction = 1) |
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| 429 | #q_right = rotate(qr, normal, direction = 1) |
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| 430 | q_left = ql |
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| 431 | q_left[1] = q_left[1]*normal |
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| 432 | q_right = qr |
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| 433 | q_right[1] = q_right[1]*normal |
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| 434 | |
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| 435 | #z = (zl+zr)/2 #Take average of field values |
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| 436 | z = 0.5*(zl+zr) #Take average of field values |
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| 437 | |
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| 438 | w_left = q_left[0] #w=h+z |
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| 439 | h_left = w_left-z |
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| 440 | uh_left = q_left[1] |
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| 441 | |
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| 442 | if h_left < epsilon: |
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| 443 | u_left = 0.0 #Could have been negative |
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| 444 | h_left = 0.0 |
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| 445 | else: |
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| 446 | u_left = uh_left/h_left |
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| 447 | |
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| 448 | |
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| 449 | w_right = q_right[0] #w=h+z |
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| 450 | h_right = w_right-z |
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| 451 | uh_right = q_right[1] |
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| 452 | |
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| 453 | |
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| 454 | if h_right < epsilon: |
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| 455 | u_right = 0.0 #Could have been negative |
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| 456 | h_right = 0.0 |
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| 457 | else: |
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| 458 | u_right = uh_right/h_right |
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| 459 | |
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| 460 | #vh_left = q_left[2] |
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| 461 | #vh_right = q_right[2] |
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| 462 | |
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| 463 | #soundspeed_left = sqrt(g*h_left) |
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| 464 | #soundspeed_right = sqrt(g*h_right) |
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| 465 | |
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| 466 | #Maximal wave speed |
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| 467 | #s_max = max(u_left+soundspeed_left, u_right+soundspeed_right, 0) |
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| 468 | s_max = max(u_left, u_right, 0) |
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| 469 | |
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| 470 | #Minimal wave speed |
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| 471 | #s_min = min(u_left-soundspeed_left, u_right-soundspeed_right, 0) |
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| 472 | s_min = min(u_left, u_right, 0) |
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| 473 | |
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| 474 | #Flux computation |
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| 475 | |
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| 476 | #flux_left = array([u_left*h_left, |
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| 477 | # u_left*uh_left + 0.5*g*h_left*h_left]) |
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| 478 | #flux_right = array([u_right*h_right, |
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| 479 | # u_right*uh_right + 0.5*g*h_right*h_right]) |
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| 480 | flux_left = array([u_left*h_left, |
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| 481 | u_left*uh_left])# + 0.5*g*h_left*h_left]) |
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| 482 | flux_right = array([u_right*h_right, |
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| 483 | u_right*uh_right])# + 0.5*g*h_right*h_right]) |
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| 484 | |
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| 485 | denom = s_max-s_min |
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| 486 | if denom == 0.0: |
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| 487 | edgeflux = array([0.0, 0.0]) |
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| 488 | max_speed = 0.0 |
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| 489 | else: |
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| 490 | edgeflux = (s_max*flux_left - s_min*flux_right)/denom |
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| 491 | edgeflux += s_max*s_min*(q_right-q_left)/denom |
---|
| 492 | |
---|
| 493 | edgeflux[1] = edgeflux[1]*normal |
---|
| 494 | |
---|
| 495 | max_speed = max(abs(s_max), abs(s_min)) |
---|
| 496 | |
---|
| 497 | return edgeflux, max_speed |
---|
| 498 | |
---|
| 499 | def compute_timestep(domain): |
---|
| 500 | import sys |
---|
| 501 | from Numeric import zeros, Float |
---|
| 502 | |
---|
| 503 | N = domain.number_of_elements |
---|
| 504 | |
---|
| 505 | #Shortcuts |
---|
| 506 | Stage = domain.quantities['stage'] |
---|
| 507 | Xmom = domain.quantities['xmomentum'] |
---|
| 508 | Bed = domain.quantities['elevation'] |
---|
| 509 | |
---|
| 510 | stage = Stage.vertex_values |
---|
| 511 | xmom = Xmom.vertex_values |
---|
| 512 | bed = Bed.vertex_values |
---|
| 513 | |
---|
| 514 | stage_bdry = Stage.boundary_values |
---|
| 515 | xmom_bdry = Xmom.boundary_values |
---|
| 516 | |
---|
| 517 | flux = zeros(2, Float) #Work array for summing up fluxes |
---|
| 518 | ql = zeros(2, Float) |
---|
| 519 | qr = zeros(2, Float) |
---|
| 520 | |
---|
| 521 | #Loop |
---|
| 522 | timestep = float(sys.maxint) |
---|
| 523 | enter = True |
---|
| 524 | for k in range(N): |
---|
| 525 | |
---|
| 526 | flux[:] = 0. #Reset work array |
---|
| 527 | for i in range(2): |
---|
| 528 | #Quantities inside volume facing neighbour i |
---|
| 529 | ql = [stage[k, i], xmom[k, i]] |
---|
| 530 | zl = bed[k, i] |
---|
| 531 | |
---|
| 532 | #Quantities at neighbour on nearest face |
---|
| 533 | n = domain.neighbours[k,i] |
---|
| 534 | if n < 0: |
---|
| 535 | m = -n-1 #Convert negative flag to index |
---|
| 536 | qr[0] = stage_bdry[m] |
---|
| 537 | qr[1] = xmom_bdry[m] |
---|
| 538 | zr = zl #Extend bed elevation to boundary |
---|
| 539 | else: |
---|
| 540 | #m = domain.neighbour_edges[k,i] |
---|
| 541 | m = domain.neighbour_vertices[k,i] |
---|
| 542 | qr[0] = stage[n, m] |
---|
| 543 | qr[1] = xmom[n, m] |
---|
| 544 | zr = bed[n, m] |
---|
| 545 | |
---|
| 546 | |
---|
| 547 | #Outward pointing normal vector |
---|
| 548 | normal = domain.normals[k, i] |
---|
| 549 | |
---|
| 550 | if domain.split == False: |
---|
| 551 | edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
---|
| 552 | elif domain.split == True: |
---|
| 553 | edgeflux, max_speed = flux_function_split(normal, ql, qr, zl, zr) |
---|
| 554 | #Update optimal_timestep |
---|
| 555 | try: |
---|
| 556 | timestep = min(timestep, domain.cfl*0.5*domain.areas[k]/max_speed) |
---|
| 557 | except ZeroDivisionError: |
---|
| 558 | pass |
---|
| 559 | |
---|
| 560 | domain.timestep = timestep |
---|
| 561 | |
---|
| 562 | def compute_fluxes(domain): |
---|
| 563 | """Compute all fluxes and the timestep suitable for all volumes |
---|
| 564 | in domain. |
---|
| 565 | |
---|
| 566 | Compute total flux for each conserved quantity using "flux_function" |
---|
| 567 | |
---|
| 568 | Fluxes across each edge are scaled by edgelengths and summed up |
---|
| 569 | Resulting flux is then scaled by area and stored in |
---|
| 570 | explicit_update for each of the three conserved quantities |
---|
| 571 | stage, xmomentum and ymomentum |
---|
| 572 | |
---|
| 573 | The maximal allowable speed computed by the flux_function for each volume |
---|
| 574 | is converted to a timestep that must not be exceeded. The minimum of |
---|
| 575 | those is computed as the next overall timestep. |
---|
| 576 | |
---|
| 577 | Post conditions: |
---|
| 578 | domain.explicit_update is reset to computed flux values |
---|
| 579 | domain.timestep is set to the largest step satisfying all volumes. |
---|
| 580 | """ |
---|
| 581 | |
---|
| 582 | #print "in compute_fluxes" |
---|
| 583 | |
---|
| 584 | import sys |
---|
| 585 | from Numeric import zeros, Float |
---|
| 586 | |
---|
| 587 | N = domain.number_of_elements |
---|
| 588 | |
---|
| 589 | #Shortcuts |
---|
| 590 | #Stage = domain.quantities['stage'] |
---|
| 591 | Height = domain.quantities['height'] |
---|
| 592 | Xmom = domain.quantities['xmomentum'] |
---|
| 593 | # Ymom = domain.quantities['ymomentum'] |
---|
| 594 | Bed = domain.quantities['elevation'] |
---|
| 595 | |
---|
| 596 | #Arrays |
---|
| 597 | #stage = Stage.edge_values |
---|
| 598 | #xmom = Xmom.edge_values |
---|
| 599 | # ymom = Ymom.edge_values |
---|
| 600 | #bed = Bed.edge_values |
---|
| 601 | |
---|
| 602 | #stage = Stage.vertex_values |
---|
| 603 | height = Height.vertex_values |
---|
| 604 | xmom = Xmom.vertex_values |
---|
| 605 | bed = Bed.vertex_values |
---|
| 606 | |
---|
| 607 | #print 'stage edge values', stage |
---|
| 608 | #print 'xmom edge values', xmom |
---|
| 609 | #print 'bed values', bed |
---|
| 610 | |
---|
| 611 | #stage_bdry = Stage.boundary_values |
---|
| 612 | height_bdry = Height.boundary_values |
---|
| 613 | xmom_bdry = Xmom.boundary_values |
---|
| 614 | #print 'stage_bdry',stage_bdry |
---|
| 615 | #print 'xmom_bdry', xmom_bdry |
---|
| 616 | # ymom_bdry = Ymom.boundary_values |
---|
| 617 | |
---|
| 618 | # flux = zeros(3, Float) #Work array for summing up fluxes |
---|
| 619 | flux = zeros(2, Float) #Work array for summing up fluxes |
---|
| 620 | ql = zeros(2, Float) |
---|
| 621 | qr = zeros(2, Float) |
---|
| 622 | |
---|
| 623 | #Loop |
---|
| 624 | timestep = float(sys.maxint) |
---|
| 625 | enter = True |
---|
| 626 | for k in range(N): |
---|
| 627 | |
---|
| 628 | flux[:] = 0. #Reset work array |
---|
| 629 | #for i in range(3): |
---|
| 630 | for i in range(2): |
---|
| 631 | #Quantities inside volume facing neighbour i |
---|
| 632 | #ql = [stage[k, i], xmom[k, i]] |
---|
| 633 | ql = [height[k, i], xmom[k, i]] |
---|
| 634 | zl = bed[k, i] |
---|
| 635 | #print "cell",k,"left state",ql[0] |
---|
| 636 | |
---|
| 637 | #Quantities at neighbour on nearest face |
---|
| 638 | n = domain.neighbours[k,i] |
---|
| 639 | if n < 0: |
---|
| 640 | m = -n-1 #Convert negative flag to index |
---|
| 641 | #qr[0] = stage_bdry[m] |
---|
| 642 | qr[0] = height_bdry[m] |
---|
| 643 | qr[1] = xmom_bdry[m] |
---|
| 644 | zr = zl #Extend bed elevation to boundary |
---|
| 645 | else: |
---|
| 646 | #m = domain.neighbour_edges[k,i] |
---|
| 647 | m = domain.neighbour_vertices[k,i] |
---|
| 648 | #qr = [stage[n, m], xmom[n, m], ymom[n, m]] |
---|
| 649 | #qr[0] = stage[n, m] |
---|
| 650 | qr[0] = height[n, m] |
---|
| 651 | qr[1] = xmom[n, m] |
---|
| 652 | zr = bed[n, m] |
---|
| 653 | #print "cell",k,"right state",qr[0] |
---|
| 654 | |
---|
| 655 | |
---|
| 656 | #Outward pointing normal vector |
---|
| 657 | normal = domain.normals[k, i] |
---|
| 658 | |
---|
| 659 | #Flux computation using provided function |
---|
| 660 | #edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
---|
| 661 | #print 'ql',ql |
---|
| 662 | #print 'qr',qr |
---|
| 663 | |
---|
| 664 | |
---|
| 665 | if domain.split == False: |
---|
| 666 | edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
---|
| 667 | #print edgeflux |
---|
| 668 | elif domain.split == True: |
---|
| 669 | edgeflux, max_speed = flux_function_split(normal, ql, qr, zl, zr) |
---|
| 670 | #print 'edgeflux', edgeflux |
---|
| 671 | |
---|
| 672 | # THIS IS THE LINE TO DEAL WITH LEFT AND RIGHT FLUXES |
---|
| 673 | # flux = edgefluxleft - edgefluxright |
---|
| 674 | flux -= edgeflux #* domain.edgelengths[k,i] |
---|
| 675 | |
---|
| 676 | #Update optimal_timestep |
---|
| 677 | try: |
---|
| 678 | #timestep = min(timestep, 0.5*domain.radii[k]/max_speed) |
---|
| 679 | timestep = min(timestep, domain.cfl*0.5*domain.areas[k]/max_speed) |
---|
| 680 | #print "cell %d wet length %f"%(k,domain.areas[k]) |
---|
| 681 | #print "timestep %f max speed %f hl %f uhl %f hr %f uhr %f" %(timestep,max_speed,ql[0],ql[1],qr[0],qr[1]) |
---|
| 682 | except ZeroDivisionError: |
---|
| 683 | pass |
---|
| 684 | |
---|
| 685 | #Normalise by area and store for when all conserved |
---|
| 686 | #quantities get updated |
---|
| 687 | flux /= domain.areas[k] |
---|
| 688 | |
---|
| 689 | #try: |
---|
| 690 | # #if flux[0] > 1.0e-6: unecessary because only min is taken |
---|
| 691 | # if Height.centroid_values[k] > 1.0e-3: |
---|
| 692 | # timestep = min(timestep, domain.cfl*0.5*Height.centroid_values[k]*domain.areas[k]/abs(flux[0])) |
---|
| 693 | #except ZeroDivisionError: |
---|
| 694 | # pass |
---|
| 695 | |
---|
| 696 | |
---|
| 697 | |
---|
| 698 | #Stage.explicit_update[k] = flux[0] |
---|
| 699 | Height.explicit_update[k] = flux[0] |
---|
| 700 | Xmom.explicit_update[k] = flux[1] |
---|
| 701 | #Ymom.explicit_update[k] = flux[2] |
---|
| 702 | |
---|
| 703 | |
---|
| 704 | domain.timestep = timestep |
---|
| 705 | #print "flux" |
---|
| 706 | #print Height.explicit_update |
---|
| 707 | |
---|
| 708 | #print "integral %f"%domain.quantities['height'].get_integral() |
---|
| 709 | |
---|
| 710 | #################################### |
---|
| 711 | |
---|
| 712 | # Module functions for gradient limiting (distribute_to_vertices_and_edges) |
---|
| 713 | |
---|
| 714 | def distribute_to_vertices_and_edges(domain): |
---|
| 715 | """Distribution from centroids to vertices specific to the |
---|
| 716 | shallow water wave |
---|
| 717 | equation. |
---|
| 718 | |
---|
| 719 | It will ensure that h (w-z) is always non-negative even in the |
---|
| 720 | presence of steep bed-slopes by taking a weighted average between shallow |
---|
| 721 | and deep cases. |
---|
| 722 | |
---|
| 723 | In addition, all conserved quantities get distributed as per either a |
---|
| 724 | constant (order==1) or a piecewise linear function (order==2). |
---|
| 725 | |
---|
| 726 | FIXME: more explanation about removal of artificial variability etc |
---|
| 727 | |
---|
| 728 | Precondition: |
---|
| 729 | All quantities defined at centroids and bed elevation defined at |
---|
| 730 | vertices. |
---|
| 731 | |
---|
| 732 | Postcondition |
---|
| 733 | Conserved quantities defined at vertices |
---|
| 734 | |
---|
| 735 | """ |
---|
| 736 | |
---|
| 737 | #print "in distribute to vertices and edges" |
---|
| 738 | #print "integral %f"%domain.quantities['height'].get_integral() |
---|
| 739 | |
---|
| 740 | #from config import optimised_gradient_limiter |
---|
| 741 | |
---|
| 742 | #Remove very thin layers of water |
---|
| 743 | #protect_against_infinitesimal_and_negative_heights(domain) |
---|
| 744 | |
---|
| 745 | #classify_wet_dry_cells(domain) |
---|
| 746 | #import copy |
---|
| 747 | #print domain.wet_nodes |
---|
| 748 | #StageQ = copy.copy(domain.quantities['stage'].centroid_values) |
---|
| 749 | #adjust_partially_submerged_cells(domain) |
---|
| 750 | #StageQ2 = domain.quantities['stage'].centroid_values |
---|
| 751 | #print StageQ-StageQ2 |
---|
| 752 | |
---|
| 753 | #Extrapolate all conserved quantities |
---|
| 754 | #if optimised_gradient_limiter: |
---|
| 755 | # #MH090605 if second order, |
---|
| 756 | # #perform the extrapolation and limiting on |
---|
| 757 | # #all of the conserved quantities |
---|
| 758 | |
---|
| 759 | # if (domain.order == 1): |
---|
| 760 | # for name in domain.conserved_quantities: |
---|
| 761 | # Q = domain.quantities[name] |
---|
| 762 | # Q.extrapolate_first_order() |
---|
| 763 | # elif domain.order == 2: |
---|
| 764 | # domain.extrapolate_second_order_sw() |
---|
| 765 | # else: |
---|
| 766 | # raise 'Unknown order' |
---|
| 767 | #else: |
---|
| 768 | #old code: |
---|
| 769 | |
---|
| 770 | for name in domain.conserved_quantities: |
---|
| 771 | Q = domain.quantities[name] |
---|
| 772 | if domain.order == 1: |
---|
| 773 | Q.extrapolate_first_order() |
---|
| 774 | elif domain.order == 2: |
---|
| 775 | #print "add extrapolate second order to shallow water" |
---|
| 776 | if (name != 'height'):#& (name != "xmomentum"): |
---|
| 777 | Q.extrapolate_second_order() |
---|
| 778 | #Q.limit() |
---|
| 779 | else: |
---|
| 780 | raise 'Unknown order' |
---|
| 781 | |
---|
| 782 | #Take bed elevation into account when water heights are small |
---|
| 783 | #balance_deep_and_shallow(domain) |
---|
| 784 | protect_dry_beds(domain) |
---|
| 785 | |
---|
| 786 | #Compute edge values by interpolation |
---|
| 787 | #for name in domain.conserved_quantities: |
---|
| 788 | # Q = domain.quantities[name] |
---|
| 789 | # Q.interpolate_from_vertices_to_edges() |
---|
| 790 | |
---|
| 791 | #print domain.quantities['stage'].centroid_values |
---|
| 792 | |
---|
| 793 | def protect_dry_beds(domain): |
---|
| 794 | #print "in protect dry beds" |
---|
| 795 | #print "integral %f"%domain.quantities['height'].get_integral() |
---|
| 796 | |
---|
| 797 | N = domain.number_of_elements |
---|
| 798 | wc = domain.quantities['stage'].centroid_values |
---|
| 799 | zc = domain.quantities['elevation'].centroid_values |
---|
| 800 | hc = domain.quantities['height'].centroid_values |
---|
| 801 | wv = domain.quantities['stage'].vertex_values |
---|
| 802 | zv = domain.quantities['elevation'].vertex_values |
---|
| 803 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
| 804 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
| 805 | min_centroid_height = 1e-3 |
---|
| 806 | |
---|
| 807 | for k in range(N): |
---|
| 808 | if hc[k] < domain.minimum_allowed_height: |
---|
| 809 | if hc[k] < domain.epsilon: |
---|
| 810 | wc[k] = zc[k] |
---|
| 811 | wv[k,0] = zv[k,0] |
---|
| 812 | wv[k,1] = zv[k,1] |
---|
| 813 | xmomc[k] = 0.0 |
---|
| 814 | xmomv[k,:] = 0.0 |
---|
| 815 | |
---|
| 816 | |
---|
| 817 | def set_initial_conserved_quanitites(domain): |
---|
| 818 | from util import calculate_new_wet_area, calculate_wetted_area |
---|
| 819 | from Numeric import allclose |
---|
| 820 | |
---|
| 821 | N = domain.number_of_elements |
---|
| 822 | wv = domain.quantities['stage'].vertex_values |
---|
| 823 | zv = domain.quantities['elevation'].vertex_values |
---|
| 824 | xv = domain.vertices |
---|
| 825 | zc = domain.quantities['elevation'].centroid_values |
---|
| 826 | wc = domain.quantities['stage'].centroid_values |
---|
| 827 | hc = domain.quantities['height'].centroid_values |
---|
| 828 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
| 829 | |
---|
| 830 | #A1 = domain.quantities['stage'].get_integral() |
---|
| 831 | for k in range(N): |
---|
| 832 | if hc[k] < 0.0: |
---|
| 833 | print "ERROR!!!!!!!!!!!!!!!!!!" |
---|
| 834 | #if (domain.wet_nodes[k,0] == 0) | (domain.wet_nodes[k,1] == 0): |
---|
| 835 | if (wv[k,0] < zv[k,0]) | (wv[k,1] < zv[k,1]): |
---|
| 836 | # cell is dry or wetted |
---|
| 837 | #print "cell %d is wetted or dry"%k |
---|
| 838 | w1 = wv[k,0] |
---|
| 839 | w2 = wv[k,1] |
---|
| 840 | z1 = zv[k,0] |
---|
| 841 | z2 = zv[k,1] |
---|
| 842 | x1 = xv[k,0] |
---|
| 843 | x2 = xv[k,1] |
---|
| 844 | #print w1,w2 |
---|
| 845 | A = calculate_wetted_area(x1,x2,z1,z2,w1,w2) |
---|
| 846 | L = x2-x1 |
---|
| 847 | w_centroid, wet_len = calculate_new_wet_area(x1,x2,z1,z2,A) |
---|
| 848 | #print "cell",k,"stage",w1,w2 |
---|
| 849 | #print A |
---|
| 850 | if A > 0.0: |
---|
| 851 | wc[k] = w_centroid # surface is flat in wetted bed |
---|
| 852 | #wv[k,0] = w1 |
---|
| 853 | #wv[k,1] = w2 |
---|
| 854 | domain.wet_nodes[k,0] = 2 # stops limiter from limiting these cells |
---|
| 855 | domain.wet_nodes[k,1] = 2 |
---|
| 856 | hc[k] = A/L |
---|
| 857 | # print "hc %f" %hc[k] |
---|
| 858 | #xmomc[k] = 0.0 |
---|
| 859 | #print "cell",k,"stage",wc[k],hc[k],wet_len |
---|
| 860 | #if wet_len > 0.0: |
---|
| 861 | #domain.areas[k] = wet_len |
---|
| 862 | else: |
---|
| 863 | #print "cell %d is not wetted but dry"%k |
---|
| 864 | wc[k] = 0.5*(w1+w2) # bed is completely dry |
---|
| 865 | wv[k,0] = zv[k,0] |
---|
| 866 | wv[k,1] = zv[k,1] |
---|
| 867 | domain.wet_nodes[k,0] = 0 |
---|
| 868 | domain.wet_nodes[k,1] = 0 |
---|
| 869 | hc[k] = 0.0 |
---|
| 870 | else: |
---|
| 871 | #print "cell",k,"is wet" |
---|
| 872 | hc[k] = wc[k]-zc[k] |
---|
| 873 | |
---|
| 874 | #A2 = domain.quantities['stage'].get_integral() |
---|
| 875 | #assert allclose(A1,A2) |
---|
| 876 | print "Must set initial conditions for momentum as well in set_initial_conserved_quanitites and adjust" |
---|
| 877 | #print hc |
---|
| 878 | |
---|
| 879 | |
---|
| 880 | def adjust_partially_submerged_cells(domain): |
---|
| 881 | #normal# |
---|
| 882 | #print "in adjust wetted_cells" |
---|
| 883 | #print "integral %f"%domain.quantities['height'].get_integral() |
---|
| 884 | |
---|
| 885 | from util import calculate_new_wet_area, analytic_cannal |
---|
| 886 | min_centroid_height = 1.0e-3 |
---|
| 887 | N = domain.number_of_elements |
---|
| 888 | wv = domain.quantities['stage'].vertex_values |
---|
| 889 | zv = domain.quantities['elevation'].vertex_values |
---|
| 890 | xv = domain.vertices |
---|
| 891 | xc = domain.centroids |
---|
| 892 | zc = domain.quantities['elevation'].centroid_values |
---|
| 893 | wc = domain.quantities['stage'].centroid_values |
---|
| 894 | hc = domain.quantities['height'].centroid_values |
---|
| 895 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
| 896 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
| 897 | |
---|
| 898 | domain.wet_nodes[:,:] = 0.0 |
---|
| 899 | |
---|
| 900 | #print hc |
---|
| 901 | |
---|
| 902 | for k in range(N): |
---|
| 903 | domain.areas[k] = xv[k,1]-xv[k,0] |
---|
| 904 | |
---|
| 905 | if hc[k] <= domain.epsilon: |
---|
| 906 | if hc[k] < 0.0: |
---|
| 907 | if hc[k+1] > domain.epsilon: |
---|
| 908 | hc[k+1] += hc[k] |
---|
| 909 | else: #hc[k-1] > domain.epsilon: |
---|
| 910 | hc[k-1] += hc[k] |
---|
| 911 | |
---|
| 912 | hc[k] = 0.0 # if this not here get negative heights means timesteping wrong |
---|
| 913 | wc[k] = zc[k] |
---|
| 914 | xmomc[k] = 0.0 |
---|
| 915 | xmomv[k,0] = 0.0 |
---|
| 916 | xmomv[k,1] = 0.0 |
---|
| 917 | else: #hc[k] > domain.epsilon: #min_centroid_height: |
---|
| 918 | z1 = zv[k,0] |
---|
| 919 | z2 = zv[k,1] |
---|
| 920 | x1 = xv[k,0] |
---|
| 921 | x2 = xv[k,1] |
---|
| 922 | L = x2-x1 |
---|
| 923 | A = hc[k]*L |
---|
| 924 | if A > 0.0: |
---|
| 925 | w_centroid, wet_len = calculate_new_wet_area(x1,x2,z1,z2,A) |
---|
| 926 | if (w_centroid > max(z1,z2)): |
---|
| 927 | wc[k] = w_centroid |
---|
| 928 | #xmomc[k] = 0.5*(uh1+uh2) |
---|
| 929 | #xmomv[k,0] = uh1 |
---|
| 930 | #xmomv[k,1] = uh2 # sets xmom to be analytic everwhere |
---|
| 931 | |
---|
| 932 | elif (w_centroid > min(z1,z2)): |
---|
| 933 | wc[k] = w_centroid # surface is flat in wetted bed |
---|
| 934 | #wv[k,0] = w1 |
---|
| 935 | #wv[k,1] = w2 # this is done by slope limiter |
---|
| 936 | domain.wet_nodes[k,0] = 2 # stops limiter from limiting these cells |
---|
| 937 | domain.wet_nodes[k,1] = 2 |
---|
| 938 | #print "cell",k, hc[k], A,L, w1,w2 |
---|
| 939 | wcrap,uhc = analytic_cannal(xc[k],domain.time+domain.timestep) |
---|
| 940 | w1,uh1 = analytic_cannal(x1,domain.time+domain.timestep) |
---|
| 941 | w2,uh2 = analytic_cannal(x2,domain.time+domain.timestep) |
---|
| 942 | |
---|
| 943 | if (w_centroid > z1): |
---|
| 944 | #w1,uh1 = analytic_cannal(xc[k-1],domain.time+domain.timestep) |
---|
| 945 | #xmomv[k,0] = uh1 |
---|
| 946 | xmomv[k,0] = 0.0 |
---|
| 947 | xmomv[k,1] = 0.0 |
---|
| 948 | #xmomc[k] = uh1 |
---|
| 949 | xmomc[k] = 0.0 |
---|
| 950 | |
---|
| 951 | else: |
---|
| 952 | #w2,uh2 = analytic_cannal(xc[k+1],domain.time+domain.timestep) |
---|
| 953 | xmomv[k,0] = 0.0 |
---|
| 954 | xmomv[k,1] = 0.0 |
---|
| 955 | #xmomv[k,1] = uh2 |
---|
| 956 | #xmomc[k] = uh2 |
---|
| 957 | xmomc[k] = 0.0 |
---|
| 958 | else: |
---|
| 959 | wc[k] = zc[k] # bed is completely dry |
---|
| 960 | domain.wet_nodes[k,0] = 0 |
---|
| 961 | domain.wet_nodes[k,1] = 0 |
---|
| 962 | hc[k] = 0.0 |
---|
| 963 | xmomc[k] = 0.0 |
---|
| 964 | xmomv[k,0] = 0.0 |
---|
| 965 | xmomv[k,1] = 0.0 |
---|
| 966 | #if wet_len > 0.0: |
---|
| 967 | #domain.areas[k] = wet_len |
---|
| 968 | # if wet_len is 0 then bed is flat and area = x2-x1 (as default) |
---|
| 969 | else: |
---|
| 970 | wc[k] = zc[k] # bed is completely dry |
---|
| 971 | domain.wet_nodes[k,0] = 0 |
---|
| 972 | domain.wet_nodes[k,1] = 0 |
---|
| 973 | hc[k] = 0.0 |
---|
| 974 | xmomc[k] = 0.0 |
---|
| 975 | xmomv[k,0] = 0.0 |
---|
| 976 | xmomv[k,1] = 0.0 |
---|
| 977 | |
---|
| 978 | #for k in range(N): |
---|
| 979 | # |
---|
| 980 | # wcrap,uhc = analytic_cannal(xc[int(N/2)],domain.time+domain.timestep) |
---|
| 981 | # if (k > 1) & (k<N-2): |
---|
| 982 | # if (wc[k-2] < max(zv[k-2,0],zv[k-2,1])) & (wc[k-2] > min(zv[k-2,0],zv[k-2,1])) & (hc[k+1] < domain.epsilon): |
---|
| 983 | # #print "TRUE" |
---|
| 984 | # xmomc[k] = uhc |
---|
| 985 | # if (wc[k+2] < max(zv[k+2,0],zv[k+2,1])) & (wc[k+2] > min(zv[k+2,0],zv[k+2,1])) & (hc[k-1] < domain.epsilon): |
---|
| 986 | # #print "FALSE" |
---|
| 987 | # xmomc[k] = uhc |
---|
| 988 | |
---|
| 989 | |
---|
| 990 | #print "integral %f"%domain.quantities['height'].get_integral() |
---|
| 991 | #print domain.quantities['height'].centroid_values |
---|
| 992 | |
---|
| 993 | def adjust_partially_submerged_cells_analytic(domain): |
---|
| 994 | #analytic# |
---|
| 995 | |
---|
| 996 | #print "in adjust wetted_cells" |
---|
| 997 | from util import calculate_new_wet_area_analytic |
---|
| 998 | min_centroid_height = 1.0e-3 |
---|
| 999 | N = domain.number_of_elements |
---|
| 1000 | wv = domain.quantities['stage'].vertex_values |
---|
| 1001 | zv = domain.quantities['elevation'].vertex_values |
---|
| 1002 | xv = domain.vertices |
---|
| 1003 | zc = domain.quantities['elevation'].centroid_values |
---|
| 1004 | wc = domain.quantities['stage'].centroid_values |
---|
| 1005 | hc = domain.quantities['height'].centroid_values |
---|
| 1006 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
| 1007 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
| 1008 | |
---|
| 1009 | domain.wet_nodes[:,:] = 0.0 |
---|
| 1010 | |
---|
| 1011 | #print hc |
---|
| 1012 | |
---|
| 1013 | for k in range(N): |
---|
| 1014 | domain.areas[k] = xv[k,1]-xv[k,0] |
---|
| 1015 | if hc[k] > domain.epsilon:#min_centroid_height: |
---|
| 1016 | z1 = zv[k,0] |
---|
| 1017 | z2 = zv[k,1] |
---|
| 1018 | x1 = xv[k,0] |
---|
| 1019 | x2 = xv[k,1] |
---|
| 1020 | L = x2-x1 |
---|
| 1021 | A = hc[k]*L |
---|
| 1022 | if A > 0.0: |
---|
| 1023 | #print "cell %d is wetted" %k |
---|
| 1024 | #print "time: %f -- is 1 sec behind real time in adjust. i.e. time has not been updated"%domain.time |
---|
| 1025 | w1,w2, wet_len,uh1,uh2 = calculate_new_wet_area_analytic(x1,x2,z1,z2,A,domain.time+1.0) |
---|
| 1026 | xmomc[k] = 0.5*(uh1+uh2) |
---|
| 1027 | xmomv[k,0] = uh1 |
---|
| 1028 | xmomv[k,1] = uh2 |
---|
| 1029 | if (w1 > z1) & (w2 > z2): |
---|
| 1030 | #wc[k] = (w1+w2)*0.5 |
---|
| 1031 | #wv[k,0] = w1 |
---|
| 1032 | #wv[k,1] = w2 |
---|
| 1033 | wc[k] = zc[k]+hc[k] |
---|
| 1034 | xmomv[k,0] = uh1 |
---|
| 1035 | xmomv[k,1] = uh2 |
---|
| 1036 | xmomc[k] = 0.5*(uh1+uh2) |
---|
| 1037 | #print w1,w2 |
---|
| 1038 | elif (w1 > min(z1,z2)) | (w2 > min(z1,z2)): |
---|
| 1039 | wc[k] = 0.5*(w1+w2) |
---|
| 1040 | wv[k,0] = w1 |
---|
| 1041 | wv[k,1] = w2 |
---|
| 1042 | #print "cell %d w1 %f w2 %f" %(k,w1,w2) |
---|
| 1043 | # stops limiter from limiting these cells |
---|
| 1044 | domain.wet_nodes[k,0] = 2 |
---|
| 1045 | domain.wet_nodes[k,1] = 2 |
---|
| 1046 | if (w1 > z1): |
---|
| 1047 | xmomv[k,0] = uh1 |
---|
| 1048 | xmomv[k,1] = 0.0 |
---|
| 1049 | else: |
---|
| 1050 | xmomv[k,0] = 0.0 |
---|
| 1051 | xmomv[k,1] = uh2 |
---|
| 1052 | else: |
---|
| 1053 | wc[k] = zc[k] # bed is completely dry |
---|
| 1054 | domain.wet_nodes[k,0] = 0 |
---|
| 1055 | domain.wet_nodes[k,1] = 0 |
---|
| 1056 | hc[k] = 0.0 |
---|
| 1057 | xmomc[k] = 0.0 |
---|
| 1058 | if wet_len > 0.0: |
---|
| 1059 | domain.areas[k] = wet_len |
---|
| 1060 | #print w1,w2 |
---|
| 1061 | #print "cell %d wet length %f"%(k,wet_len) |
---|
| 1062 | # if wet_len is 0 then bed is flat and area = x2-x1 (as default) |
---|
| 1063 | else: |
---|
| 1064 | wc[k] = zc[k] # bed is completely dry |
---|
| 1065 | domain.wet_nodes[k,0] = 0 |
---|
| 1066 | domain.wet_nodes[k,1] = 0 |
---|
| 1067 | hc[k] = 0.0 |
---|
| 1068 | #xmomc[k] = 0.0 |
---|
| 1069 | else: |
---|
| 1070 | wc[k] = zc[k] |
---|
| 1071 | xmomc[k] = 0.0 |
---|
| 1072 | |
---|
| 1073 | |
---|
| 1074 | def distribute_stage_to_height(domain): |
---|
| 1075 | |
---|
| 1076 | #print "in distribute stage to height" |
---|
| 1077 | #print "integral %f"%domain.quantities['height'].get_integral() |
---|
| 1078 | |
---|
| 1079 | #print "hv1",domain.quantities['height'].vertex_values |
---|
| 1080 | #print "hc1",domain.quantities['height'].centroid_values |
---|
| 1081 | |
---|
| 1082 | min_centroid_height = 1.0e-3 |
---|
| 1083 | N = domain.number_of_elements |
---|
| 1084 | wv = domain.quantities['stage'].vertex_values |
---|
| 1085 | zv = domain.quantities['elevation'].vertex_values |
---|
| 1086 | hv = domain.quantities['height'].vertex_values |
---|
| 1087 | hc = domain.quantities['height'].centroid_values |
---|
| 1088 | for k in range(N): |
---|
| 1089 | for i in range(2): |
---|
| 1090 | if hc[k] > domain.epsilon: |
---|
| 1091 | hv[k,i] = wv[k,i]-zv[k,i] |
---|
| 1092 | elif hc[k] < 0: |
---|
| 1093 | print "ERROR" |
---|
| 1094 | else: |
---|
| 1095 | hv[k,i] = 0.0 |
---|
| 1096 | |
---|
| 1097 | #print "hv2",domain.quantities['height'].vertex_values |
---|
| 1098 | #print "hc2",domain.quantities['height'].centroid_values |
---|
| 1099 | #print "integral %f"%domain.quantities['height'].get_integral() |
---|
| 1100 | |
---|
| 1101 | def protect_against_infinitesimal_and_negative_heights(domain): |
---|
| 1102 | """Protect against infinitesimal heights and associated high velocities |
---|
| 1103 | """ |
---|
| 1104 | |
---|
| 1105 | #Shortcuts |
---|
| 1106 | wc = domain.quantities['stage'].centroid_values |
---|
| 1107 | zc = domain.quantities['elevation'].centroid_values |
---|
| 1108 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
| 1109 | # ymomc = domain.quantities['ymomentum'].centroid_values |
---|
| 1110 | hc = wc - zc #Water depths at centroids |
---|
| 1111 | |
---|
| 1112 | zv = domain.quantities['elevation'].vertex_values |
---|
| 1113 | wv = domain.quantities['stage'].vertex_values |
---|
| 1114 | #remove the above two lines and corresponding code below |
---|
| 1115 | |
---|
| 1116 | #Update |
---|
| 1117 | for k in range(domain.number_of_elements): |
---|
| 1118 | |
---|
| 1119 | if hc[k] < domain.minimum_allowed_height: |
---|
| 1120 | #Control stage |
---|
| 1121 | if hc[k] < domain.epsilon: |
---|
| 1122 | wc[k] = zc[k] # Contain 'lost mass' error |
---|
| 1123 | wv[k,0] = zv[k,0] |
---|
| 1124 | wv[k,1] = zv[k,1] |
---|
| 1125 | |
---|
| 1126 | #Control momentum |
---|
| 1127 | #xmomc[k] = ymomc[k] = 0.0 |
---|
| 1128 | xmomc[k] = 0.0 |
---|
| 1129 | |
---|
| 1130 | def h_limiter(domain): |
---|
| 1131 | """Limit slopes for each volume to eliminate artificial variance |
---|
| 1132 | introduced by e.g. second order extrapolator |
---|
| 1133 | |
---|
| 1134 | limit on h = w-z |
---|
| 1135 | |
---|
| 1136 | This limiter depends on two quantities (w,z) so it resides within |
---|
| 1137 | this module rather than within quantity.py |
---|
| 1138 | """ |
---|
| 1139 | |
---|
| 1140 | from Numeric import zeros, Float |
---|
| 1141 | |
---|
| 1142 | N = domain.number_of_elements |
---|
| 1143 | beta_h = domain.beta_h |
---|
| 1144 | |
---|
| 1145 | #Shortcuts |
---|
| 1146 | wc = domain.quantities['stage'].centroid_values |
---|
| 1147 | zc = domain.quantities['elevation'].centroid_values |
---|
| 1148 | hc = wc - zc |
---|
| 1149 | |
---|
| 1150 | wv = domain.quantities['stage'].vertex_values |
---|
| 1151 | zv = domain.quantities['elevation'].vertex_values |
---|
| 1152 | hv = wv-zv |
---|
| 1153 | |
---|
| 1154 | hvbar = zeros(hv.shape, Float) #h-limited values |
---|
| 1155 | |
---|
| 1156 | #Find min and max of this and neighbour's centroid values |
---|
| 1157 | hmax = zeros(hc.shape, Float) |
---|
| 1158 | hmin = zeros(hc.shape, Float) |
---|
| 1159 | |
---|
| 1160 | for k in range(N): |
---|
| 1161 | hmax[k] = hmin[k] = hc[k] |
---|
| 1162 | #for i in range(3): |
---|
| 1163 | for i in range(2): |
---|
| 1164 | n = domain.neighbours[k,i] |
---|
| 1165 | if n >= 0: |
---|
| 1166 | hn = hc[n] #Neighbour's centroid value |
---|
| 1167 | |
---|
| 1168 | hmin[k] = min(hmin[k], hn) |
---|
| 1169 | hmax[k] = max(hmax[k], hn) |
---|
| 1170 | |
---|
| 1171 | |
---|
| 1172 | #Diffences between centroids and maxima/minima |
---|
| 1173 | dhmax = hmax - hc |
---|
| 1174 | dhmin = hmin - hc |
---|
| 1175 | |
---|
| 1176 | #Deltas between vertex and centroid values |
---|
| 1177 | dh = zeros(hv.shape, Float) |
---|
| 1178 | #for i in range(3): |
---|
| 1179 | for i in range(2): |
---|
| 1180 | dh[:,i] = hv[:,i] - hc |
---|
| 1181 | |
---|
| 1182 | #Phi limiter |
---|
| 1183 | for k in range(N): |
---|
| 1184 | |
---|
| 1185 | #Find the gradient limiter (phi) across vertices |
---|
| 1186 | phi = 1.0 |
---|
| 1187 | #for i in range(3): |
---|
| 1188 | for i in range(2): |
---|
| 1189 | r = 1.0 |
---|
| 1190 | if (dh[k,i] > 0): r = dhmax[k]/dh[k,i] |
---|
| 1191 | if (dh[k,i] < 0): r = dhmin[k]/dh[k,i] |
---|
| 1192 | |
---|
| 1193 | phi = min( min(r*beta_h, 1), phi ) |
---|
| 1194 | |
---|
| 1195 | #Then update using phi limiter |
---|
| 1196 | #for i in range(3): |
---|
| 1197 | for i in range(2): |
---|
| 1198 | hvbar[k,i] = hc[k] + phi*dh[k,i] |
---|
| 1199 | |
---|
| 1200 | return hvbar |
---|
| 1201 | |
---|
| 1202 | def balance_deep_and_shallow(domain): |
---|
| 1203 | """Compute linear combination between stage as computed by |
---|
| 1204 | gradient-limiters limiting using w, and stage computed by |
---|
| 1205 | gradient-limiters limiting using h (h-limiter). |
---|
| 1206 | The former takes precedence when heights are large compared to the |
---|
| 1207 | bed slope while the latter takes precedence when heights are |
---|
| 1208 | relatively small. Anything in between is computed as a balanced |
---|
| 1209 | linear combination in order to avoid numerical disturbances which |
---|
| 1210 | would otherwise appear as a result of hard switching between |
---|
| 1211 | modes. |
---|
| 1212 | |
---|
| 1213 | The h-limiter is always applied irrespective of the order. |
---|
| 1214 | """ |
---|
| 1215 | |
---|
| 1216 | #Shortcuts |
---|
| 1217 | wc = domain.quantities['stage'].centroid_values |
---|
| 1218 | zc = domain.quantities['elevation'].centroid_values |
---|
| 1219 | hc = wc - zc |
---|
| 1220 | |
---|
| 1221 | wv = domain.quantities['stage'].vertex_values |
---|
| 1222 | zv = domain.quantities['elevation'].vertex_values |
---|
| 1223 | hv = wv-zv |
---|
| 1224 | |
---|
| 1225 | #Limit h |
---|
| 1226 | hvbar = h_limiter(domain) |
---|
| 1227 | |
---|
| 1228 | for k in range(domain.number_of_elements): |
---|
| 1229 | #Compute maximal variation in bed elevation |
---|
| 1230 | # This quantitiy is |
---|
| 1231 | # dz = max_i abs(z_i - z_c) |
---|
| 1232 | # and it is independent of dimension |
---|
| 1233 | # In the 1d case zc = (z0+z1)/2 |
---|
| 1234 | # In the 2d case zc = (z0+z1+z2)/3 |
---|
| 1235 | |
---|
| 1236 | dz = max(abs(zv[k,0]-zc[k]), |
---|
| 1237 | abs(zv[k,1]-zc[k]))#, |
---|
| 1238 | # abs(zv[k,2]-zc[k])) |
---|
| 1239 | |
---|
| 1240 | |
---|
| 1241 | hmin = min( hv[k,:] ) |
---|
| 1242 | |
---|
| 1243 | #Create alpha in [0,1], where alpha==0 means using the h-limited |
---|
| 1244 | #stage and alpha==1 means using the w-limited stage as |
---|
| 1245 | #computed by the gradient limiter (both 1st or 2nd order) |
---|
| 1246 | |
---|
| 1247 | #If hmin > dz/2 then alpha = 1 and the bed will have no effect |
---|
| 1248 | #If hmin < 0 then alpha = 0 reverting to constant height above bed. |
---|
| 1249 | |
---|
| 1250 | if dz > 0.0: |
---|
| 1251 | alpha = max( min( 2*hmin/dz, 1.0), 0.0 ) |
---|
| 1252 | else: |
---|
| 1253 | #Flat bed |
---|
| 1254 | alpha = 1.0 |
---|
| 1255 | |
---|
| 1256 | alpha = 0.0 |
---|
| 1257 | #Let |
---|
| 1258 | # |
---|
| 1259 | # wvi be the w-limited stage (wvi = zvi + hvi) |
---|
| 1260 | # wvi- be the h-limited state (wvi- = zvi + hvi-) |
---|
| 1261 | # |
---|
| 1262 | # |
---|
| 1263 | #where i=0,1,2 denotes the vertex ids |
---|
| 1264 | # |
---|
| 1265 | #Weighted balance between w-limited and h-limited stage is |
---|
| 1266 | # |
---|
| 1267 | # wvi := (1-alpha)*(zvi+hvi-) + alpha*(zvi+hvi) |
---|
| 1268 | # |
---|
| 1269 | #It follows that the updated wvi is |
---|
| 1270 | # wvi := zvi + (1-alpha)*hvi- + alpha*hvi |
---|
| 1271 | # |
---|
| 1272 | # Momentum is balanced between constant and limited |
---|
| 1273 | |
---|
| 1274 | |
---|
| 1275 | #for i in range(3): |
---|
| 1276 | # wv[k,i] = zv[k,i] + hvbar[k,i] |
---|
| 1277 | |
---|
| 1278 | #return |
---|
| 1279 | |
---|
| 1280 | if alpha < 1: |
---|
| 1281 | |
---|
| 1282 | #for i in range(3): |
---|
| 1283 | for i in range(2): |
---|
| 1284 | wv[k,i] = zv[k,i] + (1.0-alpha)*hvbar[k,i] + alpha*hv[k,i] |
---|
| 1285 | |
---|
| 1286 | #Momentums at centroids |
---|
| 1287 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
| 1288 | # ymomc = domain.quantities['ymomentum'].centroid_values |
---|
| 1289 | |
---|
| 1290 | #Momentums at vertices |
---|
| 1291 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
| 1292 | # ymomv = domain.quantities['ymomentum'].vertex_values |
---|
| 1293 | |
---|
| 1294 | # Update momentum as a linear combination of |
---|
| 1295 | # xmomc and ymomc (shallow) and momentum |
---|
| 1296 | # from extrapolator xmomv and ymomv (deep). |
---|
| 1297 | xmomv[k,:] = (1.0-alpha)*xmomc[k] + alpha*xmomv[k,:] |
---|
| 1298 | # ymomv[k,:] = (1-alpha)*ymomc[k] + alpha*ymomv[k,:] |
---|
| 1299 | |
---|
| 1300 | |
---|
| 1301 | ############################################### |
---|
| 1302 | #Boundaries - specific to the shallow water wave equation |
---|
| 1303 | class Reflective_boundary(Boundary): |
---|
| 1304 | """Reflective boundary returns same conserved quantities as |
---|
| 1305 | those present in its neighbour volume but reflected. |
---|
| 1306 | |
---|
| 1307 | This class is specific to the shallow water equation as it |
---|
| 1308 | works with the momentum quantities assumed to be the second |
---|
| 1309 | and third conserved quantities. |
---|
| 1310 | """ |
---|
| 1311 | |
---|
| 1312 | def __init__(self, domain = None): |
---|
| 1313 | Boundary.__init__(self) |
---|
| 1314 | |
---|
| 1315 | if domain is None: |
---|
| 1316 | msg = 'Domain must be specified for reflective boundary' |
---|
| 1317 | raise msg |
---|
| 1318 | |
---|
| 1319 | #Handy shorthands |
---|
| 1320 | #self.stage = domain.quantities['stage'].edge_values |
---|
| 1321 | #self.xmom = domain.quantities['xmomentum'].edge_values |
---|
| 1322 | #self.ymom = domain.quantities['ymomentum'].edge_values |
---|
| 1323 | #self.normals = domain.normals |
---|
| 1324 | self.stage = domain.quantities['stage'].vertex_values |
---|
| 1325 | self.xmom = domain.quantities['xmomentum'].vertex_values |
---|
| 1326 | self.height = domain.quantities['height'].vertex_values |
---|
| 1327 | |
---|
| 1328 | from Numeric import zeros, Float |
---|
| 1329 | self.conserved_quantities = zeros(3, Float) |
---|
| 1330 | #self.conserved_quantities = zeros(2, Float) |
---|
| 1331 | |
---|
| 1332 | def __repr__(self): |
---|
| 1333 | return 'Reflective_boundary' |
---|
| 1334 | |
---|
| 1335 | |
---|
| 1336 | def evaluate(self, vol_id, edge_id): |
---|
| 1337 | """Reflective boundaries reverses the outward momentum |
---|
| 1338 | of the volume they serve. |
---|
| 1339 | """ |
---|
| 1340 | |
---|
| 1341 | q = self.conserved_quantities |
---|
| 1342 | q[0] = self.stage[vol_id, edge_id] |
---|
| 1343 | q[1] = self.xmom[vol_id, edge_id] |
---|
| 1344 | #q[2] = self.ymom[vol_id, edge_id] |
---|
| 1345 | q[2] = self.height[vol_id,edge_id] |
---|
| 1346 | #normal = self.normals[vol_id, 2*edge_id:2*edge_id+2] |
---|
| 1347 | #normal = self.normals[vol_id, 2*edge_id:2*edge_id+1] |
---|
| 1348 | |
---|
| 1349 | |
---|
| 1350 | #r = rotate(q, normal, direction = 1) |
---|
| 1351 | #r[1] = -r[1] |
---|
| 1352 | #q = rotate(r, normal, direction = -1) |
---|
| 1353 | r = q |
---|
| 1354 | r[1] = -q[1] |
---|
| 1355 | q = r |
---|
| 1356 | #For start interval there is no outward momentum so do not need to |
---|
| 1357 | #reverse direction in this case |
---|
| 1358 | |
---|
| 1359 | return q |
---|
| 1360 | |
---|
| 1361 | class Dirichlet_boundary(Boundary): |
---|
| 1362 | """Dirichlet boundary returns constant values for the |
---|
| 1363 | conserved quantities |
---|
| 1364 | """ |
---|
| 1365 | |
---|
| 1366 | |
---|
| 1367 | def __init__(self, conserved_quantities=None): |
---|
| 1368 | Boundary.__init__(self) |
---|
| 1369 | |
---|
| 1370 | if conserved_quantities is None: |
---|
| 1371 | msg = 'Must specify one value for each conserved quantity' |
---|
| 1372 | raise msg |
---|
| 1373 | |
---|
| 1374 | from Numeric import array, Float |
---|
| 1375 | self.conserved_quantities=array(conserved_quantities).astype(Float) |
---|
| 1376 | |
---|
| 1377 | def __repr__(self): |
---|
| 1378 | return 'Dirichlet boundary (%s)' %self.conserved_quantities |
---|
| 1379 | |
---|
| 1380 | def evaluate(self, vol_id=None, edge_id=None): |
---|
| 1381 | return self.conserved_quantities |
---|
| 1382 | |
---|
| 1383 | |
---|
| 1384 | ######################### |
---|
| 1385 | #Standard forcing terms: |
---|
| 1386 | # |
---|
| 1387 | def gravity(domain): |
---|
| 1388 | """Apply gravitational pull in the presence of bed slope |
---|
| 1389 | """ |
---|
| 1390 | #print "in gravity" |
---|
| 1391 | #print "integral %f"%domain.quantities['height'].get_integral() |
---|
| 1392 | from util import gradient |
---|
| 1393 | from Numeric import zeros, Float, array, sum |
---|
| 1394 | |
---|
| 1395 | xmom = domain.quantities['xmomentum'].explicit_update |
---|
| 1396 | stage = domain.quantities['stage'].explicit_update |
---|
| 1397 | # ymom = domain.quantities['ymomentum'].explicit_update |
---|
| 1398 | |
---|
| 1399 | Stage = domain.quantities['stage'] |
---|
| 1400 | Elevation = domain.quantities['elevation'] |
---|
| 1401 | Height = domain.quantities['height'] |
---|
| 1402 | #h = Stage.edge_values - Elevation.edge_values |
---|
| 1403 | h = Stage.vertex_values - Elevation.vertex_values |
---|
| 1404 | hc = Height.centroid_values |
---|
| 1405 | h = Height.vertex_values |
---|
| 1406 | b = Elevation.vertex_values |
---|
| 1407 | w = Stage.vertex_values |
---|
| 1408 | |
---|
| 1409 | x = domain.get_vertex_coordinates() |
---|
| 1410 | g = domain.g |
---|
| 1411 | |
---|
| 1412 | for k in range(domain.number_of_elements): |
---|
| 1413 | # avg_h = sum( h[k,:] )/3 |
---|
| 1414 | #avg_h = sum( h[k,:] )/2 |
---|
| 1415 | avg_h = hc[k] |
---|
| 1416 | |
---|
| 1417 | #Compute bed slope |
---|
| 1418 | #x0, y0, x1, y1, x2, y2 = x[k,:] |
---|
| 1419 | x0, x1 = x[k,:] |
---|
| 1420 | #z0, z1, z2 = v[k,:] |
---|
| 1421 | b0, b1 = b[k,:] |
---|
| 1422 | |
---|
| 1423 | w0, w1 = w[k,:] |
---|
| 1424 | wx = gradient(x0, x1, w0, w1) |
---|
| 1425 | |
---|
| 1426 | #zx, zy = gradient(x0, y0, x1, y1, x2, y2, z0, z1, z2) |
---|
| 1427 | bx = gradient(x0, x1, b0, b1) |
---|
| 1428 | |
---|
| 1429 | #Update momentum (explicit update is reset to source values) |
---|
| 1430 | if domain.split == False: |
---|
| 1431 | xmom[k] += -g*bx*avg_h |
---|
| 1432 | #xmom[k] = -g*bx*avg_h |
---|
| 1433 | #stage[k] = 0.0 |
---|
| 1434 | elif domain.split == True: |
---|
| 1435 | xmom[k] += -g*wx*avg_h |
---|
| 1436 | #xmom[k] = -g*wx*avg_h |
---|
| 1437 | #ymom[k] += -g*zy*avg_h |
---|
| 1438 | |
---|
| 1439 | def manning_friction(domain): |
---|
| 1440 | """Apply (Manning) friction to water momentum |
---|
| 1441 | """ |
---|
| 1442 | |
---|
| 1443 | from math import sqrt |
---|
| 1444 | |
---|
| 1445 | w = domain.quantities['stage'].centroid_values |
---|
| 1446 | z = domain.quantities['elevation'].centroid_values |
---|
| 1447 | h = w-z |
---|
| 1448 | |
---|
| 1449 | uh = domain.quantities['xmomentum'].centroid_values |
---|
| 1450 | #vh = domain.quantities['ymomentum'].centroid_values |
---|
| 1451 | eta = domain.quantities['friction'].centroid_values |
---|
| 1452 | |
---|
| 1453 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
---|
| 1454 | #ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
---|
| 1455 | |
---|
| 1456 | N = domain.number_of_elements |
---|
| 1457 | eps = domain.minimum_allowed_height |
---|
| 1458 | g = domain.g |
---|
| 1459 | |
---|
| 1460 | for k in range(N): |
---|
| 1461 | if eta[k] >= eps: |
---|
| 1462 | if h[k] >= eps: |
---|
| 1463 | #S = -g * eta[k]**2 * sqrt((uh[k]**2 + vh[k]**2)) |
---|
| 1464 | S = -g * eta[k]**2 * uh[k] |
---|
| 1465 | S /= h[k]**(7.0/3) |
---|
| 1466 | |
---|
| 1467 | #Update momentum |
---|
| 1468 | xmom_update[k] += S*uh[k] |
---|
| 1469 | #ymom_update[k] += S*vh[k] |
---|
| 1470 | |
---|
| 1471 | def linear_friction(domain): |
---|
| 1472 | """Apply linear friction to water momentum |
---|
| 1473 | |
---|
| 1474 | Assumes quantity: 'linear_friction' to be present |
---|
| 1475 | """ |
---|
| 1476 | |
---|
| 1477 | from math import sqrt |
---|
| 1478 | |
---|
| 1479 | w = domain.quantities['stage'].centroid_values |
---|
| 1480 | z = domain.quantities['elevation'].centroid_values |
---|
| 1481 | h = w-z |
---|
| 1482 | |
---|
| 1483 | uh = domain.quantities['xmomentum'].centroid_values |
---|
| 1484 | # vh = domain.quantities['ymomentum'].centroid_values |
---|
| 1485 | tau = domain.quantities['linear_friction'].centroid_values |
---|
| 1486 | |
---|
| 1487 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
---|
| 1488 | # ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
---|
| 1489 | |
---|
| 1490 | N = domain.number_of_elements |
---|
| 1491 | eps = domain.minimum_allowed_height |
---|
| 1492 | g = domain.g #Not necessary? Why was this added? |
---|
| 1493 | |
---|
| 1494 | for k in range(N): |
---|
| 1495 | if tau[k] >= eps: |
---|
| 1496 | if h[k] >= eps: |
---|
| 1497 | S = -tau[k]/h[k] |
---|
| 1498 | |
---|
| 1499 | #Update momentum |
---|
| 1500 | xmom_update[k] += S*uh[k] |
---|
| 1501 | # ymom_update[k] += S*vh[k] |
---|
| 1502 | |
---|
| 1503 | |
---|
| 1504 | |
---|
| 1505 | def check_forcefield(f): |
---|
| 1506 | """Check that f is either |
---|
| 1507 | 1: a callable object f(t,x,y), where x and y are vectors |
---|
| 1508 | and that it returns an array or a list of same length |
---|
| 1509 | as x and y |
---|
| 1510 | 2: a scalar |
---|
| 1511 | """ |
---|
| 1512 | |
---|
| 1513 | from Numeric import ones, Float, array |
---|
| 1514 | |
---|
| 1515 | |
---|
| 1516 | if callable(f): |
---|
| 1517 | #N = 3 |
---|
| 1518 | N = 2 |
---|
| 1519 | #x = ones(3, Float) |
---|
| 1520 | #y = ones(3, Float) |
---|
| 1521 | x = ones(2, Float) |
---|
| 1522 | #y = ones(2, Float) |
---|
| 1523 | |
---|
| 1524 | try: |
---|
| 1525 | #q = f(1.0, x=x, y=y) |
---|
| 1526 | q = f(1.0, x=x) |
---|
| 1527 | except Exception, e: |
---|
| 1528 | msg = 'Function %s could not be executed:\n%s' %(f, e) |
---|
| 1529 | #FIXME: Reconsider this semantics |
---|
| 1530 | raise msg |
---|
| 1531 | |
---|
| 1532 | try: |
---|
| 1533 | q = array(q).astype(Float) |
---|
| 1534 | except: |
---|
| 1535 | msg = 'Return value from vector function %s could ' %f |
---|
| 1536 | msg += 'not be converted into a Numeric array of floats.\n' |
---|
| 1537 | msg += 'Specified function should return either list or array.' |
---|
| 1538 | raise msg |
---|
| 1539 | |
---|
| 1540 | #Is this really what we want? |
---|
| 1541 | msg = 'Return vector from function %s ' %f |
---|
| 1542 | msg += 'must have same lenght as input vectors' |
---|
| 1543 | assert len(q) == N, msg |
---|
| 1544 | |
---|
| 1545 | else: |
---|
| 1546 | try: |
---|
| 1547 | f = float(f) |
---|
| 1548 | except: |
---|
| 1549 | msg = 'Force field %s must be either a scalar' %f |
---|
| 1550 | msg += ' or a vector function' |
---|
| 1551 | raise msg |
---|
| 1552 | return f |
---|
| 1553 | |
---|
| 1554 | class Wind_stress: |
---|
| 1555 | """Apply wind stress to water momentum in terms of |
---|
| 1556 | wind speed [m/s] and wind direction [degrees] |
---|
| 1557 | """ |
---|
| 1558 | |
---|
| 1559 | def __init__(self, *args, **kwargs): |
---|
| 1560 | """Initialise windfield from wind speed s [m/s] |
---|
| 1561 | and wind direction phi [degrees] |
---|
| 1562 | |
---|
| 1563 | Inputs v and phi can be either scalars or Python functions, e.g. |
---|
| 1564 | |
---|
| 1565 | W = Wind_stress(10, 178) |
---|
| 1566 | |
---|
| 1567 | #FIXME - 'normal' degrees are assumed for now, i.e. the |
---|
| 1568 | vector (1,0) has zero degrees. |
---|
| 1569 | We may need to convert from 'compass' degrees later on and also |
---|
| 1570 | map from True north to grid north. |
---|
| 1571 | |
---|
| 1572 | Arguments can also be Python functions of t,x,y as in |
---|
| 1573 | |
---|
| 1574 | def speed(t,x,y): |
---|
| 1575 | ... |
---|
| 1576 | return s |
---|
| 1577 | |
---|
| 1578 | def angle(t,x,y): |
---|
| 1579 | ... |
---|
| 1580 | return phi |
---|
| 1581 | |
---|
| 1582 | where x and y are vectors. |
---|
| 1583 | |
---|
| 1584 | and then pass the functions in |
---|
| 1585 | |
---|
| 1586 | W = Wind_stress(speed, angle) |
---|
| 1587 | |
---|
| 1588 | The instantiated object W can be appended to the list of |
---|
| 1589 | forcing_terms as in |
---|
| 1590 | |
---|
| 1591 | Alternatively, one vector valued function for (speed, angle) |
---|
| 1592 | can be applied, providing both quantities simultaneously. |
---|
| 1593 | As in |
---|
| 1594 | W = Wind_stress(F), where returns (speed, angle) for each t. |
---|
| 1595 | |
---|
| 1596 | domain.forcing_terms.append(W) |
---|
| 1597 | """ |
---|
| 1598 | |
---|
| 1599 | from config import rho_a, rho_w, eta_w |
---|
| 1600 | from Numeric import array, Float |
---|
| 1601 | |
---|
| 1602 | if len(args) == 2: |
---|
| 1603 | s = args[0] |
---|
| 1604 | phi = args[1] |
---|
| 1605 | elif len(args) == 1: |
---|
| 1606 | #Assume vector function returning (s, phi)(t,x,y) |
---|
| 1607 | vector_function = args[0] |
---|
| 1608 | #s = lambda t,x,y: vector_function(t,x=x,y=y)[0] |
---|
| 1609 | #phi = lambda t,x,y: vector_function(t,x=x,y=y)[1] |
---|
| 1610 | s = lambda t,x: vector_function(t,x=x)[0] |
---|
| 1611 | phi = lambda t,x: vector_function(t,x=x)[1] |
---|
| 1612 | else: |
---|
| 1613 | #Assume info is in 2 keyword arguments |
---|
| 1614 | |
---|
| 1615 | if len(kwargs) == 2: |
---|
| 1616 | s = kwargs['s'] |
---|
| 1617 | phi = kwargs['phi'] |
---|
| 1618 | else: |
---|
| 1619 | raise 'Assumes two keyword arguments: s=..., phi=....' |
---|
| 1620 | |
---|
| 1621 | print 'phi', phi |
---|
| 1622 | self.speed = check_forcefield(s) |
---|
| 1623 | self.phi = check_forcefield(phi) |
---|
| 1624 | |
---|
| 1625 | self.const = eta_w*rho_a/rho_w |
---|
| 1626 | |
---|
| 1627 | |
---|
| 1628 | def __call__(self, domain): |
---|
| 1629 | """Evaluate windfield based on values found in domain |
---|
| 1630 | """ |
---|
| 1631 | |
---|
| 1632 | from math import pi, cos, sin, sqrt |
---|
| 1633 | from Numeric import Float, ones, ArrayType |
---|
| 1634 | |
---|
| 1635 | xmom_update = domain.quantities['xmomentum'].explicit_update |
---|
| 1636 | #ymom_update = domain.quantities['ymomentum'].explicit_update |
---|
| 1637 | |
---|
| 1638 | N = domain.number_of_elements |
---|
| 1639 | t = domain.time |
---|
| 1640 | |
---|
| 1641 | if callable(self.speed): |
---|
| 1642 | xc = domain.get_centroid_coordinates() |
---|
| 1643 | #s_vec = self.speed(t, xc[:,0], xc[:,1]) |
---|
| 1644 | s_vec = self.speed(t, xc) |
---|
| 1645 | else: |
---|
| 1646 | #Assume s is a scalar |
---|
| 1647 | |
---|
| 1648 | try: |
---|
| 1649 | s_vec = self.speed * ones(N, Float) |
---|
| 1650 | except: |
---|
| 1651 | msg = 'Speed must be either callable or a scalar: %s' %self.s |
---|
| 1652 | raise msg |
---|
| 1653 | |
---|
| 1654 | |
---|
| 1655 | if callable(self.phi): |
---|
| 1656 | xc = domain.get_centroid_coordinates() |
---|
| 1657 | #phi_vec = self.phi(t, xc[:,0], xc[:,1]) |
---|
| 1658 | phi_vec = self.phi(t, xc) |
---|
| 1659 | else: |
---|
| 1660 | #Assume phi is a scalar |
---|
| 1661 | |
---|
| 1662 | try: |
---|
| 1663 | phi_vec = self.phi * ones(N, Float) |
---|
| 1664 | except: |
---|
| 1665 | msg = 'Angle must be either callable or a scalar: %s' %self.phi |
---|
| 1666 | raise msg |
---|
| 1667 | |
---|
| 1668 | #assign_windfield_values(xmom_update, ymom_update, |
---|
| 1669 | # s_vec, phi_vec, self.const) |
---|
| 1670 | assign_windfield_values(xmom_update, s_vec, phi_vec, self.const) |
---|
| 1671 | |
---|
| 1672 | |
---|
| 1673 | #def assign_windfield_values(xmom_update, ymom_update, |
---|
| 1674 | # s_vec, phi_vec, const): |
---|
| 1675 | def assign_windfield_values(xmom_update, s_vec, phi_vec, const): |
---|
| 1676 | """Python version of assigning wind field to update vectors. |
---|
| 1677 | A c version also exists (for speed) |
---|
| 1678 | """ |
---|
| 1679 | from math import pi, cos, sin, sqrt |
---|
| 1680 | |
---|
| 1681 | N = len(s_vec) |
---|
| 1682 | for k in range(N): |
---|
| 1683 | s = s_vec[k] |
---|
| 1684 | phi = phi_vec[k] |
---|
| 1685 | |
---|
| 1686 | #Convert to radians |
---|
| 1687 | phi = phi*pi/180 |
---|
| 1688 | |
---|
| 1689 | #Compute velocity vector (u, v) |
---|
| 1690 | u = s*cos(phi) |
---|
| 1691 | v = s*sin(phi) |
---|
| 1692 | |
---|
| 1693 | #Compute wind stress |
---|
| 1694 | #S = const * sqrt(u**2 + v**2) |
---|
| 1695 | S = const * u |
---|
| 1696 | xmom_update[k] += S*u |
---|
| 1697 | #ymom_update[k] += S*v |
---|