[7837] | 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 | John Jakeman, Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
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| 41 | Geoscience Australia, 2006 |
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| 42 | """ |
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| 43 | |
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| 44 | |
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| 45 | from domain import * |
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| 46 | Generic_Domain = Domain #Rename |
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| 47 | |
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| 48 | #Shallow water domain |
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| 49 | class Domain(Generic_Domain): |
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| 50 | |
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| 51 | def __init__(self, coordinates, boundary = None, tagged_elements = None): |
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| 52 | conserved_quantities = ['stage', 'xmomentum'] #['height', 'xmomentum'] |
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| 53 | evolved_quantities = ['stage', 'xmomentum', 'elevation', 'height', 'velocity'] |
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| 54 | other_quantities = ['friction'] |
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| 55 | Generic_Domain.__init__(self, coordinates, boundary, |
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| 56 | conserved_quantities, evolved_quantities, other_quantities, |
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| 57 | tagged_elements) |
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| 58 | |
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| 59 | from config import minimum_allowed_height, g, h0 |
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| 60 | self.minimum_allowed_height = minimum_allowed_height |
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| 61 | self.g = g |
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| 62 | self.h0 = h0 |
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| 63 | |
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| 64 | self.forcing_terms.append(gravity_F2) #gravity, gravity_F1, gravity_F2 |
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| 65 | #self.forcing_terms.append(manning_friction) |
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| 66 | |
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| 67 | #Realtime visualisation |
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| 68 | self.visualiser = None |
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| 69 | self.visualise = False |
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| 70 | self.visualise_color_stage = False |
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| 71 | self.visualise_stage_range = 1.0 |
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| 72 | self.visualise_timer = True |
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| 73 | self.visualise_range_z = None |
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| 74 | |
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| 75 | #Stored output |
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| 76 | self.store = True |
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| 77 | self.format = 'sww' |
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| 78 | self.smooth = True |
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| 79 | |
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| 80 | #Evolve parametrs |
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| 81 | self.cfl = 1.0 |
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| 82 | |
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| 83 | #Reduction operation for get_vertex_values |
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| 84 | from util import mean |
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| 85 | self.reduction = mean |
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| 86 | #self.reduction = min #Looks better near steep slopes |
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| 87 | |
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| 88 | self.quantities_to_be_stored = ['stage','xmomentum'] |
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| 89 | |
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| 90 | self.__doc__ = 'shallow_water_domain_avalanche' |
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| 91 | self.check_integrity() |
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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 | if q is None: |
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| 109 | self.quantities_to_be_stored = [] |
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| 110 | self.store = False |
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| 111 | return |
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| 112 | |
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| 113 | if isinstance(q, basestring): |
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| 114 | q = [q] # Turn argument into a list |
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| 115 | |
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| 116 | #Check correcness |
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| 117 | for quantity_name in q: |
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| 118 | msg = 'Quantity %s is not a valid conserved quantity' %quantity_name |
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| 119 | assert quantity_name in self.conserved_quantities, msg |
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| 120 | |
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| 121 | self.quantities_to_be_stored = q |
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| 122 | |
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| 123 | |
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| 124 | def initialise_visualiser(self,scale_z=1.0,rect=None): |
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| 125 | #Realtime visualisation |
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| 126 | if self.visualiser is None: |
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| 127 | from realtime_visualisation_new import Visualiser |
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| 128 | self.visualiser = Visualiser(self,scale_z,rect) |
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| 129 | self.visualiser.setup['elevation']=True |
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| 130 | self.visualiser.updating['stage']=True |
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| 131 | self.visualise = True |
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| 132 | if self.visualise_color_stage == True: |
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| 133 | self.visualiser.coloring['stage'] = True |
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| 134 | self.visualiser.qcolor['stage'] = (0.0, 0.0, 0.8) |
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| 135 | print 'initialise visualiser' |
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| 136 | print self.visualiser.setup |
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| 137 | print self.visualiser.updating |
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| 138 | |
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| 139 | def check_integrity(self): |
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| 140 | Generic_Domain.check_integrity(self) |
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| 141 | #Check that we are solving the shallow water wave equation |
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| 142 | |
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| 143 | msg = 'First conserved quantity must be "stage"' |
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| 144 | assert self.conserved_quantities[0] == 'stage', msg |
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| 145 | msg = 'Second conserved quantity must be "xmomentum"' |
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| 146 | assert self.conserved_quantities[1] == 'xmomentum', msg |
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| 147 | |
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| 148 | msg = 'First evolved quantity must be "stage"' |
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| 149 | assert self.evolved_quantities[0] == 'stage', msg |
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| 150 | msg = 'Second evolved quantity must be "xmomentum"' |
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| 151 | assert self.evolved_quantities[1] == 'xmomentum', msg |
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| 152 | msg = 'Third evolved quantity must be "elevation"' |
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| 153 | assert self.evolved_quantities[2] == 'elevation', msg |
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| 154 | msg = 'Fourth evolved quantity must be "height"' |
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| 155 | assert self.evolved_quantities[3] == 'height', msg |
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| 156 | msg = 'Fifth evolved quantity must be "velocity"' |
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| 157 | assert self.evolved_quantities[4] == 'velocity', msg |
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| 158 | |
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| 159 | def extrapolate_second_order_sw(self): |
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| 160 | #Call correct module function |
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| 161 | #(either from this module or C-extension) |
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| 162 | extrapolate_second_order_sw(self) |
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| 163 | |
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| 164 | def compute_fluxes(self): |
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| 165 | #Call correct module function(either from this module or C-extension) |
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| 166 | compute_fluxes_C_wellbalanced(self) |
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| 167 | #compute_fluxes_C_nonwellbalanced2(self) |
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| 168 | |
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| 169 | def compute_timestep(self): |
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| 170 | #Call correct module function |
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| 171 | compute_timestep(self) |
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| 172 | |
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| 173 | def distribute_to_vertices_and_edges(self): |
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| 174 | #Call correct module function(either from this module or C-extension) |
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| 175 | distribute_to_vertices_and_edges_shv(self) |
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| 176 | #distribute_to_vertices_and_edges_shm(self) |
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| 177 | |
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| 178 | def evolve(self, yieldstep = None, finaltime = None, duration = None, skip_initial_step = False): |
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| 179 | #Call basic machinery from parent class |
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| 180 | for t in Generic_Domain.evolve(self, yieldstep, finaltime, duration, skip_initial_step): |
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| 181 | yield(t) |
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| 182 | |
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| 183 | def initialise_storage(self): |
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| 184 | """Create and initialise self.writer object for storing data. |
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| 185 | Also, save x and bed elevation |
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| 186 | """ |
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| 187 | |
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| 188 | import data_manager |
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| 189 | |
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| 190 | #Initialise writer |
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| 191 | self.writer = data_manager.get_dataobject(self, mode = 'w') |
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| 192 | |
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| 193 | #Store vertices and connectivity |
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| 194 | self.writer.store_connectivity() |
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| 195 | |
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| 196 | |
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| 197 | def store_timestep(self, name): |
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| 198 | """Store named quantity and time. |
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| 199 | |
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| 200 | Precondition: |
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| 201 | self.write has been initialised |
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| 202 | """ |
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| 203 | self.writer.store_timestep(name) |
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| 204 | |
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| 205 | |
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| 206 | #=============== End of Shallow Water Domain =============================== |
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| 207 | |
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| 208 | #Rotation of momentum vector |
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| 209 | def rotate(q, normal, direction = 1): |
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| 210 | """Rotate the momentum component q (q[1], q[2]) |
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| 211 | from x,y coordinates to coordinates based on normal vector. |
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| 212 | |
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| 213 | If direction is negative the rotation is inverted. |
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| 214 | |
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| 215 | Input vector is preserved |
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| 216 | |
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| 217 | This function is specific to the shallow water wave equation |
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| 218 | """ |
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| 219 | |
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[7914] | 220 | from Numeric import Float |
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| 221 | from numpy import zeros |
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[7837] | 222 | |
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| 223 | assert len(q) == 3,\ |
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| 224 | 'Vector of conserved quantities must have length 3'\ |
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| 225 | 'for 2D shallow water equation' |
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| 226 | |
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| 227 | try: |
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| 228 | l = len(normal) |
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| 229 | except: |
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| 230 | raise 'Normal vector must be an Numeric array' |
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| 231 | |
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| 232 | assert l == 2, 'Normal vector must have 2 components' |
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| 233 | |
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| 234 | |
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| 235 | n1 = normal[0] |
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| 236 | n2 = normal[1] |
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| 237 | |
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| 238 | r = zeros(len(q), Float) #Rotated quantities |
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| 239 | r[0] = q[0] #First quantity, height, is not rotated |
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| 240 | |
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| 241 | if direction == -1: |
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| 242 | n2 = -n2 |
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| 243 | |
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| 244 | |
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| 245 | r[1] = n1*q[1] + n2*q[2] |
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| 246 | r[2] = -n2*q[1] + n1*q[2] |
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| 247 | |
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| 248 | return r |
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| 249 | |
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| 250 | |
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| 251 | def flux_function(normal, ql, qr, zl, zr): |
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| 252 | """Compute fluxes between volumes for the shallow water wave equation |
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| 253 | cast in terms of w = h+z using the 'central scheme' as described in |
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| 254 | |
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| 255 | Kurganov, Noelle, Petrova. 'Semidiscrete Central-Upwind Schemes For |
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| 256 | Hyperbolic Conservation Laws and Hamilton-Jacobi Equations'. |
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| 257 | Siam J. Sci. Comput. Vol. 23, No. 3, pp. 707-740. |
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| 258 | |
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| 259 | The implemented formula is given in equation (3.15) on page 714 |
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| 260 | |
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| 261 | Conserved quantities w, uh, are stored as elements 0 and 1 |
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| 262 | in the numerical vectors ql an qr. |
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| 263 | |
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| 264 | Bed elevations zl and zr. |
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| 265 | """ |
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| 266 | |
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| 267 | from config import g, epsilon, h0 |
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| 268 | from math import sqrt |
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[7914] | 269 | from numpy import array |
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[7837] | 270 | |
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| 271 | #Align momentums with x-axis |
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| 272 | q_left = ql |
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| 273 | q_left[1] = q_left[1]*normal |
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| 274 | q_right = qr |
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| 275 | q_right[1] = q_right[1]*normal |
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| 276 | |
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| 277 | z = 0.5*(zl+zr) #Take average of field values |
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| 278 | |
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| 279 | w_left = q_left[0] #w=h+z |
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| 280 | h_left = w_left-z |
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| 281 | uh_left = q_left[1] |
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| 282 | |
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| 283 | if h_left < epsilon: |
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| 284 | u_left = 0.0 #Could have been negative |
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| 285 | h_left = 0.0 |
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| 286 | else: |
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| 287 | u_left = uh_left/(h_left + h0/h_left) |
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| 288 | |
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| 289 | |
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| 290 | uh_left = u_left*h_left |
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| 291 | |
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| 292 | |
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| 293 | w_right = q_right[0] #w=h+z |
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| 294 | h_right = w_right-z |
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| 295 | uh_right = q_right[1] |
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| 296 | |
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| 297 | if h_right < epsilon: |
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| 298 | u_right = 0.0 #Could have been negative |
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| 299 | h_right = 0.0 |
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| 300 | else: |
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| 301 | u_right = uh_right/(h_right + h0/h_right) |
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| 302 | |
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| 303 | uh_right = u_right*h_right |
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| 304 | |
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| 305 | |
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| 306 | #We have got h and u at vertex, then the following is the calculation of fluxes! |
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| 307 | soundspeed_left = sqrt(g*h_left) |
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| 308 | soundspeed_right = sqrt(g*h_right) |
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| 309 | |
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| 310 | #Maximal wave speed |
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| 311 | s_max = max(u_left+soundspeed_left, u_right+soundspeed_right, 0) |
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| 312 | |
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| 313 | #Minimal wave speed |
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| 314 | s_min = min(u_left-soundspeed_left, u_right-soundspeed_right, 0) |
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| 315 | |
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| 316 | #Flux computation |
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| 317 | flux_left = array([u_left*h_left, |
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| 318 | u_left*uh_left + 0.5*g*h_left*h_left]) |
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| 319 | flux_right = array([u_right*h_right, |
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| 320 | u_right*uh_right + 0.5*g*h_right*h_right]) |
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| 321 | |
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| 322 | denom = s_max-s_min |
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| 323 | if denom == 0.0: |
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| 324 | edgeflux = array([0.0, 0.0]) |
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| 325 | max_speed = 0.0 |
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| 326 | else: |
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| 327 | edgeflux = (s_max*flux_left - s_min*flux_right)/denom |
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| 328 | edgeflux += s_max*s_min*(q_right-q_left)/denom |
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| 329 | |
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| 330 | edgeflux[1] = edgeflux[1]*normal |
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| 331 | |
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| 332 | max_speed = max(abs(s_max), abs(s_min)) |
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| 333 | |
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| 334 | return edgeflux, max_speed |
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| 335 | |
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| 336 | # |
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| 337 | def compute_timestep(domain): |
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| 338 | import sys |
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[7914] | 339 | from Numeric import Float |
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| 340 | from numpy import zeros |
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[7837] | 341 | |
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| 342 | N = domain.number_of_elements |
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| 343 | |
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| 344 | #Shortcuts |
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| 345 | Stage = domain.quantities['stage'] |
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| 346 | Xmom = domain.quantities['xmomentum'] |
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| 347 | Bed = domain.quantities['elevation'] |
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| 348 | |
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| 349 | stage = Stage.vertex_values |
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| 350 | xmom = Xmom.vertex_values |
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| 351 | bed = Bed.vertex_values |
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| 352 | |
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| 353 | stage_bdry = Stage.boundary_values |
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| 354 | xmom_bdry = Xmom.boundary_values |
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| 355 | |
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| 356 | flux = zeros(2, Float) #Work array for summing up fluxes |
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| 357 | ql = zeros(2, Float) |
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| 358 | qr = zeros(2, Float) |
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| 359 | |
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| 360 | #Loop |
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| 361 | timestep = float(sys.maxint) |
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| 362 | enter = True |
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| 363 | for k in range(N): |
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| 364 | |
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| 365 | flux[:] = 0. #Reset work array |
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| 366 | for i in range(2): |
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| 367 | #Quantities inside volume facing neighbour i |
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| 368 | ql = [stage[k, i], xmom[k, i]] |
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| 369 | zl = bed[k, i] |
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| 370 | |
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| 371 | #Quantities at neighbour on nearest face |
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| 372 | n = domain.neighbours[k,i] |
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| 373 | if n < 0: |
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| 374 | m = -n-1 #Convert negative flag to index |
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| 375 | qr[0] = stage_bdry[m] |
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| 376 | qr[1] = xmom_bdry[m] |
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| 377 | zr = zl #Extend bed elevation to boundary |
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| 378 | else: |
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| 379 | m = domain.neighbour_vertices[k,i] |
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| 380 | qr[0] = stage[n, m] |
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| 381 | qr[1] = xmom[n, m] |
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| 382 | zr = bed[n, m] |
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| 383 | |
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| 384 | |
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| 385 | #Outward pointing normal vector |
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| 386 | normal = domain.normals[k, i] |
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| 387 | |
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| 388 | edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
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| 389 | |
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| 390 | #Update optimal_timestep |
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| 391 | try: |
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| 392 | timestep = min(timestep, domain.cfl*0.5*domain.areas[k]/max_speed) |
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| 393 | except ZeroDivisionError: |
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| 394 | pass |
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| 395 | |
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| 396 | domain.timestep = timestep |
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| 397 | |
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| 398 | # Compute flux definition |
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| 399 | # ################################### |
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| 400 | def compute_fluxes_C_wellbalanced(domain): |
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| 401 | import sys |
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[7914] | 402 | from Numeric import Float |
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| 403 | from numpy import zeros |
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[7837] | 404 | |
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| 405 | N = domain.number_of_elements |
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| 406 | timestep = float(sys.maxint) |
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| 407 | epsilon = domain.epsilon |
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| 408 | g = domain.g |
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| 409 | neighbours = domain.neighbours |
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| 410 | neighbour_vertices = domain.neighbour_vertices |
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| 411 | normals = domain.normals |
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| 412 | areas = domain.areas |
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| 413 | |
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| 414 | Stage = domain.quantities['stage'] |
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| 415 | Xmom = domain.quantities['xmomentum'] |
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| 416 | Bed = domain.quantities['elevation'] |
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| 417 | Height = domain.quantities['height'] |
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| 418 | Velocity = domain.quantities['velocity'] |
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| 419 | |
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| 420 | |
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| 421 | stage_boundary_values = Stage.boundary_values |
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| 422 | xmom_boundary_values = Xmom.boundary_values |
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| 423 | bed_boundary_values = Bed.boundary_values |
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| 424 | height_boundary_values= Height.boundary_values |
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| 425 | vel_boundary_values = Velocity.boundary_values |
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| 426 | |
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| 427 | stage_explicit_update = Stage.explicit_update |
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| 428 | xmom_explicit_update = Xmom.explicit_update |
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| 429 | bed_explicit_values = Bed.explicit_update |
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| 430 | height_explicit_values= Height.explicit_update |
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| 431 | vel_explicit_values = Velocity.explicit_update |
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| 432 | |
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| 433 | max_speed_array = domain.max_speed_array |
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| 434 | |
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| 435 | domain.distribute_to_vertices_and_edges() |
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| 436 | domain.update_boundary() |
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| 437 | |
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| 438 | stage_V = Stage.vertex_values |
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| 439 | xmom_V = Xmom.vertex_values |
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| 440 | bed_V = Bed.vertex_values |
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| 441 | height_V= Height.vertex_values |
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| 442 | vel_V = Velocity.vertex_values |
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| 443 | |
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| 444 | number_of_elements = len(stage_V) |
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| 445 | |
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| 446 | from comp_flux_ext_wellbalanced import compute_fluxes_ext_wellbalanced |
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| 447 | domain.flux_timestep = compute_fluxes_ext_wellbalanced(timestep, |
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| 448 | epsilon, |
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| 449 | g, |
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| 450 | |
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| 451 | neighbours, |
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| 452 | neighbour_vertices, |
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| 453 | normals, |
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| 454 | areas, |
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| 455 | |
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| 456 | stage_V, |
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| 457 | xmom_V, |
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| 458 | bed_V, |
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| 459 | height_V, |
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| 460 | vel_V, |
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| 461 | |
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| 462 | stage_boundary_values, |
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| 463 | xmom_boundary_values, |
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| 464 | bed_boundary_values, |
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| 465 | height_boundary_values, |
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| 466 | vel_boundary_values, |
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| 467 | |
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| 468 | stage_explicit_update, |
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| 469 | xmom_explicit_update, |
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| 470 | bed_explicit_values, |
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| 471 | height_explicit_values, |
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| 472 | vel_explicit_values, |
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| 473 | |
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| 474 | number_of_elements, |
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| 475 | max_speed_array) |
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| 476 | |
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| 477 | |
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| 478 | def compute_fluxes_C_nonwellbalanced2(domain): |
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| 479 | import sys |
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[7914] | 480 | from Numeric import Float |
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| 481 | from numpy import zeros |
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[7837] | 482 | |
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| 483 | N = domain.number_of_elements |
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| 484 | timestep = float(sys.maxint) |
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| 485 | epsilon = domain.epsilon |
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| 486 | g = domain.g |
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| 487 | neighbours = domain.neighbours |
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| 488 | neighbour_vertices = domain.neighbour_vertices |
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| 489 | normals = domain.normals |
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| 490 | areas = domain.areas |
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| 491 | |
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| 492 | Stage = domain.quantities['stage'] |
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| 493 | Xmom = domain.quantities['xmomentum'] |
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| 494 | Bed = domain.quantities['elevation'] |
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| 495 | Height = domain.quantities['height'] |
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| 496 | Velocity = domain.quantities['velocity'] |
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| 497 | |
---|
| 498 | |
---|
| 499 | stage_boundary_values = Stage.boundary_values |
---|
| 500 | xmom_boundary_values = Xmom.boundary_values |
---|
| 501 | bed_boundary_values = Bed.boundary_values |
---|
| 502 | height_boundary_values= Height.boundary_values |
---|
| 503 | vel_boundary_values = Velocity.boundary_values |
---|
| 504 | |
---|
| 505 | stage_explicit_update = Stage.explicit_update |
---|
| 506 | xmom_explicit_update = Xmom.explicit_update |
---|
| 507 | bed_explicit_values = Bed.explicit_update |
---|
| 508 | height_explicit_values= Height.explicit_update |
---|
| 509 | vel_explicit_values = Velocity.explicit_update |
---|
| 510 | |
---|
| 511 | max_speed_array = domain.max_speed_array |
---|
| 512 | |
---|
| 513 | domain.distribute_to_vertices_and_edges() |
---|
| 514 | domain.update_boundary() |
---|
| 515 | |
---|
| 516 | stage_V = Stage.vertex_values |
---|
| 517 | xmom_V = Xmom.vertex_values |
---|
| 518 | bed_V = Bed.vertex_values |
---|
| 519 | height_V= Height.vertex_values |
---|
| 520 | vel_V = Velocity.vertex_values |
---|
| 521 | |
---|
| 522 | number_of_elements = len(stage_V) |
---|
| 523 | |
---|
| 524 | from comp_flux_ext_nonwellbalanced2 import compute_fluxes_ext_nonwellbalanced2 |
---|
| 525 | domain.flux_timestep = compute_fluxes_ext_nonwellbalanced2(timestep, |
---|
| 526 | epsilon, |
---|
| 527 | g, |
---|
| 528 | |
---|
| 529 | neighbours, |
---|
| 530 | neighbour_vertices, |
---|
| 531 | normals, |
---|
| 532 | areas, |
---|
| 533 | |
---|
| 534 | stage_V, |
---|
| 535 | xmom_V, |
---|
| 536 | bed_V, |
---|
| 537 | height_V, |
---|
| 538 | vel_V, |
---|
| 539 | |
---|
| 540 | stage_boundary_values, |
---|
| 541 | xmom_boundary_values, |
---|
| 542 | bed_boundary_values, |
---|
| 543 | height_boundary_values, |
---|
| 544 | vel_boundary_values, |
---|
| 545 | |
---|
| 546 | stage_explicit_update, |
---|
| 547 | xmom_explicit_update, |
---|
| 548 | bed_explicit_values, |
---|
| 549 | height_explicit_values, |
---|
| 550 | vel_explicit_values, |
---|
| 551 | |
---|
| 552 | number_of_elements, |
---|
| 553 | max_speed_array) |
---|
| 554 | |
---|
| 555 | |
---|
| 556 | # ################################### |
---|
| 557 | # Module functions for gradient limiting (distribute_to_vertices_and_edges) |
---|
| 558 | |
---|
| 559 | def distribute_to_vertices_and_edges_shv(domain): |
---|
| 560 | """Distribution from centroids to vertices specific to the |
---|
| 561 | shallow water wave |
---|
| 562 | equation. |
---|
| 563 | |
---|
| 564 | It will ensure that h (w-z) is always non-negative even in the |
---|
| 565 | presence of steep bed-slopes by taking a weighted average between shallow |
---|
| 566 | and deep cases. |
---|
| 567 | |
---|
| 568 | In addition, all conserved quantities get distributed as per either a |
---|
| 569 | constant (order==1) or a piecewise linear function (order==2). |
---|
| 570 | |
---|
| 571 | FIXME: more explanation about removal of artificial variability etc |
---|
| 572 | |
---|
| 573 | Precondition: |
---|
| 574 | All quantities defined at centroids and bed elevation defined at |
---|
| 575 | vertices. |
---|
| 576 | |
---|
| 577 | Postcondition |
---|
| 578 | Conserved quantities defined at vertices |
---|
| 579 | |
---|
| 580 | """ |
---|
| 581 | |
---|
| 582 | #from config import optimised_gradient_limiter |
---|
| 583 | |
---|
| 584 | #Remove very thin layers of water |
---|
| 585 | #protect_against_infinitesimal_and_negative_heights(domain) |
---|
| 586 | |
---|
| 587 | import sys |
---|
[7914] | 588 | from Numeric import Float |
---|
| 589 | from numpy import zeros |
---|
[7837] | 590 | from config import epsilon, h0 |
---|
| 591 | |
---|
| 592 | N = domain.number_of_elements |
---|
| 593 | |
---|
| 594 | #Shortcuts |
---|
| 595 | Stage = domain.quantities['stage'] |
---|
| 596 | Xmom = domain.quantities['xmomentum'] |
---|
| 597 | Bed = domain.quantities['elevation'] |
---|
| 598 | Height = domain.quantities['height'] |
---|
| 599 | Velocity = domain.quantities['velocity'] |
---|
| 600 | |
---|
| 601 | #Arrays |
---|
| 602 | w_C = Stage.centroid_values |
---|
| 603 | uh_C = Xmom.centroid_values |
---|
| 604 | z_C = Bed.centroid_values |
---|
| 605 | h_C = Height.centroid_values |
---|
| 606 | u_C = Velocity.centroid_values |
---|
| 607 | |
---|
| 608 | for i in range(N): |
---|
| 609 | h_C[i] = w_C[i] - z_C[i] |
---|
| 610 | if h_C[i] <= epsilon: |
---|
| 611 | uh_C[i] = 0.0 |
---|
| 612 | u_C[i] = 0.0 |
---|
| 613 | w_C[i] = z_C[i] |
---|
| 614 | else: |
---|
| 615 | u_C[i] = uh_C[i]/(h_C[i] + h0/h_C[i]) |
---|
| 616 | |
---|
| 617 | for name in ['stage', 'height', 'velocity']: |
---|
| 618 | Q = domain.quantities[name] |
---|
| 619 | if domain.order == 1: |
---|
| 620 | Q.extrapolate_first_order() |
---|
| 621 | elif domain.order == 2: |
---|
| 622 | Q.extrapolate_second_order() |
---|
| 623 | else: |
---|
| 624 | raise 'Unknown order' |
---|
| 625 | |
---|
| 626 | stage_V = domain.quantities['stage'].vertex_values |
---|
| 627 | bed_V = domain.quantities['elevation'].vertex_values |
---|
| 628 | h_V = domain.quantities['height'].vertex_values |
---|
| 629 | u_V = domain.quantities['velocity'].vertex_values |
---|
| 630 | xmom_V = domain.quantities['xmomentum'].vertex_values |
---|
| 631 | |
---|
| 632 | bed_V[:] = stage_V - h_V |
---|
| 633 | xmom_V[:] = u_V * h_V |
---|
| 634 | |
---|
| 635 | return |
---|
| 636 | |
---|
| 637 | |
---|
| 638 | |
---|
| 639 | def distribute_to_vertices_and_edges_shm(domain): |
---|
| 640 | # shm stands for STAGE, HEIGHT, MOMENTUM |
---|
| 641 | """Distribution from centroids to vertices specific to the |
---|
| 642 | shallow water wave |
---|
| 643 | equation. |
---|
| 644 | |
---|
| 645 | It will ensure that h (w-z) is always non-negative even in the |
---|
| 646 | presence of steep bed-slopes by taking a weighted average between shallow |
---|
| 647 | and deep cases. |
---|
| 648 | |
---|
| 649 | In addition, all conserved quantities get distributed as per either a |
---|
| 650 | constant (order==1) or a piecewise linear function (order==2). |
---|
| 651 | |
---|
| 652 | FIXME: more explanation about removal of artificial variability etc |
---|
| 653 | |
---|
| 654 | Precondition: |
---|
| 655 | All quantities defined at centroids and bed elevation defined at |
---|
| 656 | vertices. |
---|
| 657 | |
---|
| 658 | Postcondition |
---|
| 659 | Conserved quantities defined at vertices |
---|
| 660 | |
---|
| 661 | """ |
---|
| 662 | |
---|
| 663 | #from config import optimised_gradient_limiter |
---|
| 664 | |
---|
| 665 | #Remove very thin layers of water |
---|
| 666 | #protect_against_infinitesimal_and_negative_heights(domain) |
---|
| 667 | |
---|
| 668 | import sys |
---|
[7914] | 669 | from Numeric import Float |
---|
| 670 | from numpy import zeros |
---|
[7837] | 671 | from config import epsilon, h0 |
---|
| 672 | |
---|
| 673 | N = domain.number_of_elements |
---|
| 674 | |
---|
| 675 | #Shortcuts |
---|
| 676 | Stage = domain.quantities['stage'] |
---|
| 677 | Xmom = domain.quantities['xmomentum'] |
---|
| 678 | Bed = domain.quantities['elevation'] |
---|
| 679 | Height = domain.quantities['height'] |
---|
| 680 | Velocity = domain.quantities['velocity'] |
---|
| 681 | |
---|
| 682 | #Arrays |
---|
| 683 | w_C = Stage.centroid_values |
---|
| 684 | uh_C = Xmom.centroid_values |
---|
| 685 | z_C = Bed.centroid_values |
---|
| 686 | h_C = Height.centroid_values |
---|
| 687 | u_C = Velocity.centroid_values |
---|
| 688 | |
---|
| 689 | for i in range(N): |
---|
| 690 | h_C[i] = w_C[i] - z_C[i] |
---|
| 691 | if h_C[i] <= 0.01: #epsilon : |
---|
| 692 | #h_C[i] = 0.0 |
---|
| 693 | #w_C[i] = z_C[i] |
---|
| 694 | uh_C[i] = 0.0 |
---|
| 695 | u_C[i] = 0.0 |
---|
| 696 | |
---|
| 697 | if h_C[i] < epsilon: |
---|
| 698 | h_C[i] = 0.0 |
---|
| 699 | w_C[i] = z_C[i] |
---|
| 700 | else: |
---|
| 701 | u_C[i] = uh_C[i]/h_C[i] #+ h0/h_C[i]) |
---|
| 702 | |
---|
| 703 | for name in ['stage', 'height', 'xmomentum']: |
---|
| 704 | Q = domain.quantities[name] |
---|
| 705 | if domain.order == 1: |
---|
| 706 | Q.extrapolate_first_order() |
---|
| 707 | elif domain.order == 2: |
---|
| 708 | Q.extrapolate_second_order() |
---|
| 709 | else: |
---|
| 710 | raise 'Unknown order' |
---|
| 711 | |
---|
| 712 | stage_V = domain.quantities['stage'].vertex_values |
---|
| 713 | bed_V = domain.quantities['elevation'].vertex_values |
---|
| 714 | h_V = domain.quantities['height'].vertex_values |
---|
| 715 | u_V = domain.quantities['velocity'].vertex_values |
---|
| 716 | xmom_V = domain.quantities['xmomentum'].vertex_values |
---|
| 717 | |
---|
| 718 | bed_V[:] = stage_V - h_V |
---|
| 719 | |
---|
| 720 | for i in range(N): |
---|
| 721 | if h_V[i] <= 0.0: |
---|
| 722 | h_V[i] = 0.0 |
---|
| 723 | stage_V[i] = bed_V[i] |
---|
| 724 | xmom_V[i] = 0.0 |
---|
| 725 | |
---|
| 726 | u_V[:] = xmom_V/(h_V + h0/h_V) |
---|
| 727 | |
---|
| 728 | return |
---|
| 729 | |
---|
| 730 | |
---|
| 731 | |
---|
| 732 | |
---|
| 733 | |
---|
| 734 | # |
---|
| 735 | def protect_against_infinitesimal_and_negative_heights(domain): |
---|
| 736 | """Protect against infinitesimal heights and associated high velocities |
---|
| 737 | """ |
---|
| 738 | |
---|
| 739 | #Shortcuts |
---|
| 740 | wc = domain.quantities['stage'].centroid_values |
---|
| 741 | zc = domain.quantities['elevation'].centroid_values |
---|
| 742 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
| 743 | hc = wc - zc #Water depths at centroids |
---|
| 744 | |
---|
| 745 | zv = domain.quantities['elevation'].vertex_values |
---|
| 746 | wv = domain.quantities['stage'].vertex_values |
---|
| 747 | hv = wv-zv |
---|
| 748 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
| 749 | #remove the above two lines and corresponding code below |
---|
| 750 | |
---|
| 751 | #Update |
---|
| 752 | for k in range(domain.number_of_elements): |
---|
| 753 | |
---|
| 754 | if hc[k] < domain.minimum_allowed_height: |
---|
| 755 | #Control stage |
---|
| 756 | if hc[k] < domain.epsilon: |
---|
| 757 | wc[k] = zc[k] # Contain 'lost mass' error |
---|
| 758 | wv[k,0] = zv[k,0] |
---|
| 759 | wv[k,1] = zv[k,1] |
---|
| 760 | |
---|
| 761 | xmomc[k] = 0.0 |
---|
| 762 | |
---|
| 763 | |
---|
| 764 | def h_limiter(domain): |
---|
| 765 | """Limit slopes for each volume to eliminate artificial variance |
---|
| 766 | introduced by e.g. second order extrapolator |
---|
| 767 | |
---|
| 768 | limit on h = w-z |
---|
| 769 | |
---|
| 770 | This limiter depends on two quantities (w,z) so it resides within |
---|
| 771 | this module rather than within quantity.py |
---|
| 772 | """ |
---|
| 773 | |
---|
[7914] | 774 | from Numeric import Float |
---|
| 775 | from numpy import zeros |
---|
[7837] | 776 | |
---|
| 777 | N = domain.number_of_elements |
---|
| 778 | beta_h = domain.beta_h |
---|
| 779 | |
---|
| 780 | #Shortcuts |
---|
| 781 | wc = domain.quantities['stage'].centroid_values |
---|
| 782 | zc = domain.quantities['elevation'].centroid_values |
---|
| 783 | hc = wc - zc |
---|
| 784 | |
---|
| 785 | wv = domain.quantities['stage'].vertex_values |
---|
| 786 | zv = domain.quantities['elevation'].vertex_values |
---|
| 787 | hv = wv-zv |
---|
| 788 | |
---|
| 789 | hvbar = zeros(hv.shape, Float) #h-limited values |
---|
| 790 | |
---|
| 791 | #Find min and max of this and neighbour's centroid values |
---|
| 792 | hmax = zeros(hc.shape, Float) |
---|
| 793 | hmin = zeros(hc.shape, Float) |
---|
| 794 | |
---|
| 795 | for k in range(N): |
---|
| 796 | hmax[k] = hmin[k] = hc[k] |
---|
| 797 | for i in range(2): |
---|
| 798 | n = domain.neighbours[k,i] |
---|
| 799 | if n >= 0: |
---|
| 800 | hn = hc[n] #Neighbour's centroid value |
---|
| 801 | |
---|
| 802 | hmin[k] = min(hmin[k], hn) |
---|
| 803 | hmax[k] = max(hmax[k], hn) |
---|
| 804 | |
---|
| 805 | |
---|
| 806 | #Diffences between centroids and maxima/minima |
---|
| 807 | dhmax = hmax - hc |
---|
| 808 | dhmin = hmin - hc |
---|
| 809 | |
---|
| 810 | #Deltas between vertex and centroid values |
---|
| 811 | dh = zeros(hv.shape, Float) |
---|
| 812 | for i in range(2): |
---|
| 813 | dh[:,i] = hv[:,i] - hc |
---|
| 814 | |
---|
| 815 | #Phi limiter |
---|
| 816 | for k in range(N): |
---|
| 817 | |
---|
| 818 | #Find the gradient limiter (phi) across vertices |
---|
| 819 | phi = 1.0 |
---|
| 820 | for i in range(2): |
---|
| 821 | r = 1.0 |
---|
| 822 | if (dh[k,i] > 0): r = dhmax[k]/dh[k,i] |
---|
| 823 | if (dh[k,i] < 0): r = dhmin[k]/dh[k,i] |
---|
| 824 | |
---|
| 825 | phi = min( min(r*beta_h, 1), phi ) |
---|
| 826 | |
---|
| 827 | #Then update using phi limiter |
---|
| 828 | for i in range(2): |
---|
| 829 | hvbar[k,i] = hc[k] + phi*dh[k,i] |
---|
| 830 | |
---|
| 831 | return hvbar |
---|
| 832 | |
---|
| 833 | def balance_deep_and_shallow(domain): |
---|
| 834 | """Compute linear combination between stage as computed by |
---|
| 835 | gradient-limiters limiting using w, and stage computed by |
---|
| 836 | gradient-limiters limiting using h (h-limiter). |
---|
| 837 | The former takes precedence when heights are large compared to the |
---|
| 838 | bed slope while the latter takes precedence when heights are |
---|
| 839 | relatively small. Anything in between is computed as a balanced |
---|
| 840 | linear combination in order to avoid numerical disturbances which |
---|
| 841 | would otherwise appear as a result of hard switching between |
---|
| 842 | modes. |
---|
| 843 | |
---|
| 844 | The h-limiter is always applied irrespective of the order. |
---|
| 845 | """ |
---|
| 846 | |
---|
| 847 | #Shortcuts |
---|
| 848 | wc = domain.quantities['stage'].centroid_values |
---|
| 849 | zc = domain.quantities['elevation'].centroid_values |
---|
| 850 | hc = wc - zc |
---|
| 851 | |
---|
| 852 | wv = domain.quantities['stage'].vertex_values |
---|
| 853 | zv = domain.quantities['elevation'].vertex_values |
---|
| 854 | hv = wv-zv |
---|
| 855 | |
---|
| 856 | #Limit h |
---|
| 857 | hvbar = h_limiter(domain) |
---|
| 858 | |
---|
| 859 | for k in range(domain.number_of_elements): |
---|
| 860 | #Compute maximal variation in bed elevation |
---|
| 861 | # This quantitiy is |
---|
| 862 | # dz = max_i abs(z_i - z_c) |
---|
| 863 | # and it is independent of dimension |
---|
| 864 | # In the 1d case zc = (z0+z1)/2 |
---|
| 865 | # In the 2d case zc = (z0+z1+z2)/3 |
---|
| 866 | |
---|
| 867 | dz = max(abs(zv[k,0]-zc[k]), |
---|
| 868 | abs(zv[k,1]-zc[k]))#, |
---|
| 869 | # abs(zv[k,2]-zc[k])) |
---|
| 870 | |
---|
| 871 | |
---|
| 872 | hmin = min( hv[k,:] ) |
---|
| 873 | |
---|
| 874 | #Create alpha in [0,1], where alpha==0 means using the h-limited |
---|
| 875 | #stage and alpha==1 means using the w-limited stage as |
---|
| 876 | #computed by the gradient limiter (both 1st or 2nd order) |
---|
| 877 | |
---|
| 878 | #If hmin > dz/2 then alpha = 1 and the bed will have no effect |
---|
| 879 | #If hmin < 0 then alpha = 0 reverting to constant height above bed. |
---|
| 880 | |
---|
| 881 | if dz > 0.0: |
---|
| 882 | alpha = max( min( 2*hmin/dz, 1.0), 0.0 ) |
---|
| 883 | else: |
---|
| 884 | #Flat bed |
---|
| 885 | alpha = 1.0 |
---|
| 886 | |
---|
| 887 | alpha = 0.0 |
---|
| 888 | #Let |
---|
| 889 | # |
---|
| 890 | # wvi be the w-limited stage (wvi = zvi + hvi) |
---|
| 891 | # wvi- be the h-limited state (wvi- = zvi + hvi-) |
---|
| 892 | # |
---|
| 893 | # |
---|
| 894 | #where i=0,1,2 denotes the vertex ids |
---|
| 895 | # |
---|
| 896 | #Weighted balance between w-limited and h-limited stage is |
---|
| 897 | # |
---|
| 898 | # wvi := (1-alpha)*(zvi+hvi-) + alpha*(zvi+hvi) |
---|
| 899 | # |
---|
| 900 | #It follows that the updated wvi is |
---|
| 901 | # wvi := zvi + (1-alpha)*hvi- + alpha*hvi |
---|
| 902 | # |
---|
| 903 | # Momentum is balanced between constant and limited |
---|
| 904 | |
---|
| 905 | |
---|
| 906 | #for i in range(3): |
---|
| 907 | # wv[k,i] = zv[k,i] + hvbar[k,i] |
---|
| 908 | |
---|
| 909 | #return |
---|
| 910 | |
---|
| 911 | if alpha < 1: |
---|
| 912 | |
---|
| 913 | #for i in range(3): |
---|
| 914 | for i in range(2): |
---|
| 915 | wv[k,i] = zv[k,i] + (1.0-alpha)*hvbar[k,i] + alpha*hv[k,i] |
---|
| 916 | |
---|
| 917 | #Momentums at centroids |
---|
| 918 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
| 919 | |
---|
| 920 | |
---|
| 921 | #Momentums at vertices |
---|
| 922 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
| 923 | |
---|
| 924 | |
---|
| 925 | # Update momentum as a linear combination of |
---|
| 926 | # xmomc and ymomc (shallow) and momentum |
---|
| 927 | # from extrapolator xmomv and ymomv (deep). |
---|
| 928 | xmomv[k,:] = (1.0-alpha)*xmomc[k] + alpha*xmomv[k,:] |
---|
| 929 | |
---|
| 930 | |
---|
| 931 | |
---|
| 932 | |
---|
| 933 | |
---|
| 934 | ######################### |
---|
| 935 | #Standard forcing terms: |
---|
| 936 | # |
---|
| 937 | def gravity(domain): |
---|
| 938 | """Apply gravitational pull in the presence of bed slope |
---|
| 939 | """ |
---|
| 940 | |
---|
| 941 | from util import gradient |
---|
[7914] | 942 | from Numeric import Float |
---|
| 943 | from numpy import zeros, array, sum |
---|
[7837] | 944 | |
---|
| 945 | xmom = domain.quantities['xmomentum'].explicit_update |
---|
| 946 | stage = domain.quantities['stage'].explicit_update |
---|
| 947 | |
---|
| 948 | Stage = domain.quantities['stage'] |
---|
| 949 | Elevation = domain.quantities['elevation'] |
---|
| 950 | h = Stage.vertex_values - Elevation.vertex_values |
---|
| 951 | b = Elevation.vertex_values |
---|
| 952 | w = Stage.vertex_values |
---|
| 953 | |
---|
| 954 | x = domain.get_vertex_coordinates() |
---|
| 955 | g = domain.g |
---|
| 956 | |
---|
| 957 | for k in range(domain.number_of_elements): |
---|
| 958 | avg_h = sum( h[k,:] )/2 |
---|
| 959 | |
---|
| 960 | #Compute bed slope |
---|
| 961 | x0, x1 = x[k,:] |
---|
| 962 | b0, b1 = b[k,:] |
---|
| 963 | |
---|
| 964 | w0, w1 = w[k,:] |
---|
| 965 | wx = gradient(x0, x1, w0, w1) |
---|
| 966 | bx = gradient(x0, x1, b0, b1) |
---|
| 967 | |
---|
| 968 | #Update momentum (explicit update is reset to source values) |
---|
| 969 | xmom[k] += -g*bx*avg_h |
---|
| 970 | |
---|
| 971 | |
---|
| 972 | def gravity_F1(domain): |
---|
| 973 | """Apply gravitational pull in the presence of bed slope |
---|
| 974 | """ |
---|
| 975 | |
---|
| 976 | from util import gradient |
---|
[7914] | 977 | from Numeric import Float |
---|
| 978 | from numpy import zeros, array, sum |
---|
[7837] | 979 | from parameters import F1#This is an additional friction!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
---|
| 980 | |
---|
| 981 | xmom = domain.quantities['xmomentum'].explicit_update |
---|
| 982 | stage = domain.quantities['stage'].explicit_update |
---|
| 983 | |
---|
| 984 | Stage = domain.quantities['stage'] |
---|
| 985 | Elevation = domain.quantities['elevation'] |
---|
| 986 | h = Stage.vertex_values - Elevation.vertex_values |
---|
| 987 | b = Elevation.vertex_values |
---|
| 988 | w = Stage.vertex_values |
---|
| 989 | |
---|
| 990 | x = domain.get_vertex_coordinates() |
---|
| 991 | g = domain.g |
---|
| 992 | |
---|
| 993 | for k in range(domain.number_of_elements): |
---|
| 994 | avg_h = sum( h[k,:] )/2 |
---|
| 995 | |
---|
| 996 | #Compute bed slope |
---|
| 997 | x0, x1 = x[k,:] |
---|
| 998 | b0, b1 = b[k,:] |
---|
| 999 | |
---|
| 1000 | w0, w1 = w[k,:] |
---|
| 1001 | wx = gradient(x0, x1, w0, w1) |
---|
| 1002 | bx = gradient(x0, x1, b0, b1) |
---|
| 1003 | |
---|
| 1004 | #Update momentum (explicit update is reset to source values) |
---|
| 1005 | xmom[k] += -g*bx*avg_h + avg_h*F1#This is an additional friction!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
---|
| 1006 | |
---|
| 1007 | |
---|
| 1008 | |
---|
| 1009 | def gravity_F2(domain): |
---|
| 1010 | """Apply gravitational pull in the presence of bed slope |
---|
| 1011 | """ |
---|
| 1012 | |
---|
| 1013 | from util import gradient |
---|
[7914] | 1014 | from Numeric import Float |
---|
| 1015 | from numpy import zeros, array, sum |
---|
[7837] | 1016 | from parameters import F2#This is an additional friction!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
---|
| 1017 | |
---|
| 1018 | xmom = domain.quantities['xmomentum'].explicit_update |
---|
| 1019 | stage = domain.quantities['stage'].explicit_update |
---|
| 1020 | |
---|
| 1021 | Stage = domain.quantities['stage'] |
---|
| 1022 | Elevation = domain.quantities['elevation'] |
---|
| 1023 | h = Stage.vertex_values - Elevation.vertex_values |
---|
| 1024 | b = Elevation.vertex_values |
---|
| 1025 | w = Stage.vertex_values |
---|
| 1026 | |
---|
| 1027 | x = domain.get_vertex_coordinates() |
---|
| 1028 | g = domain.g |
---|
| 1029 | |
---|
| 1030 | for k in range(domain.number_of_elements): |
---|
| 1031 | avg_h = sum( h[k,:] )/2 |
---|
| 1032 | |
---|
| 1033 | #Compute bed slope |
---|
| 1034 | x0, x1 = x[k,:] |
---|
| 1035 | b0, b1 = b[k,:] |
---|
| 1036 | |
---|
| 1037 | w0, w1 = w[k,:] |
---|
| 1038 | wx = gradient(x0, x1, w0, w1) |
---|
| 1039 | bx = gradient(x0, x1, b0, b1) |
---|
| 1040 | |
---|
| 1041 | #Update momentum (explicit update is reset to source values) |
---|
| 1042 | xmom[k] += -g*bx*avg_h + avg_h*F2#This is an additional friction!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
---|
| 1043 | |
---|
| 1044 | |
---|
| 1045 | |
---|
| 1046 | |
---|
| 1047 | |
---|
| 1048 | def manning_friction(domain): |
---|
| 1049 | """Apply (Manning) friction to water momentum |
---|
| 1050 | """ |
---|
| 1051 | |
---|
| 1052 | from math import sqrt |
---|
| 1053 | |
---|
| 1054 | w = domain.quantities['stage'].centroid_values |
---|
| 1055 | z = domain.quantities['elevation'].centroid_values |
---|
| 1056 | h = w-z |
---|
| 1057 | |
---|
| 1058 | uh = domain.quantities['xmomentum'].centroid_values |
---|
| 1059 | eta = domain.quantities['friction'].centroid_values |
---|
| 1060 | |
---|
| 1061 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
---|
| 1062 | |
---|
| 1063 | N = domain.number_of_elements |
---|
| 1064 | eps = domain.minimum_allowed_height |
---|
| 1065 | g = domain.g |
---|
| 1066 | |
---|
| 1067 | for k in range(N): |
---|
| 1068 | if eta[k] >= eps: |
---|
| 1069 | if h[k] >= eps: |
---|
| 1070 | S = -g * eta[k]**2 * uh[k] |
---|
| 1071 | S /= h[k]**(7.0/3) |
---|
| 1072 | |
---|
| 1073 | #Update momentum |
---|
| 1074 | xmom_update[k] += S*uh[k] |
---|
| 1075 | |
---|
| 1076 | def linear_friction(domain): |
---|
| 1077 | """Apply linear friction to water momentum |
---|
| 1078 | |
---|
| 1079 | Assumes quantity: 'linear_friction' to be present |
---|
| 1080 | """ |
---|
| 1081 | |
---|
| 1082 | from math import sqrt |
---|
| 1083 | |
---|
| 1084 | w = domain.quantities['stage'].centroid_values |
---|
| 1085 | z = domain.quantities['elevation'].centroid_values |
---|
| 1086 | h = w-z |
---|
| 1087 | |
---|
| 1088 | uh = domain.quantities['xmomentum'].centroid_values |
---|
| 1089 | tau = domain.quantities['linear_friction'].centroid_values |
---|
| 1090 | |
---|
| 1091 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
---|
| 1092 | |
---|
| 1093 | N = domain.number_of_elements |
---|
| 1094 | eps = domain.minimum_allowed_height |
---|
| 1095 | g = domain.g #Not necessary? Why was this added? |
---|
| 1096 | |
---|
| 1097 | for k in range(N): |
---|
| 1098 | if tau[k] >= eps: |
---|
| 1099 | if h[k] >= eps: |
---|
| 1100 | S = -tau[k]/h[k] |
---|
| 1101 | |
---|
| 1102 | #Update momentum |
---|
| 1103 | xmom_update[k] += S*uh[k] |
---|
| 1104 | |
---|
| 1105 | |
---|
| 1106 | |
---|
| 1107 | def check_forcefield(f): |
---|
| 1108 | """Check that f is either |
---|
| 1109 | 1: a callable object f(t,x,y), where x and y are vectors |
---|
| 1110 | and that it returns an array or a list of same length |
---|
| 1111 | as x and y |
---|
| 1112 | 2: a scalar |
---|
| 1113 | """ |
---|
| 1114 | |
---|
[7914] | 1115 | from Numeric import Float |
---|
| 1116 | from numpy import ones, array |
---|
[7837] | 1117 | |
---|
| 1118 | |
---|
| 1119 | if callable(f): |
---|
| 1120 | N = 2 |
---|
| 1121 | x = ones(2, Float) |
---|
| 1122 | |
---|
| 1123 | try: |
---|
| 1124 | q = f(1.0, x=x) |
---|
| 1125 | except Exception, e: |
---|
| 1126 | msg = 'Function %s could not be executed:\n%s' %(f, e) |
---|
| 1127 | #FIXME: Reconsider this semantics |
---|
| 1128 | raise msg |
---|
| 1129 | |
---|
| 1130 | try: |
---|
| 1131 | q = array(q).astype(Float) |
---|
| 1132 | except: |
---|
| 1133 | msg = 'Return value from vector function %s could ' %f |
---|
| 1134 | msg += 'not be converted into a Numeric array of floats.\n' |
---|
| 1135 | msg += 'Specified function should return either list or array.' |
---|
| 1136 | raise msg |
---|
| 1137 | |
---|
| 1138 | #Is this really what we want? |
---|
| 1139 | msg = 'Return vector from function %s ' %f |
---|
| 1140 | msg += 'must have same lenght as input vectors' |
---|
| 1141 | assert len(q) == N, msg |
---|
| 1142 | |
---|
| 1143 | else: |
---|
| 1144 | try: |
---|
| 1145 | f = float(f) |
---|
| 1146 | except: |
---|
| 1147 | msg = 'Force field %s must be either a scalar' %f |
---|
| 1148 | msg += ' or a vector function' |
---|
| 1149 | raise msg |
---|
| 1150 | return f |
---|
| 1151 | |
---|
| 1152 | class Wind_stress: |
---|
| 1153 | """Apply wind stress to water momentum in terms of |
---|
| 1154 | wind speed [m/s] and wind direction [degrees] |
---|
| 1155 | """ |
---|
| 1156 | |
---|
| 1157 | def __init__(self, *args, **kwargs): |
---|
| 1158 | """Initialise windfield from wind speed s [m/s] |
---|
| 1159 | and wind direction phi [degrees] |
---|
| 1160 | |
---|
| 1161 | Inputs v and phi can be either scalars or Python functions, e.g. |
---|
| 1162 | |
---|
| 1163 | W = Wind_stress(10, 178) |
---|
| 1164 | |
---|
| 1165 | #FIXME - 'normal' degrees are assumed for now, i.e. the |
---|
| 1166 | vector (1,0) has zero degrees. |
---|
| 1167 | We may need to convert from 'compass' degrees later on and also |
---|
| 1168 | map from True north to grid north. |
---|
| 1169 | |
---|
| 1170 | Arguments can also be Python functions of t,x,y as in |
---|
| 1171 | |
---|
| 1172 | def speed(t,x,y): |
---|
| 1173 | ... |
---|
| 1174 | return s |
---|
| 1175 | |
---|
| 1176 | def angle(t,x,y): |
---|
| 1177 | ... |
---|
| 1178 | return phi |
---|
| 1179 | |
---|
| 1180 | where x and y are vectors. |
---|
| 1181 | |
---|
| 1182 | and then pass the functions in |
---|
| 1183 | |
---|
| 1184 | W = Wind_stress(speed, angle) |
---|
| 1185 | |
---|
| 1186 | The instantiated object W can be appended to the list of |
---|
| 1187 | forcing_terms as in |
---|
| 1188 | |
---|
| 1189 | Alternatively, one vector valued function for (speed, angle) |
---|
| 1190 | can be applied, providing both quantities simultaneously. |
---|
| 1191 | As in |
---|
| 1192 | W = Wind_stress(F), where returns (speed, angle) for each t. |
---|
| 1193 | |
---|
| 1194 | domain.forcing_terms.append(W) |
---|
| 1195 | """ |
---|
| 1196 | |
---|
| 1197 | from config import rho_a, rho_w, eta_w |
---|
[7914] | 1198 | from Numeric import Float |
---|
| 1199 | from numpy import array |
---|
[7837] | 1200 | |
---|
| 1201 | if len(args) == 2: |
---|
| 1202 | s = args[0] |
---|
| 1203 | phi = args[1] |
---|
| 1204 | elif len(args) == 1: |
---|
| 1205 | #Assume vector function returning (s, phi)(t,x,y) |
---|
| 1206 | vector_function = args[0] |
---|
| 1207 | s = lambda t,x: vector_function(t,x=x)[0] |
---|
| 1208 | phi = lambda t,x: vector_function(t,x=x)[1] |
---|
| 1209 | else: |
---|
| 1210 | #Assume info is in 2 keyword arguments |
---|
| 1211 | |
---|
| 1212 | if len(kwargs) == 2: |
---|
| 1213 | s = kwargs['s'] |
---|
| 1214 | phi = kwargs['phi'] |
---|
| 1215 | else: |
---|
| 1216 | raise 'Assumes two keyword arguments: s=..., phi=....' |
---|
| 1217 | |
---|
| 1218 | print 'phi', phi |
---|
| 1219 | self.speed = check_forcefield(s) |
---|
| 1220 | self.phi = check_forcefield(phi) |
---|
| 1221 | |
---|
| 1222 | self.const = eta_w*rho_a/rho_w |
---|
| 1223 | |
---|
| 1224 | |
---|
| 1225 | def __call__(self, domain): |
---|
| 1226 | """Evaluate windfield based on values found in domain |
---|
| 1227 | """ |
---|
| 1228 | |
---|
| 1229 | from math import pi, cos, sin, sqrt |
---|
[7914] | 1230 | from Numeric import Float, ArrayType |
---|
| 1231 | from numpy import ones |
---|
[7837] | 1232 | |
---|
| 1233 | xmom_update = domain.quantities['xmomentum'].explicit_update |
---|
| 1234 | |
---|
| 1235 | N = domain.number_of_elements |
---|
| 1236 | t = domain.time |
---|
| 1237 | |
---|
| 1238 | if callable(self.speed): |
---|
| 1239 | xc = domain.get_centroid_coordinates() |
---|
| 1240 | s_vec = self.speed(t, xc) |
---|
| 1241 | else: |
---|
| 1242 | #Assume s is a scalar |
---|
| 1243 | |
---|
| 1244 | try: |
---|
| 1245 | s_vec = self.speed * ones(N, Float) |
---|
| 1246 | except: |
---|
| 1247 | msg = 'Speed must be either callable or a scalar: %s' %self.s |
---|
| 1248 | raise msg |
---|
| 1249 | |
---|
| 1250 | |
---|
| 1251 | if callable(self.phi): |
---|
| 1252 | xc = domain.get_centroid_coordinates() |
---|
| 1253 | phi_vec = self.phi(t, xc) |
---|
| 1254 | else: |
---|
| 1255 | #Assume phi is a scalar |
---|
| 1256 | |
---|
| 1257 | try: |
---|
| 1258 | phi_vec = self.phi * ones(N, Float) |
---|
| 1259 | except: |
---|
| 1260 | msg = 'Angle must be either callable or a scalar: %s' %self.phi |
---|
| 1261 | raise msg |
---|
| 1262 | |
---|
| 1263 | #assign_windfield_values(xmom_update, ymom_update, |
---|
| 1264 | # s_vec, phi_vec, self.const) |
---|
| 1265 | assign_windfield_values(xmom_update, s_vec, phi_vec, self.const) |
---|
| 1266 | |
---|
| 1267 | |
---|
| 1268 | #def assign_windfield_values(xmom_update, ymom_update, |
---|
| 1269 | # s_vec, phi_vec, const): |
---|
| 1270 | def assign_windfield_values(xmom_update, s_vec, phi_vec, const): |
---|
| 1271 | """Python version of assigning wind field to update vectors. |
---|
| 1272 | A c version also exists (for speed) |
---|
| 1273 | """ |
---|
| 1274 | from math import pi, cos, sin, sqrt |
---|
| 1275 | |
---|
| 1276 | N = len(s_vec) |
---|
| 1277 | for k in range(N): |
---|
| 1278 | s = s_vec[k] |
---|
| 1279 | phi = phi_vec[k] |
---|
| 1280 | |
---|
| 1281 | #Convert to radians |
---|
| 1282 | phi = phi*pi/180 |
---|
| 1283 | |
---|
| 1284 | #Compute velocity vector (u, v) |
---|
| 1285 | u = s*cos(phi) |
---|
| 1286 | v = s*sin(phi) |
---|
| 1287 | |
---|
| 1288 | #Compute wind stress |
---|
| 1289 | S = const * u |
---|
| 1290 | xmom_update[k] += S*u |
---|