| 1 | import sys |
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| 2 | from os import sep |
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| 3 | sys.path.append('..'+sep+'pyvolution') |
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| 4 | |
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| 5 | """Class Domain - |
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| 6 | 2D triangular domains for finite-volume computations of |
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| 7 | the advection equation. |
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| 8 | |
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| 9 | This module contains a specialisation of class Domain from module domain.py |
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| 10 | consisting of methods specific to the advection equantion |
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| 11 | |
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| 12 | The equation is |
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| 13 | |
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| 14 | u_t + (v_1 u)_x + (v_2 u)_y = 0 |
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| 15 | |
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| 16 | There is only one conserved quantity, the stage u |
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| 17 | |
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| 18 | The advection equation is a very simple specialisation of the generic |
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| 19 | domain and may serve as an instructive example or a test of other |
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| 20 | components such as visualisation. |
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| 21 | |
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| 22 | Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
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| 23 | Geoscience Australia, 2004 |
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| 24 | """ |
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| 25 | |
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| 26 | |
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| 27 | import logging, logging.config |
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| 28 | logger = logging.getLogger('advection') |
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| 29 | logger.setLevel(logging.WARNING) |
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| 30 | |
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| 31 | try: |
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| 32 | logging.config.fileConfig('log.ini') |
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| 33 | except: |
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| 34 | pass |
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| 35 | |
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| 36 | |
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| 37 | from domain import * |
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| 38 | Generic_domain = Domain #Rename |
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| 39 | |
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| 40 | class Domain(Generic_domain): |
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| 41 | |
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| 42 | def __init__(self, |
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| 43 | coordinates, |
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| 44 | vertices, |
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| 45 | boundary = None, |
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| 46 | tagged_elements = None, |
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| 47 | geo_reference = None, |
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| 48 | use_inscribed_circle=False, |
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| 49 | velocity = None, |
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| 50 | full_send_dict=None, |
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| 51 | ghost_recv_dict=None, |
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| 52 | processor=0, |
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| 53 | numproc=1 |
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| 54 | ): |
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| 55 | |
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| 56 | conserved_quantities = ['stage'] |
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| 57 | other_quantities = [] |
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| 58 | Generic_domain.__init__(self, |
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| 59 | source=coordinates, |
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| 60 | triangles=vertices, |
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| 61 | boundary=boundary, |
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| 62 | conserved_quantities=conserved_quantities, |
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| 63 | other_quantities=other_quantities, |
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| 64 | tagged_elements=tagged_elements, |
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| 65 | geo_reference=geo_reference, |
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| 66 | use_inscribed_circle=use_inscribed_circle, |
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| 67 | full_send_dict=full_send_dict, |
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| 68 | ghost_recv_dict=ghost_recv_dict, |
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| 69 | processor=processor, |
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| 70 | numproc=numproc) |
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| 71 | |
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| 72 | |
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| 73 | if velocity is None: |
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| 74 | self.velocity = [1,0] |
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| 75 | else: |
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| 76 | self.velocity = velocity |
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| 77 | |
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| 78 | #Only first is implemented for advection |
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| 79 | self.default_order = self.order = 1 |
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| 80 | |
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| 81 | #Realtime visualisation |
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| 82 | self.visualiser = None |
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| 83 | self.visualise = False |
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| 84 | self.visualise_color_stage = False |
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| 85 | self.visualise_stage_range = 1.0 |
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| 86 | self.visualise_timer = True |
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| 87 | self.visualise_range_z = None |
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| 88 | |
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| 89 | |
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| 90 | self.smooth = True |
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| 91 | |
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| 92 | def initialise_visualiser(self,scale_z=1.0,rect=None): |
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| 93 | #Realtime visualisation |
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| 94 | if self.visualiser is None: |
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| 95 | from realtime_visualisation_new import Visualiser |
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| 96 | # from vtk_realtime_visualiser import Visualiser |
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| 97 | self.visualiser = Visualiser(self,scale_z,rect) |
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| 98 | self.visualise = True |
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| 99 | |
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| 100 | |
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| 101 | def check_integrity(self): |
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| 102 | Generic_domain.check_integrity(self) |
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| 103 | |
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| 104 | msg = 'Conserved quantity must be "stage"' |
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| 105 | assert self.conserved_quantities[0] == 'stage', msg |
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| 106 | |
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| 107 | |
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| 108 | def flux_function(self, normal, ql, qr, zl=None, zr=None): |
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| 109 | """Compute outward flux as inner product between velocity |
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| 110 | vector v=(v_1, v_2) and normal vector n. |
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| 111 | |
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| 112 | if <n,v> > 0 flux direction is outward bound and its magnitude is |
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| 113 | determined by the quantity inside volume: ql. |
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| 114 | Otherwise it is inbound and magnitude is determined by the |
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| 115 | quantity outside the volume: qr. |
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| 116 | """ |
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| 117 | |
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| 118 | v1 = self.velocity[0] |
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| 119 | v2 = self.velocity[1] |
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| 120 | |
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| 121 | |
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| 122 | normal_velocity = v1*normal[0] + v2*normal[1] |
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| 123 | |
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| 124 | if normal_velocity < 0: |
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| 125 | flux = qr * normal_velocity |
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| 126 | else: |
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| 127 | flux = ql * normal_velocity |
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| 128 | |
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| 129 | max_speed = abs(normal_velocity) |
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| 130 | return flux, max_speed |
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| 131 | |
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| 132 | def compute_fluxes(self): |
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| 133 | |
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| 134 | try: |
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| 135 | import weave |
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| 136 | self.weave_available = True |
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| 137 | except: |
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| 138 | self.weave_available = False |
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| 139 | |
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| 140 | if self.weave_available: |
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| 141 | self.compute_fluxes_weave() |
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| 142 | else: |
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| 143 | self.compute_fluxes_python() |
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| 144 | |
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| 145 | |
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| 146 | |
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| 147 | def compute_fluxes_python(self): |
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| 148 | """Compute all fluxes and the timestep suitable for all volumes |
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| 149 | in domain. |
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| 150 | |
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| 151 | Compute total flux for each conserved quantity using "flux_function" |
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| 152 | |
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| 153 | Fluxes across each edge are scaled by edgelengths and summed up |
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| 154 | Resulting flux is then scaled by area and stored in |
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| 155 | domain.explicit_update |
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| 156 | |
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| 157 | The maximal allowable speed computed by the flux_function |
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| 158 | for each volume |
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| 159 | is converted to a timestep that must not be exceeded. The minimum of |
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| 160 | those is computed as the next overall timestep. |
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| 161 | |
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| 162 | Post conditions: |
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| 163 | domain.explicit_update is reset to computed flux values |
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| 164 | domain.timestep is set to the largest step satisfying all volumes. |
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| 165 | """ |
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| 166 | |
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| 167 | import sys |
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| 168 | from Numeric import zeros, Float |
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| 169 | from config import max_timestep |
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| 170 | |
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| 171 | N = self.number_of_elements |
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| 172 | |
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| 173 | neighbours = self.neighbours |
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| 174 | neighbour_edges = self.neighbour_edges |
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| 175 | normals = self.normals |
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| 176 | |
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| 177 | areas = self.areas |
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| 178 | radii = self.radii |
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| 179 | edgelengths = self.edgelengths |
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| 180 | |
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| 181 | timestep = max_timestep #FIXME: Get rid of this |
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| 182 | |
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| 183 | #Shortcuts |
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| 184 | Stage = self.quantities['stage'] |
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| 185 | |
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| 186 | #Arrays |
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| 187 | stage = Stage.edge_values |
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| 188 | |
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| 189 | stage_bdry = Stage.boundary_values |
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| 190 | |
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| 191 | flux = zeros(1, Float) #Work array for summing up fluxes |
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| 192 | |
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| 193 | #Loop |
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| 194 | for k in range(N): |
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| 195 | optimal_timestep = float(sys.maxint) |
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| 196 | |
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| 197 | flux[:] = 0. #Reset work array |
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| 198 | for i in range(3): |
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| 199 | #Quantities inside volume facing neighbour i |
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| 200 | ql = stage[k, i] |
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| 201 | |
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| 202 | #Quantities at neighbour on nearest face |
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| 203 | n = neighbours[k,i] |
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| 204 | if n < 0: |
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| 205 | m = -n-1 #Convert neg flag to index |
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| 206 | qr = stage_bdry[m] |
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| 207 | else: |
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| 208 | m = neighbour_edges[k,i] |
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| 209 | qr = stage[n, m] |
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| 210 | |
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| 211 | |
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| 212 | #Outward pointing normal vector |
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| 213 | normal = normals[k, 2*i:2*i+2] |
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| 214 | |
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| 215 | #Flux computation using provided function |
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| 216 | edgeflux, max_speed = self.flux_function(normal, ql, qr) |
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| 217 | flux -= edgeflux * edgelengths[k,i] |
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| 218 | |
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| 219 | #Update optimal_timestep |
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| 220 | try: |
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| 221 | optimal_timestep = min(optimal_timestep, radii[k]/max_speed) |
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| 222 | except ZeroDivisionError: |
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| 223 | pass |
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| 224 | |
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| 225 | #Normalise by area and store for when all conserved |
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| 226 | #quantities get updated |
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| 227 | flux /= areas[k] |
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| 228 | Stage.explicit_update[k] = flux[0] |
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| 229 | |
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| 230 | timestep = min(timestep, optimal_timestep) |
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| 231 | |
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| 232 | self.timestep = timestep |
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| 233 | |
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| 234 | def compute_fluxes_weave(self): |
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| 235 | """Compute all fluxes and the timestep suitable for all volumes |
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| 236 | in domain. |
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| 237 | |
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| 238 | Compute total flux for each conserved quantity using "flux_function" |
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| 239 | |
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| 240 | Fluxes across each edge are scaled by edgelengths and summed up |
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| 241 | Resulting flux is then scaled by area and stored in |
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| 242 | domain.explicit_update |
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| 243 | |
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| 244 | The maximal allowable speed computed by the flux_function |
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| 245 | for each volume |
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| 246 | is converted to a timestep that must not be exceeded. The minimum of |
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| 247 | those is computed as the next overall timestep. |
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| 248 | |
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| 249 | Post conditions: |
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| 250 | domain.explicit_update is reset to computed flux values |
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| 251 | domain.timestep is set to the largest step satisfying all volumes. |
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| 252 | """ |
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| 253 | |
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| 254 | import sys |
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| 255 | from Numeric import zeros, Float |
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| 256 | from config import max_timestep |
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| 257 | |
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| 258 | import weave |
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| 259 | from weave import converters |
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| 260 | |
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| 261 | N = self.number_of_elements |
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| 262 | |
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| 263 | |
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| 264 | timestep = zeros( 1, Float); |
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| 265 | timestep[0] = float(max_timestep) #FIXME: Get rid of this |
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| 266 | |
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| 267 | #Shortcuts |
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| 268 | Stage = self.quantities['stage'] |
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| 269 | |
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| 270 | #Arrays |
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| 271 | neighbours = self.neighbours |
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| 272 | neighbour_edges = self.neighbour_edges |
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| 273 | normals = self.normals |
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| 274 | areas = self.areas |
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| 275 | radii = self.radii |
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| 276 | edgelengths = self.edgelengths |
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| 277 | |
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| 278 | stage_edge = Stage.edge_values |
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| 279 | stage_bdry = Stage.boundary_values |
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| 280 | stage_update = Stage.explicit_update |
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| 281 | |
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| 282 | huge_timestep = float(sys.maxint) |
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| 283 | |
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| 284 | v1 = self.velocity[0] |
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| 285 | v2 = self.velocity[1] |
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| 286 | |
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| 287 | code = """ |
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| 288 | //Loop |
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| 289 | |
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| 290 | double qr,ql; |
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| 291 | int m,n; |
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| 292 | double normal[2]; |
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| 293 | double normal_velocity; |
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| 294 | double flux, edgeflux; |
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| 295 | double max_speed; |
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| 296 | double optimal_timestep; |
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| 297 | for (int k=0; k<N; k++){ |
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| 298 | |
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| 299 | optimal_timestep = huge_timestep; |
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| 300 | flux = 0.0; //Reset work array |
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| 301 | for (int i=0; i<3; i++){ |
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| 302 | //Quantities inside volume facing neighbour i |
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| 303 | ql = stage_edge(k, i); |
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| 304 | |
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| 305 | //Quantities at neighbour on nearest face |
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| 306 | n = neighbours(k,i); |
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| 307 | if (n < 0) { |
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| 308 | m = -n-1; //Convert neg flag to index |
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| 309 | qr = stage_bdry(m); |
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| 310 | } else { |
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| 311 | m = neighbour_edges(k,i); |
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| 312 | qr = stage_edge(n, m); |
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| 313 | } |
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| 314 | |
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| 315 | |
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| 316 | //Outward pointing normal vector |
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| 317 | for (int j=0; j<2; j++){ |
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| 318 | normal[j] = normals(k, 2*i+j); |
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| 319 | } |
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| 320 | |
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| 321 | |
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| 322 | //Flux computation using provided function |
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| 323 | normal_velocity = v1*normal[0] + v2*normal[1]; |
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| 324 | |
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| 325 | if (normal_velocity < 0) { |
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| 326 | edgeflux = qr * normal_velocity; |
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| 327 | } else { |
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| 328 | edgeflux = ql * normal_velocity; |
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| 329 | } |
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| 330 | |
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| 331 | max_speed = fabs(normal_velocity); |
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| 332 | flux = flux - edgeflux * edgelengths(k,i); |
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| 333 | |
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| 334 | //Update optimal_timestep |
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| 335 | if (max_speed != 0.0) { |
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| 336 | optimal_timestep = (optimal_timestep>radii(k)/max_speed) ? radii(k)/max_speed : optimal_timestep; |
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| 337 | } |
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| 338 | |
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| 339 | } |
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| 340 | |
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| 341 | //Normalise by area and store for when all conserved |
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| 342 | //quantities get updated |
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| 343 | stage_update(k) = flux/areas(k); |
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| 344 | |
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| 345 | timestep(0) = (timestep(0)>optimal_timestep) ? optimal_timestep : timestep(0); |
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| 346 | |
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| 347 | } |
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| 348 | """ |
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| 349 | |
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| 350 | logger.debug('Trying to weave advection.compute_fluxes') |
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| 351 | weave.inline(code, ['stage_edge','stage_bdry','stage_update', |
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| 352 | 'neighbours','neighbour_edges','normals', |
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| 353 | 'areas','radii','edgelengths','huge_timestep', |
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| 354 | 'timestep','v1','v2','N'], |
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| 355 | type_converters = converters.blitz, compiler='gcc'); |
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| 356 | |
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| 357 | self.timestep = timestep[0] |
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| 358 | |
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| 359 | |
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| 360 | |
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| 361 | def evolve(self, |
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| 362 | yieldstep = None, |
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| 363 | finaltime = None, |
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| 364 | duration = None, |
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| 365 | skip_initial_step = False): |
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| 366 | |
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| 367 | """Specialisation of basic evolve method from parent class |
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| 368 | """ |
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| 369 | |
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| 370 | #Initialise real time viz if requested |
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| 371 | if self.visualise is True and self.time == 0.0: |
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| 372 | #pass |
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| 373 | #import realtime_visualisation_new as visualise |
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| 374 | #visualise.create_surface(self) |
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| 375 | self.initialise_visualiser() |
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| 376 | self.visualiser.setup_all() |
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| 377 | self.visualiser.update_timer() |
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| 378 | |
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| 379 | |
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| 380 | #Call basic machinery from parent class |
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| 381 | for t in Generic_domain.evolve(self, |
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| 382 | yieldstep=yieldstep, |
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| 383 | finaltime=finaltime, |
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| 384 | duration=duration, |
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| 385 | skip_initial_step=skip_initial_step): |
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| 386 | |
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| 387 | |
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| 388 | |
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| 389 | |
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| 390 | #Real time viz |
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| 391 | if self.visualise is True: |
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| 392 | #pass |
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| 393 | self.visualiser.update_all() |
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| 394 | self.visualiser.update_timer() |
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| 395 | |
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| 396 | |
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| 397 | #Pass control on to outer loop for more specific actions |
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| 398 | yield(t) |
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