"""Class Domain - 2D triangular domains for finite-volume computations of the Euler equation. This module contains a specialisation of class Domain from module domain.py consisting of methods specific to the Shallow Water Wave Equation U_t + E_x + G_y = 0 where U = [rho, mx, my, E] u = mx/rho v = my/rho E = [u rho, u mx + p, u my, u(E + p)] G = [v rho, v mx, v my + p, v(E + p)] and _t, _x, _y denote the derivative with respect to t, x and y respectively. The quantities are symbol variable name explanation x x horizontal distance from origin [m] y y vertical distance from origin [m] rho density density [kg/m^2] u speed in the x direction [m/s] v speed in the y direction [m/s] mx xmomentum momentum density in the x direction [kg/m/s^2] my ymomentum momentum density in the y direction [kg/m/s^2] E energy energy density [J/m^2] gamma gamma gamma law gas (1.4 for air) p pressure pressure [N/m The conserved quantities are rho, mx, my, E Gamma law relates pressure with conserved quantities p = (gamma-1)[E - rho/2(u^2 + v^2)] Stephen Roberts, ANU 2006 """ #Subversion keywords: # #$LastChangedDate: 2005-10-14 12:02:18 +1000 (Fri, 14 Oct 2005) $ #$LastChangedRevision: 1922 $ #$LastChangedBy: duncan $ from domain import * from region import * Generic_domain = Domain #Rename #Euler domain class Domain(Generic_domain): def __init__(self, coordinates, vertices, boundary = None, tagged_elements = None, geo_reference = None, use_inscribed_circle=False): conserved_quantities = ['density', 'xmomentum', 'ymomentum', 'energy'] other_quantities = ['pressure'] Generic_domain.__init__(self, coordinates, vertices, boundary, conserved_quantities, other_quantities, tagged_elements, geo_reference, use_inscribed_circle) from euler_config import minimum_allowed_density self.minimum_allowed_density = minimum_allowed_density #Realtime visualisation self.visualiser = None self.visualise = False self.visualise_color_stage = False self.visualise_stage_range = 1.0 self.visualise_timer = True self.visualise_range_z = None #Stored output self.store = False self.format = 'sww' self.smooth = False #Reduction operation for get_vertex_values from anuga.pyvolution.util import mean self.reduction = mean #self.reduction = min #Looks better near steep slopes self.quantities_to_be_stored = ['density', 'xmomentum', 'ymomentum', 'energy', 'pressure'] #Establish shortcuts to relevant quantities (for efficiency) self.rho = self.quantities['density'] self.mx = self.quantities['xmomentum'] self.my = self.quantities['ymomentum'] self.E = self.quantities['energy'] def initialise_visualiser(self,scale_z=1.0,rect=None): #Realtime visualisation if self.visualiser is None: from realtime_visualisation_new import Visualiser self.visualiser = Visualiser(self,scale_z,rect) self.visualise = True def check_integrity(self): Generic_domain.check_integrity(self) #Check that we are solving the Euler equation msg = 'First conserved quantity must be "density"' assert self.conserved_quantities[0] == 'stage', msg msg = 'Second conserved quantity must be "xmomentum"' assert self.conserved_quantities[1] == 'xmomentum', msg msg = 'Third conserved quantity must be "ymomentum"' assert self.conserved_quantities[2] == 'ymomentum', msg msg = 'Fourth conserved quantity must be "energy"' assert self.conserved_quantities[2] == 'ymomentum', msg def extrapolate_second_order_sw(self): #Call correct module function #(either from this module or C-extension) extrapolate_second_order_sw(self) def compute_fluxes(self): #Call correct module function #(either from this module or C-extension) compute_fluxes(self) def distribute_to_vertices_and_edges(self): #Call correct module function #(either from this module or C-extension) distribute_to_vertices_and_edges(self) def evolve(self, yieldstep = None, finaltime = None, duration = None, skip_initial_step = False): """Specialisation of basic evolve method from parent class """ #Call check integrity here rather than from user scripts #self.check_integrity() msg = 'Parameter beta must be in the interval [0, 1[' assert 0 <= self.beta < 1.0, msg #Initial update of vertex and edge values before any storage #and or visualisation self.distribute_to_vertices_and_edges() #Initialise real time viz if requested if self.visualise is True and self.time == 0.0: import realtime_visualisation_new as visualise self.initialise_visualiser() self.visualiser.setup_all() self.visualiser.update_timer() #Store model data, e.g. for visualisation if self.store is True and self.time == 0.0: self.initialise_storage() else: pass #Call basic machinery from parent class #for t in Generic_domain.evolve(self, yieldstep, finaltime, # skip_initial_step): for t in Generic_domain.evolve(self, yieldstep=yieldstep, finaltime=finaltime, duration=duration, skip_initial_step=skip_initial_step): #Real time viz if self.visualise is True: self.visualiser.update_all() self.visualiser.update_timer() #Store model data, e.g. for subsequent visualisation if self.store is True: self.store_timestep(self.quantities_to_be_stored) #FIXME: Could maybe be taken from specified list #of 'store every step' quantities #Pass control on to outer loop for more specific actions yield(t) def initialise_storage(self): """ Create and initialise self.writer object for storing data. Also, save x,y and bed elevation """ import anuga.pyvolution.data_manager #Initialise writer self.writer = data_manager.get_dataobject(self, mode = 'w') #Store vertices and connectivity self.writer.store_connectivity() def store_timestep(self, name): """Store named quantity and time. Precondition: self.write has been initialised """ self.writer.store_timestep(name) ####################MH 090605 new extrapolation function belonging to domain class def extrapolate_second_order_sw(domain): """extrapolate conserved quntities to the vertices of the triangles Python version to be written after the C version """ msg = 'Method extrapolate_second_order_sw should be implemented in C' raise msg ####################MH 090605 ########################################### def initialise_visualiser(self,scale_z=1.0,rect=None): #Realtime visualisation if self.visualiser is None: from realtime_visualisation_new import Visualiser from Numeric import array, Float if rect is None: rect = array(self.xy_extent, Float) self.visualiser = Visualiser(self,scale_z,rect) self.visualise = True #Rotation of momentum vector def rotate(q, normal, direction = 1): """Rotate the momentum component q (q[1], q[2]) from x,y coordinates to coordinates based on normal vector. If direction is negative the rotation is inverted. Input vector is preserved This function is specific to the shallow water wave equation """ from Numeric import zeros, Float assert len(q) == 3,\ 'Vector of conserved quantities must have length 3'\ 'for 2D shallow water equation' try: l = len(normal) except: raise 'Normal vector must be an Numeric array' assert l == 2, 'Normal vector must have 2 components' n1 = normal[0] n2 = normal[1] r = zeros(len(q), Float) #Rotated quantities r[0] = q[0] #First quantity, height, is not rotated if direction == -1: n2 = -n2 r[1] = n1*q[1] + n2*q[2] r[2] = -n2*q[1] + n1*q[2] return r #################################### # Flux computation def flux_function(normal, ql, qr, zl, zr): """Compute fluxes between volumes for the shallow water wave equation cast in terms of w = h+z using the 'central scheme' as described in Kurganov, Noelle, Petrova. 'Semidiscrete Central-Upwind Schemes For Hyperbolic Conservation Laws and Hamilton-Jacobi Equations'. Siam J. Sci. Comput. Vol. 23, No. 3, pp. 707-740. The implemented formula is given in equation (3.15) on page 714 Conserved quantities w, uh, vh are stored as elements 0, 1 and 2 in the numerical vectors ql an qr. Bed elevations zl and zr. """ from anuga.pyvolution.config import g, epsilon from math import sqrt from Numeric import array #Align momentums with x-axis q_left = rotate(ql, normal, direction = 1) q_right = rotate(qr, normal, direction = 1) z = (zl+zr)/2 #Take average of field values w_left = q_left[0] #w=h+z h_left = w_left-z uh_left = q_left[1] if h_left < epsilon: u_left = 0.0 #Could have been negative h_left = 0.0 else: u_left = uh_left/h_left w_right = q_right[0] #w=h+z h_right = w_right-z uh_right = q_right[1] if h_right < epsilon: u_right = 0.0 #Could have been negative h_right = 0.0 else: u_right = uh_right/h_right vh_left = q_left[2] vh_right = q_right[2] soundspeed_left = sqrt(g*h_left) soundspeed_right = sqrt(g*h_right) #Maximal wave speed s_max = max(u_left+soundspeed_left, u_right+soundspeed_right, 0) #Minimal wave speed s_min = min(u_left-soundspeed_left, u_right-soundspeed_right, 0) #Flux computation #FIXME(Ole): Why is it again that we don't #use uh_left and uh_right directly in the first entries? flux_left = array([u_left*h_left, u_left*uh_left + 0.5*g*h_left**2, u_left*vh_left]) flux_right = array([u_right*h_right, u_right*uh_right + 0.5*g*h_right**2, u_right*vh_right]) denom = s_max-s_min if denom == 0.0: edgeflux = array([0.0, 0.0, 0.0]) max_speed = 0.0 else: edgeflux = (s_max*flux_left - s_min*flux_right)/denom edgeflux += s_max*s_min*(q_right-q_left)/denom edgeflux = rotate(edgeflux, normal, direction=-1) max_speed = max(abs(s_max), abs(s_min)) return edgeflux, max_speed def compute_fluxes(domain): """Compute all fluxes and the timestep suitable for all volumes in domain. Compute total flux for each conserved quantity using "flux_function" Fluxes across each edge are scaled by edgelengths and summed up Resulting flux is then scaled by area and stored in explicit_update for each of the three conserved quantities stage, xmomentum and ymomentum The maximal allowable speed computed by the flux_function for each volume is converted to a timestep that must not be exceeded. The minimum of those is computed as the next overall timestep. Post conditions: domain.explicit_update is reset to computed flux values domain.timestep is set to the largest step satisfying all volumes. """ import sys from Numeric import zeros, Float N = domain.number_of_elements #Shortcuts Stage = domain.quantities['stage'] Xmom = domain.quantities['xmomentum'] Ymom = domain.quantities['ymomentum'] Bed = domain.quantities['elevation'] #Arrays stage = Stage.edge_values xmom = Xmom.edge_values ymom = Ymom.edge_values bed = Bed.edge_values stage_bdry = Stage.boundary_values xmom_bdry = Xmom.boundary_values ymom_bdry = Ymom.boundary_values flux = zeros(3, Float) #Work array for summing up fluxes #Loop timestep = float(sys.maxint) for k in range(N): flux[:] = 0. #Reset work array for i in range(3): #Quantities inside volume facing neighbour i ql = [stage[k, i], xmom[k, i], ymom[k, i]] zl = bed[k, i] #Quantities at neighbour on nearest face n = domain.neighbours[k,i] if n < 0: m = -n-1 #Convert negative flag to index qr = [stage_bdry[m], xmom_bdry[m], ymom_bdry[m]] zr = zl #Extend bed elevation to boundary else: m = domain.neighbour_edges[k,i] qr = [stage[n, m], xmom[n, m], ymom[n, m]] zr = bed[n, m] #Outward pointing normal vector normal = domain.normals[k, 2*i:2*i+2] #Flux computation using provided function edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) flux -= edgeflux * domain.edgelengths[k,i] #Update optimal_timestep try: timestep = min(timestep, 0.5*domain.radii[k]/max_speed) except ZeroDivisionError: pass #Normalise by area and store for when all conserved #quantities get updated flux /= domain.areas[k] Stage.explicit_update[k] = flux[0] Xmom.explicit_update[k] = flux[1] Ymom.explicit_update[k] = flux[2] domain.timestep = timestep #MH090605 The following method belongs to the shallow_water domain class #see comments in the corresponding method in shallow_water_ext.c def extrapolate_second_order_sw_c(domain): """Wrapper calling C version of extrapolate_second_order_sw """ import sys from Numeric import zeros, Float N = domain.number_of_elements #Shortcuts Stage = domain.quantities['stage'] Xmom = domain.quantities['xmomentum'] Ymom = domain.quantities['ymomentum'] from shallow_water_ext import extrapolate_second_order_sw extrapolate_second_order_sw(domain,domain.surrogate_neighbours, domain.number_of_boundaries, domain.centroid_coordinates, Stage.centroid_values, Xmom.centroid_values, Ymom.centroid_values, domain.vertex_coordinates, Stage.vertex_values, Xmom.vertex_values, Ymom.vertex_values) def compute_fluxes_c(domain): """Wrapper calling C version of compute fluxes """ import sys from Numeric import zeros, Float N = domain.number_of_elements #Shortcuts Stage = domain.quantities['stage'] Xmom = domain.quantities['xmomentum'] Ymom = domain.quantities['ymomentum'] Bed = domain.quantities['elevation'] timestep = float(sys.maxint) from shallow_water_ext import compute_fluxes domain.timestep = compute_fluxes(timestep, domain.epsilon, domain.g, domain.neighbours, domain.neighbour_edges, domain.normals, domain.edgelengths, domain.radii, domain.areas, Stage.edge_values, Xmom.edge_values, Ymom.edge_values, Bed.edge_values, Stage.boundary_values, Xmom.boundary_values, Ymom.boundary_values, Stage.explicit_update, Xmom.explicit_update, Ymom.explicit_update, domain.already_computed_flux) #################################### # Module functions for gradient limiting (distribute_to_vertices_and_edges) def distribute_to_vertices_and_edges(domain): """Distribution from centroids to vertices specific to the shallow water wave equation. It will ensure that h (w-z) is always non-negative even in the presence of steep bed-slopes by taking a weighted average between shallow and deep cases. In addition, all conserved quantities get distributed as per either a constant (order==1) or a piecewise linear function (order==2). FIXME: more explanation about removal of artificial variability etc Precondition: All quantities defined at centroids and bed elevation defined at vertices. Postcondition Conserved quantities defined at vertices """ from config import optimised_gradient_limiter #Remove very thin layers of water protect_against_infinitesimal_and_negative_heights(domain) #Extrapolate all conserved quantities if optimised_gradient_limiter: #MH090605 if second order, #perform the extrapolation and limiting on #all of the conserved quantitie if (domain.order == 1): for name in domain.conserved_quantities: Q = domain.quantities[name] Q.extrapolate_first_order() elif domain.order == 2: domain.extrapolate_second_order_sw() else: raise 'Unknown order' else: #old code: for name in domain.conserved_quantities: Q = domain.quantities[name] if domain.order == 1: Q.extrapolate_first_order() elif domain.order == 2: Q.extrapolate_second_order() Q.limit() else: raise 'Unknown order' #Take bed elevation into account when water heights are small balance_deep_and_shallow(domain) #Compute edge values by interpolation for name in domain.conserved_quantities: Q = domain.quantities[name] Q.interpolate_from_vertices_to_edges() def protect_against_infinitesimal_and_negative_heights(domain): """Protect against infinitesimal heights and associated high velocities """ #Shortcuts wc = domain.quantities['stage'].centroid_values zc = domain.quantities['elevation'].centroid_values xmomc = domain.quantities['xmomentum'].centroid_values ymomc = domain.quantities['ymomentum'].centroid_values hc = wc - zc #Water depths at centroids #Update for k in range(domain.number_of_elements): if hc[k] < domain.minimum_allowed_height: #Control stage if hc[k] < domain.epsilon: wc[k] = zc[k] # Contain 'lost mass' error #Control momentum xmomc[k] = ymomc[k] = 0.0 def protect_against_infinitesimal_and_negative_heights_c(domain): """Protect against infinitesimal heights and associated high velocities """ #Shortcuts wc = domain.quantities['stage'].centroid_values zc = domain.quantities['elevation'].centroid_values xmomc = domain.quantities['xmomentum'].centroid_values ymomc = domain.quantities['ymomentum'].centroid_values from shallow_water_ext import protect protect(domain.minimum_allowed_height, domain.epsilon, wc, zc, xmomc, ymomc) def h_limiter(domain): """Limit slopes for each volume to eliminate artificial variance introduced by e.g. second order extrapolator limit on h = w-z This limiter depends on two quantities (w,z) so it resides within this module rather than within quantity.py """ from Numeric import zeros, Float N = domain.number_of_elements beta_h = domain.beta_h #Shortcuts wc = domain.quantities['stage'].centroid_values zc = domain.quantities['elevation'].centroid_values hc = wc - zc wv = domain.quantities['stage'].vertex_values zv = domain.quantities['elevation'].vertex_values hv = wv-zv hvbar = zeros(hv.shape, Float) #h-limited values #Find min and max of this and neighbour's centroid values hmax = zeros(hc.shape, Float) hmin = zeros(hc.shape, Float) for k in range(N): hmax[k] = hmin[k] = hc[k] for i in range(3): n = domain.neighbours[k,i] if n >= 0: hn = hc[n] #Neighbour's centroid value hmin[k] = min(hmin[k], hn) hmax[k] = max(hmax[k], hn) #Diffences between centroids and maxima/minima dhmax = hmax - hc dhmin = hmin - hc #Deltas between vertex and centroid values dh = zeros(hv.shape, Float) for i in range(3): dh[:,i] = hv[:,i] - hc #Phi limiter for k in range(N): #Find the gradient limiter (phi) across vertices phi = 1.0 for i in range(3): r = 1.0 if (dh[k,i] > 0): r = dhmax[k]/dh[k,i] if (dh[k,i] < 0): r = dhmin[k]/dh[k,i] phi = min( min(r*beta_h, 1), phi ) #Then update using phi limiter for i in range(3): hvbar[k,i] = hc[k] + phi*dh[k,i] return hvbar def h_limiter_c(domain): """Limit slopes for each volume to eliminate artificial variance introduced by e.g. second order extrapolator limit on h = w-z This limiter depends on two quantities (w,z) so it resides within this module rather than within quantity.py Wrapper for c-extension """ from Numeric import zeros, Float N = domain.number_of_elements beta_h = domain.beta_h #Shortcuts wc = domain.quantities['stage'].centroid_values zc = domain.quantities['elevation'].centroid_values hc = wc - zc wv = domain.quantities['stage'].vertex_values zv = domain.quantities['elevation'].vertex_values hv = wv - zv #Call C-extension from shallow_water_ext import h_limiter_sw as h_limiter hvbar = h_limiter(domain, hc, hv) return hvbar def balance_deep_and_shallow(domain): """Compute linear combination between stage as computed by gradient-limiters limiting using w, and stage computed by gradient-limiters limiting using h (h-limiter). The former takes precedence when heights are large compared to the bed slope while the latter takes precedence when heights are relatively small. Anything in between is computed as a balanced linear combination in order to avoid numerical disturbances which would otherwise appear as a result of hard switching between modes. The h-limiter is always applied irrespective of the order. """ #Shortcuts wc = domain.quantities['stage'].centroid_values zc = domain.quantities['elevation'].centroid_values hc = wc - zc wv = domain.quantities['stage'].vertex_values zv = domain.quantities['elevation'].vertex_values hv = wv-zv #Limit h hvbar = h_limiter(domain) for k in range(domain.number_of_elements): #Compute maximal variation in bed elevation # This quantitiy is # dz = max_i abs(z_i - z_c) # and it is independent of dimension # In the 1d case zc = (z0+z1)/2 # In the 2d case zc = (z0+z1+z2)/3 dz = max(abs(zv[k,0]-zc[k]), abs(zv[k,1]-zc[k]), abs(zv[k,2]-zc[k])) hmin = min( hv[k,:] ) #Create alpha in [0,1], where alpha==0 means using the h-limited #stage and alpha==1 means using the w-limited stage as #computed by the gradient limiter (both 1st or 2nd order) #If hmin > dz/2 then alpha = 1 and the bed will have no effect #If hmin < 0 then alpha = 0 reverting to constant height above bed. if dz > 0.0: alpha = max( min( 2*hmin/dz, 1.0), 0.0 ) else: #Flat bed alpha = 1.0 #Let # # wvi be the w-limited stage (wvi = zvi + hvi) # wvi- be the h-limited state (wvi- = zvi + hvi-) # # #where i=0,1,2 denotes the vertex ids # #Weighted balance between w-limited and h-limited stage is # # wvi := (1-alpha)*(zvi+hvi-) + alpha*(zvi+hvi) # #It follows that the updated wvi is # wvi := zvi + (1-alpha)*hvi- + alpha*hvi # # Momentum is balanced between constant and limited #for i in range(3): # wv[k,i] = zv[k,i] + hvbar[k,i] #return if alpha < 1: for i in range(3): wv[k,i] = zv[k,i] + (1-alpha)*hvbar[k,i] + alpha*hv[k,i] #Momentums at centroids xmomc = domain.quantities['xmomentum'].centroid_values ymomc = domain.quantities['ymomentum'].centroid_values #Momentums at vertices xmomv = domain.quantities['xmomentum'].vertex_values ymomv = domain.quantities['ymomentum'].vertex_values # Update momentum as a linear combination of # xmomc and ymomc (shallow) and momentum # from extrapolator xmomv and ymomv (deep). xmomv[k,:] = (1-alpha)*xmomc[k] + alpha*xmomv[k,:] ymomv[k,:] = (1-alpha)*ymomc[k] + alpha*ymomv[k,:] def balance_deep_and_shallow_c(domain): """Wrapper for C implementation """ #Shortcuts wc = domain.quantities['stage'].centroid_values zc = domain.quantities['elevation'].centroid_values hc = wc - zc wv = domain.quantities['stage'].vertex_values zv = domain.quantities['elevation'].vertex_values hv = wv - zv #Momentums at centroids xmomc = domain.quantities['xmomentum'].centroid_values ymomc = domain.quantities['ymomentum'].centroid_values #Momentums at vertices xmomv = domain.quantities['xmomentum'].vertex_values ymomv = domain.quantities['ymomentum'].vertex_values #Limit h hvbar = h_limiter(domain) #This is how one would make a first order h_limited value #as in the old balancer (pre 17 Feb 2005): #from Numeric import zeros, Float #hvbar = zeros( (len(hc), 3), Float) #for i in range(3): # hvbar[:,i] = hc[:] from shallow_water_ext import balance_deep_and_shallow balance_deep_and_shallow(wc, zc, hc, wv, zv, hv, hvbar, xmomc, ymomc, xmomv, ymomv) ############################################### #Boundaries - specific to the shallow water wave equation class Reflective_boundary(Boundary): """Reflective boundary returns same conserved quantities as those present in its neighbour volume but reflected. This class is specific to the shallow water equation as it works with the momentum quantities assumed to be the second and third conserved quantities. """ def __init__(self, domain = None): Boundary.__init__(self) if domain is None: msg = 'Domain must be specified for reflective boundary' raise msg #Handy shorthands self.stage = domain.quantities['stage'].edge_values self.xmom = domain.quantities['xmomentum'].edge_values self.ymom = domain.quantities['ymomentum'].edge_values self.normals = domain.normals from Numeric import zeros, Float self.conserved_quantities = zeros(3, Float) def __repr__(self): return 'Reflective_boundary' def evaluate(self, vol_id, edge_id): """Reflective boundaries reverses the outward momentum of the volume they serve. """ q = self.conserved_quantities q[0] = self.stage[vol_id, edge_id] q[1] = self.xmom[vol_id, edge_id] q[2] = self.ymom[vol_id, edge_id] normal = self.normals[vol_id, 2*edge_id:2*edge_id+2] r = rotate(q, normal, direction = 1) r[1] = -r[1] q = rotate(r, normal, direction = -1) return q class Transmissive_Momentum_Set_Stage_boundary(Boundary): """Returns same momentum conserved quantities as those present in its neighbour volume. Sets stage Underlying domain must be specified when boundary is instantiated """ def __init__(self, domain = None, function=None): Boundary.__init__(self) if domain is None: msg = 'Domain must be specified for this type boundary' raise msg if function is None: msg = 'Function must be specified for this type boundary' raise msg self.domain = domain self.function = function def __repr__(self): return 'Transmissive_Momentum_Set_Stage_boundary(%s)' %self.domain def evaluate(self, vol_id, edge_id): """Transmissive Momentum Set Stage boundaries return the edge momentum values of the volume they serve. """ q = self.domain.get_conserved_quantities(vol_id, edge = edge_id) value = self.function(self.domain.time) q[0] = value[0] return q #FIXME: Consider this (taken from File_boundary) to allow #spatial variation #if vol_id is not None and edge_id is not None: # i = self.boundary_indices[ vol_id, edge_id ] # return self.F(t, point_id = i) #else: # return self.F(t) class Dirichlet_Discharge_boundary(Boundary): """Sets stage (h0) - FIXME: Should we use w0? Sets momentum (wh0) in the inward normal direction. Underlying domain must be specified when boundary is instantiated """ def __init__(self, domain = None, h0=None, wh0=None): Boundary.__init__(self) if domain is None: msg = 'Domain must be specified for this type boundary' raise msg if h0 is None: h0 = 0.0 if wh0 is None: wh0 = 0.0 self.domain = domain self.h0 = h0 self.wh0 = wh0 def __repr__(self): return 'Dirichlet_Discharge_boundary(%s)' %self.domain def evaluate(self, vol_id, edge_id): """Set discharge in the (inward) normal direction """ normal = self.domain.get_normal(vol_id,edge_id) q = [self.h0, -self.wh0*normal[0], -self.wh0*normal[1]] return q #FIXME: Consider this (taken from File_boundary) to allow #spatial variation #if vol_id is not None and edge_id is not None: # i = self.boundary_indices[ vol_id, edge_id ] # return self.F(t, point_id = i) #else: # return self.F(t) #class Spatio_temporal_boundary(Boundary): # """The spatio-temporal boundary, reads values for the conserved # quantities from an sww NetCDF file, and returns interpolated values # at the midpoints of each associated boundaty segment. # Time dependency is interpolated linearly as in util.File_function.# # # Example: # Bf = Spatio_temporal_boundary('source_file.sww', domain) # # """ Spatio_temporal_boundary = File_boundary ######################### #Standard forcing terms: # def gravity(domain): """Apply gravitational pull in the presence of bed slope """ from anuga.pyvolution.util import gradient from Numeric import zeros, Float, array, sum xmom = domain.quantities['xmomentum'].explicit_update ymom = domain.quantities['ymomentum'].explicit_update Stage = domain.quantities['stage'] Elevation = domain.quantities['elevation'] h = Stage.edge_values - Elevation.edge_values v = Elevation.vertex_values x = domain.get_vertex_coordinates() g = domain.g for k in range(domain.number_of_elements): avg_h = sum( h[k,:] )/3 #Compute bed slope x0, y0, x1, y1, x2, y2 = x[k,:] z0, z1, z2 = v[k,:] zx, zy = gradient(x0, y0, x1, y1, x2, y2, z0, z1, z2) #Update momentum xmom[k] += -g*zx*avg_h ymom[k] += -g*zy*avg_h def gravity_c(domain): """Wrapper calling C version """ xmom = domain.quantities['xmomentum'].explicit_update ymom = domain.quantities['ymomentum'].explicit_update Stage = domain.quantities['stage'] Elevation = domain.quantities['elevation'] h = Stage.edge_values - Elevation.edge_values v = Elevation.vertex_values x = domain.get_vertex_coordinates() g = domain.g from shallow_water_ext import gravity gravity(g, h, v, x, xmom, ymom) def manning_friction(domain): """Apply (Manning) friction to water momentum """ from math import sqrt w = domain.quantities['stage'].centroid_values z = domain.quantities['elevation'].centroid_values h = w-z uh = domain.quantities['xmomentum'].centroid_values vh = domain.quantities['ymomentum'].centroid_values eta = domain.quantities['friction'].centroid_values xmom_update = domain.quantities['xmomentum'].semi_implicit_update ymom_update = domain.quantities['ymomentum'].semi_implicit_update N = domain.number_of_elements eps = domain.minimum_allowed_height g = domain.g for k in range(N): if eta[k] >= eps: if h[k] >= eps: S = -g * eta[k]**2 * sqrt((uh[k]**2 + vh[k]**2)) S /= h[k]**(7.0/3) #Update momentum xmom_update[k] += S*uh[k] ymom_update[k] += S*vh[k] def manning_friction_c(domain): """Wrapper for c version """ xmom = domain.quantities['xmomentum'] ymom = domain.quantities['ymomentum'] w = domain.quantities['stage'].centroid_values z = domain.quantities['elevation'].centroid_values uh = xmom.centroid_values vh = ymom.centroid_values eta = domain.quantities['friction'].centroid_values xmom_update = xmom.semi_implicit_update ymom_update = ymom.semi_implicit_update N = domain.number_of_elements eps = domain.minimum_allowed_height g = domain.g from shallow_water_ext import manning_friction manning_friction(g, eps, w, z, uh, vh, eta, xmom_update, ymom_update) def linear_friction(domain): """Apply linear friction to water momentum Assumes quantity: 'linear_friction' to be present """ from math import sqrt w = domain.quantities['stage'].centroid_values z = domain.quantities['elevation'].centroid_values h = w-z uh = domain.quantities['xmomentum'].centroid_values vh = domain.quantities['ymomentum'].centroid_values tau = domain.quantities['linear_friction'].centroid_values xmom_update = domain.quantities['xmomentum'].semi_implicit_update ymom_update = domain.quantities['ymomentum'].semi_implicit_update N = domain.number_of_elements eps = domain.minimum_allowed_height g = domain.g #Not necessary? Why was this added? for k in range(N): if tau[k] >= eps: if h[k] >= eps: S = -tau[k]/h[k] #Update momentum xmom_update[k] += S*uh[k] ymom_update[k] += S*vh[k] def check_forcefield(f): """Check that f is either 1: a callable object f(t,x,y), where x and y are vectors and that it returns an array or a list of same length as x and y 2: a scalar """ from Numeric import ones, Float, array if callable(f): N = 3 x = ones(3, Float) y = ones(3, Float) try: q = f(1.0, x=x, y=y) except Exception, e: msg = 'Function %s could not be executed:\n%s' %(f, e) #FIXME: Reconsider this semantics raise msg try: q = array(q).astype(Float) except: msg = 'Return value from vector function %s could ' %f msg += 'not be converted into a Numeric array of floats.\n' msg += 'Specified function should return either list or array.' raise msg #Is this really what we want? msg = 'Return vector from function %s ' %f msg += 'must have same lenght as input vectors' assert len(q) == N, msg else: try: f = float(f) except: msg = 'Force field %s must be either a scalar' %f msg += ' or a vector function' raise msg return f class Wind_stress: """Apply wind stress to water momentum in terms of wind speed [m/s] and wind direction [degrees] """ def __init__(self, *args, **kwargs): """Initialise windfield from wind speed s [m/s] and wind direction phi [degrees] Inputs v and phi can be either scalars or Python functions, e.g. W = Wind_stress(10, 178) #FIXME - 'normal' degrees are assumed for now, i.e. the vector (1,0) has zero degrees. We may need to convert from 'compass' degrees later on and also map from True north to grid north. Arguments can also be Python functions of t,x,y as in def speed(t,x,y): ... return s def angle(t,x,y): ... return phi where x and y are vectors. and then pass the functions in W = Wind_stress(speed, angle) The instantiated object W can be appended to the list of forcing_terms as in Alternatively, one vector valued function for (speed, angle) can be applied, providing both quantities simultaneously. As in W = Wind_stress(F), where returns (speed, angle) for each t. domain.forcing_terms.append(W) """ from config import rho_a, rho_w, eta_w from Numeric import array, Float if len(args) == 2: s = args[0] phi = args[1] elif len(args) == 1: #Assume vector function returning (s, phi)(t,x,y) vector_function = args[0] s = lambda t,x,y: vector_function(t,x=x,y=y)[0] phi = lambda t,x,y: vector_function(t,x=x,y=y)[1] else: #Assume info is in 2 keyword arguments if len(kwargs) == 2: s = kwargs['s'] phi = kwargs['phi'] else: raise 'Assumes two keyword arguments: s=..., phi=....' self.speed = check_forcefield(s) self.phi = check_forcefield(phi) self.const = eta_w*rho_a/rho_w def __call__(self, domain): """Evaluate windfield based on values found in domain """ from math import pi, cos, sin, sqrt from Numeric import Float, ones, ArrayType xmom_update = domain.quantities['xmomentum'].explicit_update ymom_update = domain.quantities['ymomentum'].explicit_update N = domain.number_of_elements t = domain.time if callable(self.speed): xc = domain.get_centroid_coordinates() s_vec = self.speed(t, xc[:,0], xc[:,1]) else: #Assume s is a scalar try: s_vec = self.speed * ones(N, Float) except: msg = 'Speed must be either callable or a scalar: %s' %self.s raise msg if callable(self.phi): xc = domain.get_centroid_coordinates() phi_vec = self.phi(t, xc[:,0], xc[:,1]) else: #Assume phi is a scalar try: phi_vec = self.phi * ones(N, Float) except: msg = 'Angle must be either callable or a scalar: %s' %self.phi raise msg assign_windfield_values(xmom_update, ymom_update, s_vec, phi_vec, self.const) def assign_windfield_values(xmom_update, ymom_update, s_vec, phi_vec, const): """Python version of assigning wind field to update vectors. A c version also exists (for speed) """ from math import pi, cos, sin, sqrt N = len(s_vec) for k in range(N): s = s_vec[k] phi = phi_vec[k] #Convert to radians phi = phi*pi/180 #Compute velocity vector (u, v) u = s*cos(phi) v = s*sin(phi) #Compute wind stress S = const * sqrt(u**2 + v**2) xmom_update[k] += S*u ymom_update[k] += S*v ############################## #OBSOLETE STUFF def balance_deep_and_shallow_old(domain): """Compute linear combination between stage as computed by gradient-limiters and stage computed as constant height above bed. The former takes precedence when heights are large compared to the bed slope while the latter takes precedence when heights are relatively small. Anything in between is computed as a balanced linear combination in order to avoid numerical disturbances which would otherwise appear as a result of hard switching between modes. """ #OBSOLETE #Shortcuts wc = domain.quantities['stage'].centroid_values zc = domain.quantities['elevation'].centroid_values hc = wc - zc wv = domain.quantities['stage'].vertex_values zv = domain.quantities['elevation'].vertex_values hv = wv-zv #Computed linear combination between constant stages and and #stages parallel to the bed elevation. for k in range(domain.number_of_elements): #Compute maximal variation in bed elevation # This quantitiy is # dz = max_i abs(z_i - z_c) # and it is independent of dimension # In the 1d case zc = (z0+z1)/2 # In the 2d case zc = (z0+z1+z2)/3 dz = max(abs(zv[k,0]-zc[k]), abs(zv[k,1]-zc[k]), abs(zv[k,2]-zc[k])) hmin = min( hv[k,:] ) #Create alpha in [0,1], where alpha==0 means using shallow #first order scheme and alpha==1 means using the stage w as #computed by the gradient limiter (1st or 2nd order) # #If hmin > dz/2 then alpha = 1 and the bed will have no effect #If hmin < 0 then alpha = 0 reverting to constant height above bed. if dz > 0.0: alpha = max( min( 2*hmin/dz, 1.0), 0.0 ) else: #Flat bed alpha = 1.0 #Weighted balance between stage parallel to bed elevation #(wvi = zvi + hc) and stage as computed by 1st or 2nd #order gradient limiter #(wvi = zvi + hvi) where i=0,1,2 denotes the vertex ids # #It follows that the updated wvi is # wvi := (1-alpha)*(zvi+hc) + alpha*(zvi+hvi) = # zvi + hc + alpha*(hvi - hc) # #Note that hvi = zc+hc-zvi in the first order case (constant). if alpha < 1: for i in range(3): wv[k,i] = zv[k,i] + hc[k] + alpha*(hv[k,i]-hc[k]) #Momentums at centroids xmomc = domain.quantities['xmomentum'].centroid_values ymomc = domain.quantities['ymomentum'].centroid_values #Momentums at vertices xmomv = domain.quantities['xmomentum'].vertex_values ymomv = domain.quantities['ymomentum'].vertex_values # Update momentum as a linear combination of # xmomc and ymomc (shallow) and momentum # from extrapolator xmomv and ymomv (deep). xmomv[k,:] = (1-alpha)*xmomc[k] + alpha*xmomv[k,:] ymomv[k,:] = (1-alpha)*ymomc[k] + alpha*ymomv[k,:] ########################### ########################### #Geometries #FIXME: Rethink this way of creating values. class Weir: """Set a bathymetry for weir with a hole and a downstream gutter x,y are assumed to be in the unit square """ def __init__(self, stage): self.inflow_stage = stage def __call__(self, x, y): from Numeric import zeros, Float from math import sqrt N = len(x) assert N == len(y) z = zeros(N, Float) for i in range(N): z[i] = -x[i]/2 #General slope #Flattish bit to the left if x[i] < 0.3: z[i] = -x[i]/10 #Weir if x[i] >= 0.3 and x[i] < 0.4: z[i] = -x[i]+0.9 #Dip x0 = 0.6 #depth = -1.3 depth = -1.0 #plateaux = -0.9 plateaux = -0.6 if y[i] < 0.7: if x[i] > x0 and x[i] < 0.9: z[i] = depth #RHS plateaux if x[i] >= 0.9: z[i] = plateaux elif y[i] >= 0.7 and y[i] < 1.5: #Restrict and deepen if x[i] >= x0 and x[i] < 0.8: z[i] = depth-(y[i]/3-0.3) #z[i] = depth-y[i]/5 #z[i] = depth elif x[i] >= 0.8: #RHS plateaux z[i] = plateaux elif y[i] >= 1.5: if x[i] >= x0 and x[i] < 0.8 + (y[i]-1.5)/1.2: #Widen up and stay at constant depth z[i] = depth-1.5/5 elif x[i] >= 0.8 + (y[i]-1.5)/1.2: #RHS plateaux z[i] = plateaux #Hole in weir (slightly higher than inflow condition) if x[i] >= 0.3 and x[i] < 0.4 and y[i] > 0.2 and y[i] < 0.4: z[i] = -x[i]+self.inflow_stage + 0.02 #Channel behind weir x0 = 0.5 if x[i] >= 0.4 and x[i] < x0 and y[i] > 0.2 and y[i] < 0.4: z[i] = -x[i]+self.inflow_stage + 0.02 if x[i] >= x0 and x[i] < 0.6 and y[i] > 0.2 and y[i] < 0.4: #Flatten it out towards the end z[i] = -x0+self.inflow_stage + 0.02 + (x0-x[i])/5 #Hole to the east x0 = 1.1; y0 = 0.35 #if x[i] < -0.2 and y < 0.5: if sqrt((2*(x[i]-x0))**2 + (2*(y[i]-y0))**2) < 0.2: z[i] = sqrt(((x[i]-x0))**2 + ((y[i]-y0))**2)-1.0 #Tiny channel draining hole if x[i] >= 1.14 and x[i] < 1.2 and y[i] >= 0.4 and y[i] < 0.6: z[i] = -0.9 #North south if x[i] >= 0.9 and x[i] < 1.18 and y[i] >= 0.58 and y[i] < 0.65: z[i] = -1.0 + (x[i]-0.9)/3 #East west #Stuff not in use #Upward slope at inlet to the north west #if x[i] < 0.0: # and y[i] > 0.5: # #z[i] = -y[i]+0.5 #-x[i]/2 # z[i] = x[i]/4 - y[i]**2 + 0.5 #Hole to the west #x0 = -0.4; y0 = 0.35 # center #if sqrt((2*(x[i]-x0))**2 + (2*(y[i]-y0))**2) < 0.2: # z[i] = sqrt(((x[i]-x0))**2 + ((y[i]-y0))**2)-0.2 return z/2 class Weir_simple: """Set a bathymetry for weir with a hole and a downstream gutter x,y are assumed to be in the unit square """ def __init__(self, stage): self.inflow_stage = stage def __call__(self, x, y): from Numeric import zeros, Float N = len(x) assert N == len(y) z = zeros(N, Float) for i in range(N): z[i] = -x[i] #General slope #Flat bit to the left if x[i] < 0.3: z[i] = -x[i]/10 #General slope #Weir if x[i] > 0.3 and x[i] < 0.4: z[i] = -x[i]+0.9 #Dip if x[i] > 0.6 and x[i] < 0.9: z[i] = -x[i]-0.5 #-y[i]/5 #Hole in weir (slightly higher than inflow condition) if x[i] > 0.3 and x[i] < 0.4 and y[i] > 0.2 and y[i] < 0.4: z[i] = -x[i]+self.inflow_stage + 0.05 return z/2 class Constant_stage: """Set an initial condition with constant stage """ def __init__(self, s): self.s = s def __call__(self, x, y): return self.s class Constant_height: """Set an initial condition with constant water height, e.g stage s = z+h """ def __init__(self, W, h): self.W = W self.h = h def __call__(self, x, y): if self.W is None: from Numeric import ones, Float return self.h*ones(len(x), Float) else: return self.W(x,y) + self.h def compute_fluxes_python(domain): """Compute all fluxes and the timestep suitable for all volumes in domain. Compute total flux for each conserved quantity using "flux_function" Fluxes across each edge are scaled by edgelengths and summed up Resulting flux is then scaled by area and stored in explicit_update for each of the three conserved quantities stage, xmomentum and ymomentum The maximal allowable speed computed by the flux_function for each volume is converted to a timestep that must not be exceeded. The minimum of those is computed as the next overall timestep. Post conditions: domain.explicit_update is reset to computed flux values domain.timestep is set to the largest step satisfying all volumes. """ import sys from Numeric import zeros, Float N = domain.number_of_elements #Shortcuts Stage = domain.quantities['stage'] Xmom = domain.quantities['xmomentum'] Ymom = domain.quantities['ymomentum'] Bed = domain.quantities['elevation'] #Arrays stage = Stage.edge_values xmom = Xmom.edge_values ymom = Ymom.edge_values bed = Bed.edge_values stage_bdry = Stage.boundary_values xmom_bdry = Xmom.boundary_values ymom_bdry = Ymom.boundary_values flux = zeros((N,3), Float) #Work array for summing up fluxes #Loop timestep = float(sys.maxint) for k in range(N): for i in range(3): #Quantities inside volume facing neighbour i ql = [stage[k, i], xmom[k, i], ymom[k, i]] zl = bed[k, i] #Quantities at neighbour on nearest face n = domain.neighbours[k,i] if n < 0: m = -n-1 #Convert negative flag to index qr = [stage_bdry[m], xmom_bdry[m], ymom_bdry[m]] zr = zl #Extend bed elevation to boundary else: m = domain.neighbour_edges[k,i] qr = [stage[n, m], xmom[n, m], ymom[n, m]] zr = bed[n, m] #Outward pointing normal vector normal = domain.normals[k, 2*i:2*i+2] #Flux computation using provided function edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) flux[k,:] = edgeflux return flux ############################################## #Initialise module from anuga.utilities import compile if compile.can_use_C_extension('shallow_water_ext.c'): #Replace python version with c implementations from shallow_water_ext import rotate, assign_windfield_values compute_fluxes = compute_fluxes_c extrapolate_second_order_sw=extrapolate_second_order_sw_c gravity = gravity_c manning_friction = manning_friction_c h_limiter = h_limiter_c balance_deep_and_shallow = balance_deep_and_shallow_c protect_against_infinitesimal_and_negative_heights = protect_against_infinitesimal_and_negative_heights_c #distribute_to_vertices_and_edges = distribute_to_vertices_and_edges_c #(like MH's) #Optimisation with psyco from config import use_psyco if use_psyco: try: import psyco except: import os if os.name == 'posix' and os.uname()[4] == 'x86_64': pass #Psyco isn't supported on 64 bit systems, but it doesn't matter else: msg = 'WARNING: psyco (speedup) could not import'+\ ', you may want to consider installing it' print msg else: psyco.bind(Domain.distribute_to_vertices_and_edges) psyco.bind(Domain.compute_fluxes) if __name__ == "__main__": pass