"""Class Domain - 2D triangular domains for finite-volume computations of the shallow water wave 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 = S where U = [w, uh, vh] E = [uh, u^2h + gh^2/2, uvh] G = [vh, uvh, v^2h + gh^2/2] S represents source terms forcing the system (e.g. gravity, friction, wind stress, ...) The quantities are symbol variable name explanation z elevation elevation of bed on which flow is modelled h height water height above z w stage water level, w = z+h u speed in the x direction v speed in the y direction uh xmomentum momentum in the x direction vh ymomentum momentum in the y direction eta mannings friction coefficient nu wind stress coefficient The conserved quantities are w, uh, vh For details see e.g. Christopher Zoppou and Stephen Roberts, Catastrophic Collapse of Water Supply Reservoirs in Urban Areas, Journal of Hydraulic Engineering, vol. 127, No. 7 July 1999 Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou Geoscience Australia, 2004 """ from domain import * from region import * Generic_domain = Domain #Rename class Domain(Generic_domain): def __init__(self, coordinates, vertices, boundary = None, tagged_elements = None): conserved_quantities = ['level', 'xmomentum', 'ymomentum'] other_quantities = ['elevation', 'friction'] Generic_domain.__init__(self, coordinates, vertices, boundary, conserved_quantities, other_quantities, tagged_elements) from config import minimum_allowed_height, g self.minimum_allowed_height = minimum_allowed_height self.g = g self.forcing_terms.append(gravity) self.forcing_terms.append(manning_friction) #Realtime visualisation self.visualise = False #Stored output self.store = False self.format = 'sww' self.smooth = True #Reduction operation for get_vertex_values #from util import mean #self.reduction = mean self.reduction = min #Looks better near steep slopes self.quantities_to_be_stored = ['level'] #Establish shortcuts to relevant quantities (for efficiency) #self.w = self.quantities['level'] #self.uh = self.quantities['xmomentum'] #self.vh = self.quantities['ymomentum'] #self.z = self.quantities['elevation'] #self.eta = self.quantities['friction'] def check_integrity(self): Generic_domain.check_integrity(self) #Check that we are solving the shallow water wave equation msg = 'First conserved quantity must be "level"' assert self.conserved_quantities[0] == 'level', 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 #Check that levels are >= bed elevation from Numeric import alltrue, greater_equal level = self.quantities['level'] bed = self.quantities['elevation'] 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) #FIXME: Under construction # def set_defaults(self): # """Set default values for uninitialised quantities. # This is specific to the shallow water wave equation # Defaults for 'elevation', 'friction', 'xmomentum' and 'ymomentum' # are 0.0. Default for 'level' is whatever the value of 'elevation'. # """ # for name in self.other_quantities + self.conserved_quantities: # print name # print self.quantities.keys() # if not self.quantities.has_key(name): # if name == 'level': # if self.quantities.has_key('elevation'): # z = self.quantities['elevation'].vertex_values # self.set_quantity(name, z) # else: # self.set_quantity(name, 0.0) # else: # self.set_quantity(name, 0.0) # #Lift negative heights up # #z = self.quantities['elevation'].vertex_values # #w = self.quantities['level'].vertex_values # #h = w-z # #for k in range(h.shape[0]): # # for i in range(3): # # if h[k, i] < 0.0: # # w[k, i] = z[k, i] # #self.quantities['level'].interpolate() def evolve(self, yieldstep = None, finaltime = None): """Specialisation of basic evolve method from parent class """ #Call check integrity here rather than from user scripts #self.check_integrity() #Initialise real time viz if requested if self.visualise is True and self.time == 0.0: import realtime_visualisation as visualise visualise.create_surface(self) #Store model data, e.g. for visualisation if self.store is True and self.time == 0.0: self.initialise_storage() #print 'Storing results in ' + self.writer.filename else: #print 'Results will not be stored.' #print 'To store results set domain.store = True' pass #FIXME: Diagnostic output should be controlled by # a 'verbose' flag living in domain (or in a parent class) #Call basic machinery from parent class for t in Generic_domain.evolve(self, yieldstep, finaltime): #Real time viz if self.visualise is True: visualise.update(self) #Store model data, e.g. for subsequent visualisation if self.store is True: #self.store_timestep(['level', 'xmomentum', 'ymomentum']) 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 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) #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 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 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 level, 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 Level = domain.quantities['level'] Xmom = domain.quantities['xmomentum'] Ymom = domain.quantities['ymomentum'] Bed = domain.quantities['elevation'] #Arrays level = Level.edge_values xmom = Xmom.edge_values ymom = Ymom.edge_values bed = Bed.edge_values level_bdry = Level.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 = [level[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 = [level_bdry[m], xmom_bdry[m], ymom_bdry[m]] zr = zl #Extend bed elevation to boundary else: m = domain.neighbour_edges[k,i] qr = [level[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, domain.radii[k]/max_speed) except ZeroDivisionError: pass #Normalise by area and store for when all conserved #quantities get updated flux /= domain.areas[k] Level.explicit_update[k] = flux[0] Xmom.explicit_update[k] = flux[1] Ymom.explicit_update[k] = flux[2] domain.timestep = timestep 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 Level = domain.quantities['level'] 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, Level.edge_values, Xmom.edge_values, Ymom.edge_values, Bed.edge_values, Level.boundary_values, Xmom.boundary_values, Ymom.boundary_values, Level.explicit_update, Xmom.explicit_update, Ymom.explicit_update) #################################### # 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 """ #Remove very thin layers of water protect_against_infinitesimal_and_negative_heights(domain) #Extrapolate all conserved quantities 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 dry(domain): """Protect against infinitesimal heights and associated high velocities at vertices """ #FIXME: Experimental (from old version). Not in use at the moment #Shortcuts wv = domain.quantities['level'].vertex_values zv = domain.quantities['elevation'].vertex_values xmomv = domain.quantities['xmomentum'].vertex_values ymomv = domain.quantities['ymomentum'].vertex_values hv = wv - zv #Water depths at vertices #Update for k in range(domain.number_of_elements): hmax = max(hv[k, :]) if hmax < domain.minimum_allowed_height: #Control level wv[k, :] = zv[k, :] #Control momentum xmomv[k,:] = ymomv[k,:] = 0.0 def protect_against_infinitesimal_and_negative_heights(domain): """Protect against infinitesimal heights and associated high velocities """ #Shortcuts wc = domain.quantities['level'].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 level wc[k] = zc[k] #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['level'].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, wc, zc, xmomc, ymomc) def balance_deep_and_shallow(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. """ #Shortcuts wc = domain.quantities['level'].centroid_values zc = domain.quantities['elevation'].centroid_values hc = wc - zc wv = domain.quantities['level'].vertex_values zv = domain.quantities['elevation'].vertex_values hv = wv-zv #Computed linear combination between constant levels and and #levels 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,:] def balance_deep_and_shallow_c(domain): """Wrapper for C implementation """ #Shortcuts wc = domain.quantities['level'].centroid_values zc = domain.quantities['elevation'].centroid_values hc = wc - zc wv = domain.quantities['level'].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 from shallow_water_ext import balance_deep_and_shallow balance_deep_and_shallow(wc, zc, hc, wv, zv, hv, xmomc, ymomc, xmomv, ymomv) ############################################### #Boundary - 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.level = domain.quantities['level'].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.level[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 ######################### #Standard forcing terms: # def gravity(domain): """Apply gravitational pull in the presence of bed slope """ from util import gradient from Numeric import zeros, Float, array, sum xmom = domain.quantities['xmomentum'].explicit_update ymom = domain.quantities['ymomentum'].explicit_update Level = domain.quantities['level'] Elevation = domain.quantities['elevation'] h = Level.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 Level = domain.quantities['level'] Elevation = domain.quantities['elevation'] h = Level.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['level'].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['level'].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['level'].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 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, y) except Exception, e: msg = 'Function %s could not be executed:\n%s' %(f, e) 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 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,y)[0] phi = lambda t,x,y: vector_function(t,x,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 ########################### ########################### #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_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 ############################################## #Initialise module 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 gravity = gravity_c manning_friction = manning_friction_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 #Optimisation with psyco from config import use_psyco if use_psyco: try: import psyco except: 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