"""Class Domain - 1D interval 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 = S where U = [w, uh] E = [uh, u^2h + gh^2/2] S represents source terms forcing the system (e.g. gravity, friction, wind stress, ...) and _t, _x, _y denote the derivative with respect to t, x and y respectiely. The quantities are symbol variable name explanation x x horizontal distance from origin [m] z elevation elevation of bed on which flow is modelled [m] h height water height above z [m] w stage absolute water level, w = z+h [m] u speed in the x direction [m/s] uh xmomentum momentum in the x direction [m^2/s] eta mannings friction coefficient [to appear] nu wind stress coefficient [to appear] The conserved quantities are w, uh 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 John Jakeman, Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou Geoscience Australia, 2006 """ from domain import * Generic_Domain = Domain #Rename #Shallow water domain class Domain(Generic_Domain): def __init__(self, coordinates, boundary = None, tagged_elements = None): conserved_quantities = ['stage', 'xmomentum'] #['height', 'xmomentum'] evolved_quantities = ['stage', 'xmomentum', 'elevation', 'height', 'velocity'] other_quantities = ['friction'] Generic_Domain.__init__(self, coordinates, boundary, conserved_quantities, evolved_quantities, other_quantities, tagged_elements) from config import minimum_allowed_height, g, h0 self.minimum_allowed_height = minimum_allowed_height self.g = g self.h0 = h0 self.forcing_terms.append(gravity_F2) #gravity, gravity_F1, gravity_F2 #self.forcing_terms.append(manning_friction) #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 = True self.format = 'sww' self.smooth = True #Evolve parametrs self.cfl = 1.0 #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 = ['stage','xmomentum'] self.__doc__ = 'shallow_water_domain_avalanche' self.check_integrity() def set_quantities_to_be_stored(self, q): """Specify which quantities will be stored in the sww file. q must be either: - the name of a quantity - a list of quantity names - None In the two first cases, the named quantities will be stored at each yieldstep (This is in addition to the quantities elevation and friction) If q is None, storage will be switched off altogether. """ if q is None: self.quantities_to_be_stored = [] self.store = False return if isinstance(q, basestring): q = [q] # Turn argument into a list #Check correcness for quantity_name in q: msg = 'Quantity %s is not a valid conserved quantity' %quantity_name assert quantity_name in self.conserved_quantities, msg self.quantities_to_be_stored = q 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.visualiser.setup['elevation']=True self.visualiser.updating['stage']=True self.visualise = True if self.visualise_color_stage == True: self.visualiser.coloring['stage'] = True self.visualiser.qcolor['stage'] = (0.0, 0.0, 0.8) print 'initialise visualiser' print self.visualiser.setup print self.visualiser.updating 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 "stage"' assert self.conserved_quantities[0] == 'stage', msg msg = 'Second conserved quantity must be "xmomentum"' assert self.conserved_quantities[1] == 'xmomentum', msg msg = 'First evolved quantity must be "stage"' assert self.evolved_quantities[0] == 'stage', msg msg = 'Second evolved quantity must be "xmomentum"' assert self.evolved_quantities[1] == 'xmomentum', msg msg = 'Third evolved quantity must be "elevation"' assert self.evolved_quantities[2] == 'elevation', msg msg = 'Fourth evolved quantity must be "height"' assert self.evolved_quantities[3] == 'height', msg msg = 'Fifth evolved quantity must be "velocity"' assert self.evolved_quantities[4] == 'velocity', 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_C_wellbalanced(self) #compute_fluxes_C_nonwellbalanced2(self) def compute_timestep(self): #Call correct module function compute_timestep(self) def distribute_to_vertices_and_edges(self): #Call correct module function(either from this module or C-extension) distribute_to_vertices_and_edges_shv(self) #distribute_to_vertices_and_edges_shm(self) def evolve(self, yieldstep = None, finaltime = None, duration = None, skip_initial_step = False): #Call basic machinery from parent class for t in Generic_Domain.evolve(self, yieldstep, finaltime, duration, skip_initial_step): yield(t) def initialise_storage(self): """Create and initialise self.writer object for storing data. Also, save x 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) #=============== End of Shallow Water Domain =============================== #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 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, are stored as elements 0 and 1 in the numerical vectors ql an qr. Bed elevations zl and zr. """ from config import g, epsilon, h0 from math import sqrt from Numeric import array #Align momentums with x-axis q_left = ql q_left[1] = q_left[1]*normal q_right = qr q_right[1] = q_right[1]*normal z = 0.5*(zl+zr) #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 + h0/h_left) uh_left = u_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 + h0/h_right) uh_right = u_right*h_right #We have got h and u at vertex, then the following is the calculation of fluxes! 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*h_left]) flux_right = array([u_right*h_right, u_right*uh_right + 0.5*g*h_right*h_right]) denom = s_max-s_min if denom == 0.0: edgeflux = array([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[1] = edgeflux[1]*normal max_speed = max(abs(s_max), abs(s_min)) return edgeflux, max_speed # def compute_timestep(domain): import sys from Numeric import zeros, Float N = domain.number_of_elements #Shortcuts Stage = domain.quantities['stage'] Xmom = domain.quantities['xmomentum'] Bed = domain.quantities['elevation'] stage = Stage.vertex_values xmom = Xmom.vertex_values bed = Bed.vertex_values stage_bdry = Stage.boundary_values xmom_bdry = Xmom.boundary_values flux = zeros(2, Float) #Work array for summing up fluxes ql = zeros(2, Float) qr = zeros(2, Float) #Loop timestep = float(sys.maxint) enter = True for k in range(N): flux[:] = 0. #Reset work array for i in range(2): #Quantities inside volume facing neighbour i ql = [stage[k, i], xmom[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[0] = stage_bdry[m] qr[1] = xmom_bdry[m] zr = zl #Extend bed elevation to boundary else: m = domain.neighbour_vertices[k,i] qr[0] = stage[n, m] qr[1] = xmom[n, m] zr = bed[n, m] #Outward pointing normal vector normal = domain.normals[k, i] edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) #Update optimal_timestep try: timestep = min(timestep, domain.cfl*0.5*domain.areas[k]/max_speed) except ZeroDivisionError: pass domain.timestep = timestep # Compute flux definition # ################################### def compute_fluxes_C_wellbalanced(domain): import sys from Numeric import zeros, Float N = domain.number_of_elements timestep = float(sys.maxint) epsilon = domain.epsilon g = domain.g neighbours = domain.neighbours neighbour_vertices = domain.neighbour_vertices normals = domain.normals areas = domain.areas Stage = domain.quantities['stage'] Xmom = domain.quantities['xmomentum'] Bed = domain.quantities['elevation'] Height = domain.quantities['height'] Velocity = domain.quantities['velocity'] stage_boundary_values = Stage.boundary_values xmom_boundary_values = Xmom.boundary_values bed_boundary_values = Bed.boundary_values height_boundary_values= Height.boundary_values vel_boundary_values = Velocity.boundary_values stage_explicit_update = Stage.explicit_update xmom_explicit_update = Xmom.explicit_update bed_explicit_values = Bed.explicit_update height_explicit_values= Height.explicit_update vel_explicit_values = Velocity.explicit_update max_speed_array = domain.max_speed_array domain.distribute_to_vertices_and_edges() domain.update_boundary() stage_V = Stage.vertex_values xmom_V = Xmom.vertex_values bed_V = Bed.vertex_values height_V= Height.vertex_values vel_V = Velocity.vertex_values number_of_elements = len(stage_V) from comp_flux_ext_wellbalanced import compute_fluxes_ext_wellbalanced domain.flux_timestep = compute_fluxes_ext_wellbalanced(timestep, epsilon, g, neighbours, neighbour_vertices, normals, areas, stage_V, xmom_V, bed_V, height_V, vel_V, stage_boundary_values, xmom_boundary_values, bed_boundary_values, height_boundary_values, vel_boundary_values, stage_explicit_update, xmom_explicit_update, bed_explicit_values, height_explicit_values, vel_explicit_values, number_of_elements, max_speed_array) def compute_fluxes_C_nonwellbalanced2(domain): import sys from Numeric import zeros, Float N = domain.number_of_elements timestep = float(sys.maxint) epsilon = domain.epsilon g = domain.g neighbours = domain.neighbours neighbour_vertices = domain.neighbour_vertices normals = domain.normals areas = domain.areas Stage = domain.quantities['stage'] Xmom = domain.quantities['xmomentum'] Bed = domain.quantities['elevation'] Height = domain.quantities['height'] Velocity = domain.quantities['velocity'] stage_boundary_values = Stage.boundary_values xmom_boundary_values = Xmom.boundary_values bed_boundary_values = Bed.boundary_values height_boundary_values= Height.boundary_values vel_boundary_values = Velocity.boundary_values stage_explicit_update = Stage.explicit_update xmom_explicit_update = Xmom.explicit_update bed_explicit_values = Bed.explicit_update height_explicit_values= Height.explicit_update vel_explicit_values = Velocity.explicit_update max_speed_array = domain.max_speed_array domain.distribute_to_vertices_and_edges() domain.update_boundary() stage_V = Stage.vertex_values xmom_V = Xmom.vertex_values bed_V = Bed.vertex_values height_V= Height.vertex_values vel_V = Velocity.vertex_values number_of_elements = len(stage_V) from comp_flux_ext_nonwellbalanced2 import compute_fluxes_ext_nonwellbalanced2 domain.flux_timestep = compute_fluxes_ext_nonwellbalanced2(timestep, epsilon, g, neighbours, neighbour_vertices, normals, areas, stage_V, xmom_V, bed_V, height_V, vel_V, stage_boundary_values, xmom_boundary_values, bed_boundary_values, height_boundary_values, vel_boundary_values, stage_explicit_update, xmom_explicit_update, bed_explicit_values, height_explicit_values, vel_explicit_values, number_of_elements, max_speed_array) # ################################### # Module functions for gradient limiting (distribute_to_vertices_and_edges) def distribute_to_vertices_and_edges_shv(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) import sys from Numeric import zeros, Float from config import epsilon, h0 N = domain.number_of_elements #Shortcuts Stage = domain.quantities['stage'] Xmom = domain.quantities['xmomentum'] Bed = domain.quantities['elevation'] Height = domain.quantities['height'] Velocity = domain.quantities['velocity'] #Arrays w_C = Stage.centroid_values uh_C = Xmom.centroid_values z_C = Bed.centroid_values h_C = Height.centroid_values u_C = Velocity.centroid_values for i in range(N): h_C[i] = w_C[i] - z_C[i] if h_C[i] <= epsilon: uh_C[i] = 0.0 u_C[i] = 0.0 w_C[i] = z_C[i] else: u_C[i] = uh_C[i]/(h_C[i] + h0/h_C[i]) for name in ['stage', 'height', 'velocity']: Q = domain.quantities[name] if domain.order == 1: Q.extrapolate_first_order() elif domain.order == 2: Q.extrapolate_second_order() else: raise 'Unknown order' stage_V = domain.quantities['stage'].vertex_values bed_V = domain.quantities['elevation'].vertex_values h_V = domain.quantities['height'].vertex_values u_V = domain.quantities['velocity'].vertex_values xmom_V = domain.quantities['xmomentum'].vertex_values bed_V[:] = stage_V - h_V xmom_V[:] = u_V * h_V return def distribute_to_vertices_and_edges_shm(domain): # shm stands for STAGE, HEIGHT, MOMENTUM """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) import sys from Numeric import zeros, Float from config import epsilon, h0 N = domain.number_of_elements #Shortcuts Stage = domain.quantities['stage'] Xmom = domain.quantities['xmomentum'] Bed = domain.quantities['elevation'] Height = domain.quantities['height'] Velocity = domain.quantities['velocity'] #Arrays w_C = Stage.centroid_values uh_C = Xmom.centroid_values z_C = Bed.centroid_values h_C = Height.centroid_values u_C = Velocity.centroid_values for i in range(N): h_C[i] = w_C[i] - z_C[i] if h_C[i] <= 0.01: #epsilon : #h_C[i] = 0.0 #w_C[i] = z_C[i] uh_C[i] = 0.0 u_C[i] = 0.0 if h_C[i] < epsilon: h_C[i] = 0.0 w_C[i] = z_C[i] else: u_C[i] = uh_C[i]/h_C[i] #+ h0/h_C[i]) for name in ['stage', 'height', 'xmomentum']: Q = domain.quantities[name] if domain.order == 1: Q.extrapolate_first_order() elif domain.order == 2: Q.extrapolate_second_order() else: raise 'Unknown order' stage_V = domain.quantities['stage'].vertex_values bed_V = domain.quantities['elevation'].vertex_values h_V = domain.quantities['height'].vertex_values u_V = domain.quantities['velocity'].vertex_values xmom_V = domain.quantities['xmomentum'].vertex_values bed_V[:] = stage_V - h_V for i in range(N): if h_V[i] <= 0.0: h_V[i] = 0.0 stage_V[i] = bed_V[i] xmom_V[i] = 0.0 u_V[:] = xmom_V/(h_V + h0/h_V) return # 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 hc = wc - zc #Water depths at centroids zv = domain.quantities['elevation'].vertex_values wv = domain.quantities['stage'].vertex_values hv = wv-zv xmomv = domain.quantities['xmomentum'].vertex_values #remove the above two lines and corresponding code below #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 wv[k,0] = zv[k,0] wv[k,1] = zv[k,1] xmomc[k] = 0.0 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(2): 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(2): 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(2): 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(2): hvbar[k,i] = hc[k] + phi*dh[k,i] 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 alpha = 0.0 #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): for i in range(2): wv[k,i] = zv[k,i] + (1.0-alpha)*hvbar[k,i] + alpha*hv[k,i] #Momentums at centroids xmomc = domain.quantities['xmomentum'].centroid_values #Momentums at vertices xmomv = domain.quantities['xmomentum'].vertex_values # Update momentum as a linear combination of # xmomc and ymomc (shallow) and momentum # from extrapolator xmomv and ymomv (deep). xmomv[k,:] = (1.0-alpha)*xmomc[k] + alpha*xmomv[k,:] ######################### #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 stage = domain.quantities['stage'].explicit_update Stage = domain.quantities['stage'] Elevation = domain.quantities['elevation'] h = Stage.vertex_values - Elevation.vertex_values b = Elevation.vertex_values w = Stage.vertex_values x = domain.get_vertex_coordinates() g = domain.g for k in range(domain.number_of_elements): avg_h = sum( h[k,:] )/2 #Compute bed slope x0, x1 = x[k,:] b0, b1 = b[k,:] w0, w1 = w[k,:] wx = gradient(x0, x1, w0, w1) bx = gradient(x0, x1, b0, b1) #Update momentum (explicit update is reset to source values) xmom[k] += -g*bx*avg_h def gravity_F1(domain): """Apply gravitational pull in the presence of bed slope """ from util import gradient from Numeric import zeros, Float, array, sum from parameters import F1#This is an additional friction!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! xmom = domain.quantities['xmomentum'].explicit_update stage = domain.quantities['stage'].explicit_update Stage = domain.quantities['stage'] Elevation = domain.quantities['elevation'] h = Stage.vertex_values - Elevation.vertex_values b = Elevation.vertex_values w = Stage.vertex_values x = domain.get_vertex_coordinates() g = domain.g for k in range(domain.number_of_elements): avg_h = sum( h[k,:] )/2 #Compute bed slope x0, x1 = x[k,:] b0, b1 = b[k,:] w0, w1 = w[k,:] wx = gradient(x0, x1, w0, w1) bx = gradient(x0, x1, b0, b1) #Update momentum (explicit update is reset to source values) xmom[k] += -g*bx*avg_h + avg_h*F1#This is an additional friction!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! def gravity_F2(domain): """Apply gravitational pull in the presence of bed slope """ from util import gradient from Numeric import zeros, Float, array, sum from parameters import F2#This is an additional friction!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! xmom = domain.quantities['xmomentum'].explicit_update stage = domain.quantities['stage'].explicit_update Stage = domain.quantities['stage'] Elevation = domain.quantities['elevation'] h = Stage.vertex_values - Elevation.vertex_values b = Elevation.vertex_values w = Stage.vertex_values x = domain.get_vertex_coordinates() g = domain.g for k in range(domain.number_of_elements): avg_h = sum( h[k,:] )/2 #Compute bed slope x0, x1 = x[k,:] b0, b1 = b[k,:] w0, w1 = w[k,:] wx = gradient(x0, x1, w0, w1) bx = gradient(x0, x1, b0, b1) #Update momentum (explicit update is reset to source values) xmom[k] += -g*bx*avg_h + avg_h*F2#This is an additional friction!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 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 eta = domain.quantities['friction'].centroid_values xmom_update = domain.quantities['xmomentum'].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 * uh[k] S /= h[k]**(7.0/3) #Update momentum xmom_update[k] += S*uh[k] 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 tau = domain.quantities['linear_friction'].centroid_values xmom_update = domain.quantities['xmomentum'].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] 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 = 2 x = ones(2, Float) try: q = f(1.0, x=x) 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: vector_function(t,x=x)[0] phi = lambda t,x: vector_function(t,x=x)[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=....' print 'phi', 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 N = domain.number_of_elements t = domain.time if callable(self.speed): xc = domain.get_centroid_coordinates() s_vec = self.speed(t, xc) 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) 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) assign_windfield_values(xmom_update, s_vec, phi_vec, self.const) #def assign_windfield_values(xmom_update, ymom_update, # s_vec, phi_vec, const): def assign_windfield_values(xmom_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 * u xmom_update[k] += S*u