def timestep(self,dt): #performs one timestep, i.e. calculates a new surface elev, thickness from prev one
D = np.zeros(self.num_nodes)
slopes = tools.calculate_slopes(self.surface_elev, self.dx)
for i in range(0,self.num_nodes):
if(i<20):
D[i] = (((-2*self.glenns_a*(self.p*self.g)**self.glenns_n)/(self.glenns_n+2))*(self.ice_thickness[i]**(self.glenns_n+2))*(abs((slopes[i])**(self.glenns_n-1))))-(self.bslip_1*self.p*self.g*(self.ice_thickness[i]**2))
elif(i<40):
D[i] = (((-2*self.glenns_a*(self.p*self.g)**self.glenns_n)/(self.glenns_n+2))*(self.ice_thickness[i]**(self.glenns_n+2))*(abs((slopes[i])**(self.glenns_n-1))))-(self.bslip_2*self.p*self.g*(self.ice_thickness[i]**2))
else:
D[i] = (((-2*self.glenns_a*(self.p*self.g)**self.glenns_n)/(self.glenns_n+2))*(self.ice_thickness[i]**(self.glenns_n+2))*(abs((slopes[i])**(self.glenns_n-1))))-(self.bslip_3*self.p*self.g*(self.ice_thickness[i]**2))
A = sparse.lil_matrix((self.num_nodes,self.num_nodes))
A[0, 0] = 1
A[self.num_nodes-1, self.num_nodes-1] = 1
B = np.zeros(self.num_nodes)
B[0] = self.bed_elev[0]
B[self.num_nodes-1] = self.bed_elev[self.num_nodes-1]
for i in range(1, self.num_nodes-1):
alpha = (dt/(4.0*self.dx**2))*(D[i] + D[i+1])
beta = (dt/(4.0*self.dx**2))*(D[i-1] + D[i])
A[i, i-1] = beta
A[i, i] = 1 - alpha - beta
A[i, i+1] = alpha
B[i] = (-alpha*self.surface_elev[i+1]) + ((1 + alpha + beta)*self.surface_elev[i]) - (beta*self.surface_elev[i-1]) + (self.mass_balance[i]*dt)
self.surface_elev, info=linalg.bicgstab(A, B)
for i in range(self.num_nodes):
if(self.surface_elev[i] < self.bed_elev[i]):
self.surface_elev[i] = self.bed_elev[i]
self.ice_thickness = self.surface_elev - self.bed_elev
self.time += dt
def calculate_basal_velocity(self): #this calculates the basal sliding portion of velocity to see if it's reasonable
slopes = tools.calculate_slopes(self.surface_elev, self.dx)
basal_velocity = np.zeros(self.num_nodes)
for i in range(self.num_nodes):
basal_velocity[i] = -(self.bslip[i]*self.p*-self.g*self.ice_thickness[i]*slopes[i]) #g should be negative??)
print 'basal velocity at node ', i, 'is: ', basal_velocity[i]
return basal_velocity
def calculate_velocity(self): #calculates and prints out the current SURFACE velocity at each node
slopes = tools.calculate_slopes(self.surface_elev, self.dx)
velocity = np.zeros(self.num_nodes)
for i in range(self.num_nodes):
velocity[i] = ((-(2*self.glenns_a*(self.p*-self.g)**self.glenns_n)/(self.glenns_n+1))*(self.ice_thickness[i]**(self.glenns_n+1))*(abs((slopes[i])**(self.glenns_n-1))))*(slopes[i])-(self.bslip[i]*self.p*-self.g*self.ice_thickness[i]*slopes[i])
print 'velocity at node ', i, 'is: ', velocity[i]
return velocity
def calculate_velocity(self): #calculates and prints out the current velocity at each node
slopes = tools.calculate_slopes(self.surface_elev, self.dx)
velocity = np.zeros(self.num_nodes)
for i in range(self.num_nodes):
velocity[i] = ((-(2*self.glenns_a*(self.p*-9.81)**self.glenns_n)/(self.glenns_n+1))*(self.ice_thickness[i]**(self.glenns_n+1))*(abs((slopes[i])**(self.glenns_n-1))))*(slopes[i])-(self.slide_parameter*self.p*-9.81*self.ice_thickness[i]*slopes[i])
print('velocity at node ', i, 'is: ', velocity[i])
