Terminator

transport/nair_lauritzen_non_divergent.py

@@ -87,8 +87,8 @@ def u_t(t):
 # Specify locations of the two bumps
 theta_c1 = 0.0
 theta_c2 = 0.0
-lamda_c1 = -pi/6
-lamda_c2 = pi/6
+lamda_c1 = -pi/4
+lamda_c2 = pi/4
 
 if scalar_case == 'cosine_bells':
 

transport/terminator_toy.py

@@ -0,0 +1,152 @@
+from gusto import *
+from firedrake import IcosahedralSphereMesh, exp, cos, \
+    sin, SpatialCoordinate, pi, max_value, as_vector
+
+import numpy as np
+
+# This script runs the Laurtizen et al. (2015) Terminator Toy
+# test case. This examines the interaction of two species
+# in the transport equation. There is coupling
+# between the two species to model combination
+# and dissociation.
+
+######################
+
+# Time parameters
+day = 24.*60.*60.
+dt = 900.
+tmax = 12*day # this is 1036800s
+
+# Radius of the Earth
+R = 6371220.
+
+# Domain
+mesh = IcosahedralSphereMesh(radius=R,
+                             refinement_level=3, degree=2)
+
+x = SpatialCoordinate(mesh)
+
+# get lat lon coordinates
+lamda, theta, _ = lonlatr_from_xyz(x[0], x[1], x[2])
+
+domain = Domain(mesh, dt, 'BDM', 1)
+
+# Define the dry density and the two species as tracers
+rho_d = ActiveTracer(name='rho_d', space='DG',
+                     variable_type=TracerVariableType.density,
+                     transport_eqn=TransportEquationType.conservative)
+
+X = ActiveTracer(name='X', space='DG',
+                 variable_type=TracerVariableType.mixing_ratio,
+                 transport_eqn=TransportEquationType.advective)
+
+X2 = ActiveTracer(name='X2', space='DG',
+                  variable_type=TracerVariableType.mixing_ratio,
+                  transport_eqn=TransportEquationType.advective)
+
+tracers = [rho_d, X, X2]
+
+# Equation
+V = domain.spaces("HDiv")
+eqn = CoupledTransportEquation(domain, active_tracers=tracers, Vu = V)
+
+# I/O
+dirname = "terminator_toy"
+
+# Dump the solution at each day
+dumpfreq = int(day/dt)
+
+# Set dump_nc = True to use tomplot.
+output = OutputParameters(dirname=dirname,
+                          dumpfreq=dumpfreq,
+                          dump_nc=True,
+                          dump_vtus=True)
+
+# Define intermediate sums to be able to use the TracerDensity diagnostic
+X_plus_X2 = Sum('X', 'X2')
+X_plus_X2_plus_X2 = Sum('X_plus_X2', 'X2')
+tracer_diagnostic = TracerDensity('X_plus_X2_plus_X2', 'rho_d')
+
+io = IO(domain, output, diagnostic_fields = [X_plus_X2, X_plus_X2_plus_X2, tracer_diagnostic])
+
+# Define the reaction rates:
+theta_c = np.pi/9.
+lamda_c = -np.pi/3.
+
+k1 = max_value(0, sin(theta)*sin(theta_c) + cos(theta)*cos(theta_c)*cos(lamda-lamda_c))
+k2 = 1
+
+terminator_stepper = BackwardEuler(domain)
+
+physics_schemes = [(TerminatorToy(eqn, k1=k1, k2=k2, species1_name='X',
+                    species2_name='X2'), terminator_stepper)]
+
+# Set up a non-divergent, time-varying, velocity field
+def u_t(t):
+    u_zonal = k*(sin(lamda - 2*pi*t/T)**2)*sin(2*theta)*cos(pi*t/T) + ((2*pi*R)/T)*cos(theta)
+    u_merid = k*sin(2*(lamda - 2*pi*t/T))*cos(theta)*cos(pi*t/T)
+
+    cartesian_u_expr = -u_zonal*sin(lamda) - u_merid*sin(theta)*cos(lamda)
+    cartesian_v_expr = u_zonal*cos(lamda) - u_merid*sin(theta)*sin(lamda)
+    cartesian_w_expr = u_merid*cos(theta)
+
+    u_expr = as_vector((cartesian_u_expr, cartesian_v_expr, cartesian_w_expr))
+
+    return u_expr
+
+# Define limiters for the interacting species
+limiter_space = domain.spaces('DG')
+sublimiters = {'X': DG1Limiter(limiter_space), 'X2': DG1Limiter(limiter_space)}
+MixedLimiter = MixedFSLimiter(eqn, sublimiters)
+
+transport_scheme = SSPRK3(domain, limiter=MixedLimiter)
+transport_method = [DGUpwind(eqn, 'rho_d'), DGUpwind(eqn, 'X'), DGUpwind(eqn, 'X2')]
+
+# Timstepper that solves the physics separately to the dynamics
+# with a defined prescribed transporting velocity
+stepper = SplitPrescribedTransport(eqn, transport_scheme, io,
+                                    spatial_methods=transport_method,
+                                    physics_schemes=physics_schemes,
+                                    prescribed_transporting_velocity=u_t)
+
+# Set up two Gaussian bumps for the initial density field
+theta_c1 = 0.0
+theta_c2 = 0.0
+lamda_c1 = -pi/4
+lamda_c2 = pi/4
+
+X = cos(theta)*cos(lamda)
+Y = cos(theta)*sin(lamda)
+Z = sin(theta)
+
+X1 = cos(theta_c1)*cos(lamda_c1)
+Y1 = cos(theta_c1)*sin(lamda_c1)
+Z1 = sin(theta_c1)
+
+X2 = cos(theta_c2)*cos(lamda_c2)
+Y2 = cos(theta_c2)*sin(lamda_c2)
+Z2 = sin(theta_c2)
+
+g1 = exp(-5*((X-X1)**2 + (Y-Y1)**2 + (Z-Z1)**2))
+g2 = exp(-5*((X-X2)**2 + (Y-Y2)**2 + (Z-Z2)**2))
+
+rho_expr = g1 + g2
+
+X_T_0 = 4e-6
+r = k1/(4*k2)
+D_val = sqrt(r**2 + 2*X_T_0*r)
+
+# Initial condition for each species
+X_0 = D_val - r
+X2_0 = 0.5*(X_T_0 - D_val + r)
+
+T = tmax
+k = 10*R/T
+
+# Initial conditions
+stepper.fields("rho_d").interpolate(rho_expr)
+stepper.fields("X").interpolate(X_0)
+stepper.fields("X2").interpolate(X2_0)
+
+# Run until Termination!
+stepper.run(t=0, tmax=tmax)