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double_gyre.py
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double_gyre.py
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"""
Double-gyre on octogonal domain
"""
import numpy as np
import os
import time
import torch
from qgm import QGFV
torch.backends.cudnn.deterministic = True
device = 'cuda' if torch.cuda.is_available() else 'cpu'
dtype = torch.float64
print(device, dtype)
# grid
n_ens = 1
nl = 3
nx = 256
ny = 256
dt = 4000
# nx = 512
# ny = 512
# dt = 2000
output_dir = f'run_outputs/{nx}x{ny}_dt{dt}/'
os.makedirs(output_dir) if not os.path.isdir(output_dir) else None
Lx = 5120.0e3
Ly = 5120.0e3
dx = Lx / nx
dy = Ly / ny
# vertex grid
xv = torch.linspace(0, Lx, nx+1, dtype=torch.float64, device=device)
yv = torch.linspace(0, Ly, ny+1, dtype=torch.float64, device=device)
x, y = torch.meshgrid(xv, yv, indexing='ij')
# layer thickness
H = torch.zeros(nl,1,1, dtype=dtype, device=device)
H[0,0,0] = 400.
H[1,0,0] = 1100.
H[2,0,0] = 2600.
# gravity
g_prime = torch.zeros(nl,1,1, dtype=dtype, device=device)
g_prime[0,0,0] = 9.81
g_prime[1,0,0] = 0.025
g_prime[2,0,0] = 0.0125
# Coriolis beta plane
f0 = 9.375e-5 # mean coriolis (s^-1)
beta = 1.754e-11 # coriolis gradient (m^-1 s^-1)
# forcing
yc = 0.5 * (yv[1:] + yv[:-1]) # cell centers
tau0 = 0.08 / 1000
curl_tau = -tau0*2*torch.pi/Ly*torch.sin(2*torch.pi*yc/Ly).tile((nx, 1))
curl_tau = curl_tau.unsqueeze(0).repeat(n_ens, 1, 1, 1)
# drag
delta_ek = 2.
bottom_drag_coef = delta_ek / H[-1].cpu().item() * f0 / 2
# octogonal domain
mask = torch.ones(nx, ny)
for i in range(nx//4):
for j in range(ny//4):
if i+j < min(nx//4, ny//4):
mask[i,j] = 0.
mask[i,-1-j] = 0.
mask[-1-i,j] = 0.
mask[-1-i,-1-j] = 0.
param = {
'nx': nx,
'ny': ny,
'nl': nl,
'n_ens': n_ens,
'mask': mask,
'Lx': Lx,
'Ly': Ly,
'flux_stencil': 5,
'H': H,
'g_prime': g_prime,
'tau0': tau0,
'f0': f0,
'beta': beta,
'bottom_drag_coef': bottom_drag_coef,
'device': device,
'dt': dt, # time-step (s)
}
qg = QGFV(param)
qg.set_wind_forcing(curl_tau)
# time params
dt = param['dt']
t = 0
n_steps = int(50*365*24*3600 / dt) + 1
freq_log = 1000
n_steps_save = int(10*365*24*3600 / dt) + 1
freq_save = int(15*24*3600 / dt)
freq_plot = int(10*24*3600 / dt)
# surface vorticity plot
if freq_plot > 0:
import matplotlib.pyplot as plt
plt.ion()
f,a = plt.subplots(1,1, figsize=(20,10))
f.suptitle(f'Upper layer relative voriticy (units of f0), {t/(365*86400):.2f} yrs')
t0 = time.time()
# time integration
for n in range(1, n_steps+1):
qg.step() # one RK3 integration step
t += dt
if n % 500 == 0 and torch.isnan(qg.psi).any():
raise ValueError(f'Stopping, NAN number in p at iteration {n}.')
if freq_plot > 0 and (n % freq_plot == 0 or n == n_steps):
w_over_f0 = (qg.laplacian_h(qg.psi, qg.dx, qg.dy) / qg.f0 * qg.masks.psi).cpu()
im = a.imshow(w_over_f0[0,0].T, cmap='bwr', vmin=-0.2, vmax=0.2, origin='lower')
f.colorbar(im ) if n // freq_plot == 1 else None
f.suptitle(f'Upper layer relative vorticity (units of $f_0$), {t/(365*86400):.2f} yrs')
plt.pause(0.01)
if freq_log > 0 and n % freq_log == 0:
print(f'{n=:06d}, t={t/(365*24*60**2):.2f} yr, '\
f'q: {qg.q.sum().cpu().item():+.5E}, '\
f'qabs: {qg.q.abs().sum().cpu().item():+.5E}')
if freq_save > 0 and n > n_steps_save and n % freq_save == 0:
n_years, n_days = int(t // (365*24*3600)), int(t % (365*24*3600) // (24*3600))
fname = os.path.join(output_dir, f'psi_{n_years:03d}y_{n_days:03d}d.npy')
np.save(fname, qg.psi.cpu().numpy().astype('float32'))
print(f'saved psi to {fname}')
total_time = time.time() - t0
print(total_time)
print(f'{total_time // 3600}h {(total_time % 3600) // 60} min')