#nus = [.5, .1, .05, .01, .005, 0.001, .0005, .0001, .00005, .00001, .000005, .000001]
nus = [.5, .1, .05, .01, .005, 0.001, .0005, .00005, .00001]
#nus = [.5, .1, .05, .01, .005]
ET = 1.
nxs = []
for nu in nus:
nx = 25
oldqoi = None
f, ax = plt.subplots(3)
l, l2 = [], []
qois = []
while True:
print(nu, nx)
x = np.linspace(0, np.pi, nx + 2)[:-1]
dx = x[1] - x[0]
u = geturec(nu=nu, x=x, evolution_time=ET, n_save_t=1)[:, -1]
l.append(ax[0].plot(x, u, label=nx, lw=.5)[0])
gradu = u.copy()
gradu[1:-1] = (u[2:] - u[:-2]) / (2 * dx)
gradu[-1] = (u[0] - u[-2]) / (2 * dx)
gradu[0] = (u[1] - u[-1]) / (2 * dx)
l2.append(ax[1].plot(x, gradu, label=nx, lw=.5)[0])
qoi = np.max(np.abs(gradu))
#qoi = x[np.argmax(gradu)]
qois.append(qoi)
if oldqoi is not None:
print(qoi, oldqoi, np.max(gradu), np.abs(qoi - oldqoi) / qoi)
if np.abs(qoi - oldqoi) / qoi < 1e-2:
#if np.sqrt(np.sum((u[0::2] - oldu)**2)/oldu.size) < 1e-2:
break
oldqoi = qoi
return np.max(np.abs(gradu))
x1 = np.linspace(0, np.pi, 5002)[:-1]
dx1 = x1[1] - x1[0]
x2 = np.linspace(0, np.pi, 50002)[:-1]
dx2 = x1[1] - x1[0]
ET = 1.
np.random.seed(299)
#nus = np.random.uniform(0.00001, .00000005, 2)
nus = np.random.uniform(1e-4, 1e-5, 500)
logg = open('sampsagainagain.dat', 'w')
logg.write('nu,nx5000_4,nx50000_2,nx50000_4\n')
for nu in nus:
print(nu)
u1 = geturec(x=x1, nu=nu, evolution_time=ET)
qoi1 = mgrad(u1[:, -1], dx=dx1)
u2 = geturec(x=x2,
nu=nu,
evolution_time=ET,
convstrategy='2c',
diffstrategy='3c',
timestrategy='fe')
qoi2 = mgrad(u2[:, -1], dx=dx2)
print('ok...')
u3 = geturec(x=x2, nu=nu, evolution_time=ET)
qoi3 = mgrad(u3[:, -1], dx=dx2)
print(nu, qoi1, qoi2, qoi3)
logg.write(','.join([str(s) for s in [nu, qoi1, qoi2, qoi3]]) + '\n')
logg.close()
# x points
nx = 7000
x = np.linspace(0, np.pi, nx + 2)[:-1]
dx = x[1] - x[0]
# prescribe u dt / dx = 0.01
evolution_time = 1.
# baseline viscosity
nu = 1e-5
n_save_t = 20
u_record = np.load('./urec%f.npy' % nu)
#u_record = geturec(nu=nu, x=x, evolution_time=evolution_time)
#np.save('urec%f'%nu, u_record)
dt = geturec(nu=nu, x=x, evolution_time=evolution_time, returndt=True)
nt = int(evolution_time / dt)
divider = int(nt / float(n_save_t))
# SVD the covariance matrix
psi, D, phi = np.linalg.svd(u_record) # P D Q is the approximation
S = np.zeros((nx + 1, u_record.shape[1]))
mm = min(nx + 1, u_record.shape[1])
S[:mm, :mm] = np.diag(D)
assert (np.allclose(u_record, np.dot(psi,
np.dot(S, phi)))) # check that a = P D Q
Q = np.dot(S, phi.T)
phi = phi.T
# choose # of modes to keep
logg.write('nu,TOL,ET,nx')
for TOL in [1e-2]:
for ET in ETs:
for nu in nus:
nx = 25
oldqoi = None
f, ax = plt.subplots(3)
plt.subplots_adjust(bottom=-.8)
l, l2 = [], []
qois = []
nxs = [nx]
while True:
print(nu, nx)
x = np.linspace(0, np.pi, nx+2)[:-1]
dx = x[1] - x[0]
u = geturec(nu=nu, x=x, evolution_time=ET, timestrategy='fe', diffstrategy='3c', convstrategy='2c', n_save_t=1)[:, -1]
l.append(ax[0].plot(x, u, label=nx, lw=LW)[0])
gradu = u.copy()
gradu[1:-1] = (u[2:] - u[:-2]) / ( 2 * dx)
gradu[-1] = (u[0] - u[-2]) / ( 2 * dx)
gradu[0] = (u[1] - u[-1]) / ( 2 * dx)
l2.append(ax[1].plot(x, np.abs(gradu), label=nx, lw=LW)[0])
qoi = np.max(np.abs(gradu))
#qoi = x[np.argmax(gradu)]
qois.append(qoi)
if oldqoi is not None:
print(qoi, oldqoi, np.max(gradu), np.abs(qoi - oldqoi)/qoi < 1e-3, (qoi - oldqoi)/qoi)
if np.abs(qoi - oldqoi)/qoi < TOL:
#if np.sqrt(np.sum((u[0::2] - oldu)**2)/oldu.size) < 1e-2:
break
oldqoi = qoi
# Let's evolve burgers' equation in time
# x points
nx = 7000
x = np.linspace(0, np.pi, nx + 2)[:-1]
dx = x[1] - x[0]
# prescribe u dt / dx = 0.01
evolution_time = 1.
# baseline viscosity
nu = 1e-5
n_save_t = 20
dt = geturec(nu=nu, x=x, evolution_time=evolution_time, returndt=True)
nt = int(evolution_time / dt)
divider = int(nt / float(n_save_t))
#u_record = geturec(nu=nu, x=x, evolution_time=evolution_time, n_save_t=100)
#np.save('urec%f'%nu, u_record)
u_record = np.load('./urec%f.npy' % nu)
ubar = u_record.mean(1)
u_record -= ubar.reshape(-1, 1)
print('flow fielded')
# SVD the covariance matrix
psi, D, phi = np.linalg.svd(u_record, full_matrices=False)
for ii in range(psi.shape[1]):
psi[:, ii] /= np.sqrt(dx)
phi[ii, :] *= np.sqrt(dx)
assert (np.allclose(u_record, np.dot(psi * D, phi)))