import numpy as np from scipy.interpolate import interp1d from laminar import LaminarEquation from utils import load_data, load_solution_laminar from objectives import BayesianObjective from inverse import InverseSolver dirname = "." N = 30 y = np.linspace(0.0, 0.5, N).astype(np.complex) h = 0.5 / (N - 1) u = np.zeros_like(y) beta = np.ones_like(y) Retau = 550.0 eqn = LaminarEquation(y, u, Retau) eqn.writedir = "." eqn.beta[:] = beta[:] eqn.solve() sigma_prior = 1.0 sigma_obs = 1e-10 q_target = eqn.q[:] + np.random.randn(np.size(eqn.q)) * sigma_obs eqn.beta[:] = 2.0 eqn.solve() q_prior = eqn.q.copy() beta_prior = eqn.beta.copy() eqn.objective = BayesianObjective(q_target, beta_prior, sigma_obs, sigma_prior)
import sys sys.path.insert(1, "../../src") import matplotlib.pyplot as plt import numpy as np from laminar import LaminarEquation from utils import load_data, load_solution_laminar dirname ="base_solution" y, u = load_solution_laminar(dirname) Retau = 550.0 eqn = LaminarEquation(y, u, Retau) eqn.writedir = "solution" eqn.solve() dns, wilcox = load_data() plt.figure(1) plt.semilogx(eqn.yp, eqn.up, 'r-', label=r'$k-\omega$') plt.semilogx(eqn.yp[::5], eqn.uap[::5], 'bo', label=r'Analytic', mfc="white") plt.xlabel(r"$y^+$") plt.ylabel(r"$u^+$") plt.legend(loc=2) plt.tight_layout() plt.show()
sys.path.insert(1, "../")
import matplotlib.pyplot as plt
import numpy as np
from scipy.interpolate import interp1d
from laminar import LaminarEquation
from utils import load_data, load_solution_laminar
dirname ="."
N = 100
y = np.linspace(0.0, 0.5, N).astype(np.complex)
h = 0.5/(N-1)
u = np.zeros_like(y)
beta = np.ones_like(y)
Retau = 550.0
eqn = LaminarEquation(y, u, Retau)
eqn.writedir = "."
eqn.beta[:] = beta[:]
eqn.solve()
dJdbeta = eqn.calc_sensitivity()
# complex step calculation
dJdbeta_fd = np.zeros_like(y)
J_base = eqn.objective.objective(eqn.q, eqn.beta)
dbeta = 1e-4
for i in range(len(beta)):
beta[i] = beta[i] + dbeta
eqn = LaminarEquation(y, u, Retau)
eqn.writedir = "solution"
eqn.beta[:] = beta[:]
eqn.solve()
dJdbeta_fd[i] = (eqn.objective.objective(eqn.q, eqn.beta) - J_base)/dbeta
