|
|
| """
|
| Benchmark comparison of PIV results against JHTDB ground truth.
|
|
|
| Compares:
|
| - Mean velocity profile U+ vs y+
|
| - Reynolds normal stresses uu+, vv+ vs y+
|
| - Reynolds shear stress uv+ vs y+
|
|
|
| Excludes first/last 5mm in x-direction (out-of-plane particle loss).
|
| """
|
|
|
| import numpy as np
|
| import scipy.io as sio
|
| from scipy.interpolate import interp1d
|
| import matplotlib.pyplot as plt
|
| import matplotlib as mpl
|
| from pathlib import Path
|
|
|
|
|
| mpl.rcParams.update({
|
| 'font.family': 'serif',
|
| 'font.serif': ['CMU Serif', 'Computer Modern Roman', 'DejaVu Serif'],
|
| 'mathtext.fontset': 'cm',
|
| 'axes.unicode_minus': False,
|
| 'text.usetex': False,
|
| })
|
|
|
|
|
| def log_smooth(y_plus, values, sigma_decades=0.06):
|
| """LOWESS-style smooth in log(y+) space, evaluated at original points.
|
|
|
| Each output point is a locally-weighted LINEAR regression of neighbours,
|
| where distance is measured in decades of y+. Using local linear fits
|
| instead of local averages gives:
|
| - Better peak tracking (local slope captures gradients)
|
| - Better edge behaviour (linear extrapolation, not mean bias)
|
|
|
| Parameters
|
| ----------
|
| y_plus : array
|
| y+ coordinates (positive)
|
| values : array
|
| Values to smooth
|
| sigma_decades : float
|
| Smoothing width in decades of y+ (0.06 ~ +/-15% local y+)
|
|
|
| Returns
|
| -------
|
| y_out, smoothed : arrays
|
| Sorted y+ and smoothed values (at original data points)
|
| """
|
| valid = (y_plus > 0) & ~np.isnan(values)
|
| yp = y_plus[valid]
|
| vals = values[valid]
|
| if len(yp) < 5:
|
| return yp, vals
|
|
|
|
|
| order = np.argsort(yp)
|
| yp = yp[order]
|
| vals = vals[order]
|
| log_yp = np.log10(yp)
|
|
|
|
|
| smoothed = np.empty_like(vals)
|
| for i in range(len(vals)):
|
| d = (log_yp - log_yp[i]) / sigma_decades
|
| w = np.exp(-0.5 * d * d)
|
| wsum = np.sum(w)
|
| wmean_x = np.sum(w * log_yp) / wsum
|
| wmean_y = np.sum(w * vals) / wsum
|
| dx = log_yp - wmean_x
|
| denom = np.sum(w * dx * dx)
|
| if denom > 1e-30:
|
| slope = np.sum(w * dx * vals) / denom
|
| smoothed[i] = wmean_y + slope * (log_yp[i] - wmean_x)
|
| else:
|
| smoothed[i] = wmean_y
|
|
|
| return yp, smoothed
|
|
|
|
|
| def plot_ci_band(ax, y_plus, ci_lo, ci_hi, sign=1, color='k', alpha=0.3, zorder=1):
|
| """Plot a 95% CI shaded band around a reference line.
|
|
|
| Parameters
|
| ----------
|
| ax : matplotlib Axes
|
| y_plus : array
|
| x-axis values (y+ coordinates)
|
| ci_lo, ci_hi : array
|
| Lower/upper CI bounds (same units as the plotted variable)
|
| sign : int
|
| 1 or -1 (for variables like -uv+ that flip sign)
|
| color : str
|
| Fill color
|
| alpha : float
|
| Fill transparency
|
| zorder : int
|
| Drawing order
|
| """
|
| lo = sign * ci_lo if sign == 1 else sign * ci_hi
|
| hi = sign * ci_hi if sign == 1 else sign * ci_lo
|
| ax.fill_between(y_plus, lo, hi, color=color, alpha=alpha, zorder=zorder,
|
| linewidth=0)
|
|
|
| ax.plot(y_plus, lo, color=color, linewidth=0.5, alpha=0.4, zorder=zorder)
|
| ax.plot(y_plus, hi, color=color, linewidth=0.5, alpha=0.4, zorder=zorder)
|
|
|
|
|
| def load_wall_units(wall_units_path):
|
| """Load wall units from .mat file (scipy v5 or h5py v7.3).
|
|
|
| Supports three formats:
|
| - wall_units.mat with 'wall_units' struct
|
| - diagnostics.mat with 'diagnostics' group (HDF5)
|
| - direct_stats.mat with top-level u_tau, delta_nu, Re_tau keys
|
| """
|
| try:
|
| wall = sio.loadmat(wall_units_path, squeeze_me=True, struct_as_record=False)
|
|
|
|
|
| if 'u_tau' in wall and 'delta_nu' in wall and 'Re_tau' in wall:
|
| u_tau = float(wall['u_tau'])
|
| delta_nu = float(wall['delta_nu'])
|
| Re_tau = float(wall['Re_tau'])
|
| return {
|
| 'u_tau': u_tau,
|
| 'nu': u_tau * delta_nu,
|
| 'delta_nu': delta_nu,
|
| 'h_mm': float(wall['h_mm']) if 'h_mm' in wall else Re_tau * delta_nu,
|
| 'Re_tau': Re_tau,
|
| }
|
|
|
|
|
| wu = wall['wall_units']
|
| return {
|
| 'u_tau': float(wu.u_tau),
|
| 'nu': float(wu.nu),
|
| 'delta_nu': float(wu.delta_nu),
|
| 'h_mm': float(wu.h_mm),
|
| 'Re_tau': float(wu.Re_tau)
|
| }
|
| except NotImplementedError:
|
|
|
| import h5py
|
| with h5py.File(str(wall_units_path), 'r') as f:
|
| if 'wall_units' in f:
|
| grp = f['wall_units']
|
| result = {
|
| 'u_tau': float(np.array(grp['u_tau']).flat[0]),
|
| 'delta_nu': float(np.array(grp['delta_nu']).flat[0]),
|
| 'Re_tau': float(np.array(grp['Re_tau']).flat[0]),
|
| }
|
| if 'nu' in grp:
|
| result['nu'] = float(np.array(grp['nu']).flat[0])
|
| else:
|
| result['nu'] = result['u_tau'] * result['delta_nu']
|
| if 'h_mm' in grp:
|
| result['h_mm'] = float(np.array(grp['h_mm']).flat[0])
|
| else:
|
| result['h_mm'] = result['Re_tau'] * result['delta_nu']
|
| return result
|
| elif 'diagnostics' in f:
|
| grp = f['diagnostics']
|
| result = {
|
| 'u_tau': float(np.array(grp['u_tau']).flat[0]),
|
| 'delta_nu': float(np.array(grp['delta_nu']).flat[0]),
|
| 'Re_tau': float(np.array(grp['Re_tau']).flat[0]),
|
| }
|
| if 'nu' in grp:
|
| result['nu'] = float(np.array(grp['nu']).flat[0])
|
| else:
|
| result['nu'] = result['u_tau'] * result['delta_nu']
|
| if 'h_mm' in grp:
|
| result['h_mm'] = float(np.array(grp['h_mm']).flat[0])
|
| else:
|
| result['h_mm'] = result['Re_tau'] * result['delta_nu']
|
| return result
|
| else:
|
| raise ValueError(f"No 'wall_units' or 'diagnostics' group in {wall_units_path}")
|
|
|
|
|
| def load_ground_truth(profiles_path, wall_units_path=None):
|
| """Load ground truth profiles (scipy v5 or h5py v7.3).
|
|
|
| Supports three formats:
|
| - profiles.mat with 'profiles.win_1px' struct
|
| - ensemble_statistics_full.mat with 'ref_profile' + 'ensemble_stats' (HDF5)
|
| - direct_stats.mat with top-level y_plus, U_plus, stress_plus arrays
|
| """
|
| try:
|
| profiles = sio.loadmat(profiles_path, squeeze_me=True, struct_as_record=False)
|
|
|
|
|
| if 'U_plus' in profiles and 'stress_plus' in profiles and 'y_plus' in profiles:
|
| y_plus_full = profiles['y_plus']
|
| Re_tau = float(profiles['Re_tau'])
|
| u_tau = float(profiles['u_tau'])
|
| delta_nu = float(profiles['delta_nu'])
|
| u_tau2 = u_tau ** 2
|
|
|
|
|
| mask = y_plus_full <= Re_tau
|
| y_plus = y_plus_full[mask]
|
| y_mm = y_plus * delta_nu
|
|
|
|
|
| U_plus = profiles['U_plus'][mask, 0]
|
| V_plus = profiles['U_plus'][mask, 1]
|
|
|
|
|
| uu_plus = profiles['stress_plus'][mask, 0, 0]
|
| vv_plus = profiles['stress_plus'][mask, 1, 1]
|
| uv_plus = profiles['stress_plus'][mask, 0, 1]
|
|
|
| result = {
|
| 'y_mm': y_mm,
|
| 'y_plus': y_plus,
|
| 'U': U_plus * u_tau,
|
| 'V': V_plus * u_tau,
|
| 'uu': uu_plus * u_tau2,
|
| 'vv': vv_plus * u_tau2,
|
| 'uv': uv_plus * u_tau2,
|
| 'U_plus': U_plus,
|
| 'uu_plus': uu_plus,
|
| 'vv_plus': vv_plus,
|
| 'uv_plus': uv_plus,
|
| }
|
|
|
|
|
| if 'stress_ci_lo' in profiles and 'stress_ci_hi' in profiles:
|
| result['uu_plus_ci_lo'] = profiles['stress_ci_lo'][mask, 0, 0]
|
| result['uu_plus_ci_hi'] = profiles['stress_ci_hi'][mask, 0, 0]
|
| result['vv_plus_ci_lo'] = profiles['stress_ci_lo'][mask, 1, 1]
|
| result['vv_plus_ci_hi'] = profiles['stress_ci_hi'][mask, 1, 1]
|
| result['uv_plus_ci_lo'] = profiles['stress_ci_lo'][mask, 0, 1]
|
| result['uv_plus_ci_hi'] = profiles['stress_ci_hi'][mask, 0, 1]
|
| if 'umean_ci_lo' in profiles and 'umean_ci_hi' in profiles:
|
| result['U_plus_ci_lo'] = profiles['umean_ci_lo'][mask, 0]
|
| result['U_plus_ci_hi'] = profiles['umean_ci_hi'][mask, 0]
|
| result['V_plus_ci_lo'] = profiles['umean_ci_lo'][mask, 1]
|
| result['V_plus_ci_hi'] = profiles['umean_ci_hi'][mask, 1]
|
|
|
| return result
|
|
|
|
|
| win1px = profiles['profiles'].win_1px
|
| return {
|
| 'y_mm': win1px.y_mm,
|
| 'y_plus': win1px.y_plus,
|
| 'U': win1px.U,
|
| 'V': win1px.V,
|
| 'uu': win1px.uu,
|
| 'vv': win1px.vv,
|
| 'uv': win1px.uv,
|
| 'U_plus': win1px.U_plus,
|
| 'uu_plus': win1px.uu_plus,
|
| 'vv_plus': win1px.vv_plus,
|
| 'uv_plus': win1px.uv_plus,
|
| }
|
| except NotImplementedError:
|
|
|
| import h5py
|
|
|
|
|
| if wall_units_path is not None:
|
| wu = load_wall_units(wall_units_path)
|
| else:
|
| wu_path = Path(profiles_path).parent / 'diagnostics.mat'
|
| if wu_path.exists():
|
| wu = load_wall_units(wu_path)
|
| else:
|
| raise ValueError("Need wall_units_path to normalise HDF5 ground truth")
|
|
|
| u_tau = wu['u_tau']
|
| u_tau2 = u_tau ** 2
|
| delta_nu = wu['delta_nu']
|
|
|
| with h5py.File(str(profiles_path), 'r') as f:
|
| ref = f['ref_profile']
|
|
|
|
|
| if 'uu' in ref:
|
| y_mm = np.array(ref['y_mm']).flatten()
|
| U = np.array(ref['U']).flatten()
|
| V = np.array(ref['V']).flatten()
|
| uu = np.array(ref['uu']).flatten()
|
| vv = np.array(ref['vv']).flatten()
|
| uv = np.array(ref['uv']).flatten()
|
| y_plus = y_mm / delta_nu
|
| return {
|
| 'y_mm': y_mm, 'y_plus': y_plus,
|
| 'U': U, 'V': V, 'uu': uu, 'vv': vv, 'uv': uv,
|
| 'U_plus': U / u_tau, 'uu_plus': uu / u_tau2,
|
| 'vv_plus': vv / u_tau2, 'uv_plus': uv / u_tau2,
|
| }
|
|
|
|
|
| if 'ensemble_stats' not in f:
|
| raise ValueError("No stress data in ref_profile and no ensemble_stats")
|
|
|
| es = f['ensemble_stats']
|
|
|
| win_idx = 0
|
|
|
| def _deref(field, idx=win_idx):
|
| refs = np.array(es[field]).flatten()
|
| return np.array(f[refs[idx]]).flatten()
|
|
|
|
|
| es_y_plus = _deref('y_plus')
|
| es_y_mm = es_y_plus * delta_nu
|
|
|
|
|
| uu_plus = _deref('uu_plus')
|
| vv_plus = _deref('vv_plus')
|
| uv_plus = _deref('uv_plus')
|
|
|
|
|
| dns_y_mm = np.array(ref['y_mm']).flatten()
|
| dns_U = np.array(ref['U']).flatten()
|
| dns_V = np.array(ref['V']).flatten()
|
| dns_y_plus = dns_y_mm / delta_nu
|
|
|
| U_interp = interp1d(dns_y_plus, dns_U, kind='linear',
|
| bounds_error=False, fill_value=np.nan)(es_y_plus)
|
| V_interp = interp1d(dns_y_plus, dns_V, kind='linear',
|
| bounds_error=False, fill_value=np.nan)(es_y_plus)
|
|
|
| return {
|
| 'y_mm': es_y_mm,
|
| 'y_plus': es_y_plus,
|
| 'U': U_interp,
|
| 'V': V_interp,
|
| 'uu': uu_plus * u_tau2,
|
| 'vv': vv_plus * u_tau2,
|
| 'uv': uv_plus * u_tau2,
|
| 'U_plus': U_interp / u_tau,
|
| 'uu_plus': uu_plus,
|
| 'vv_plus': vv_plus,
|
| 'uv_plus': uv_plus,
|
| }
|
|
|
|
|
| def load_piv_statistics(stats_path, run_idx=3):
|
| """
|
| Load PIV statistics from mean_stats.mat (instantaneous).
|
|
|
| Parameters
|
| ----------
|
| stats_path : Path
|
| Path to mean_stats.mat
|
| run_idx : int
|
| Run index (0-based). run_idx=3 corresponds to run 4 (16x16 window)
|
| """
|
| stats = sio.loadmat(stats_path, squeeze_me=True, struct_as_record=False)
|
| piv = stats['piv_result'][run_idx]
|
| coords = stats['coordinates'][run_idx]
|
|
|
| return {
|
| 'ux': piv.ux,
|
| 'uy': piv.uy,
|
| 'uu': piv.uu,
|
| 'vv': piv.vv,
|
| 'uv': piv.uv,
|
| 'x': coords.x,
|
| 'y': coords.y,
|
| }
|
|
|
|
|
| def load_ensemble_statistics(ensemble_path, coords_path, run_idx=3):
|
| """
|
| Load PIV statistics from ensemble_result.mat.
|
|
|
| Parameters
|
| ----------
|
| ensemble_path : Path
|
| Path to ensemble_result.mat
|
| coords_path : Path
|
| Path to coordinates.mat
|
| run_idx : int
|
| Run index (0-based). run_idx=3 corresponds to run 4
|
| """
|
| ens = sio.loadmat(ensemble_path, squeeze_me=True, struct_as_record=False)
|
| coords_data = sio.loadmat(coords_path, squeeze_me=True, struct_as_record=False)
|
|
|
| piv = ens['ensemble_result'][run_idx]
|
| coords = coords_data['coordinates'][run_idx]
|
|
|
| return {
|
| 'ux': piv.ux,
|
| 'uy': piv.uy,
|
| 'uu': piv.UU_stress,
|
| 'vv': piv.VV_stress,
|
| 'uv': piv.UV_stress,
|
| 'x': coords.x,
|
| 'y': coords.y,
|
| }
|
|
|
|
|
| def compute_piv_profiles(piv_data, x_exclude_vectors=4):
|
| """
|
| Compute x-averaged PIV profiles, excluding edges.
|
|
|
| Parameters
|
| ----------
|
| piv_data : dict
|
| PIV statistics dictionary (velocities in m/s, stresses in (m/s)^2)
|
| x_exclude_vectors : int
|
| Number of vectors to exclude from each side in x-direction
|
|
|
| Returns
|
| -------
|
| dict with y_mm, U, uu, vv, uv profiles (in mm/s and (mm/s)^2)
|
| """
|
| x = piv_data['x']
|
| y = piv_data['y']
|
|
|
|
|
| y_unique = y[:, 0]
|
| x_unique = x[0, :]
|
| nx = len(x_unique)
|
|
|
|
|
| x_mask = np.zeros(nx, dtype=bool)
|
| x_mask[x_exclude_vectors:nx-x_exclude_vectors] = True
|
|
|
| print(f" X range: {x_unique.min():.2f} to {x_unique.max():.2f} mm")
|
| print(f" Excluding {x_exclude_vectors} vectors from each x-edge")
|
| print(f" X points: {x_mask.sum()} / {nx}")
|
|
|
|
|
| ux_mm = piv_data['ux'] * 1000
|
| uy_mm = piv_data['uy'] * 1000
|
| uu_mm2 = piv_data['uu'] * 1e6
|
| vv_mm2 = piv_data['vv'] * 1e6
|
| uv_mm2 = piv_data['uv'] * 1e6
|
|
|
|
|
| U_profile = np.nanmean(ux_mm[:, x_mask], axis=1)
|
| V_profile = np.nanmean(uy_mm[:, x_mask], axis=1)
|
| uu_profile = np.nanmean(uu_mm2[:, x_mask], axis=1)
|
| vv_profile = np.nanmean(vv_mm2[:, x_mask], axis=1)
|
| uv_profile = np.nanmean(uv_mm2[:, x_mask], axis=1)
|
|
|
| return {
|
| 'y_mm': y_unique,
|
| 'U': U_profile,
|
| 'V': V_profile,
|
| 'uu': uu_profile,
|
| 'vv': vv_profile,
|
| 'uv': uv_profile,
|
| }
|
|
|
|
|
| def convert_to_wall_units(profiles, wall_units, y_offset_mm=0.0):
|
| """
|
| Convert profiles to wall units (plus units).
|
|
|
| Parameters
|
| ----------
|
| profiles : dict
|
| PIV profiles with y_mm, U, etc.
|
| wall_units : dict
|
| Wall unit parameters
|
| y_offset_mm : float
|
| Offset to add to y_mm before converting to y+ (for coordinate alignment)
|
| """
|
| u_tau = wall_units['u_tau']
|
| delta_nu = wall_units['delta_nu']
|
| u_tau2 = u_tau ** 2
|
|
|
|
|
| y_mm_aligned = profiles['y_mm'] + y_offset_mm
|
|
|
| return {
|
| 'y_mm': y_mm_aligned,
|
| 'y_plus': y_mm_aligned / delta_nu,
|
| 'U_plus': profiles['U'] / u_tau,
|
| 'V_plus': profiles['V'] / u_tau,
|
| 'uu_plus': profiles['uu'] / u_tau2,
|
| 'vv_plus': profiles['vv'] / u_tau2,
|
| 'uv_plus': profiles['uv'] / u_tau2,
|
| }
|
|
|
|
|
| def compute_errors(piv_plus, gt_plus, y_plus_range=(10, 500)):
|
| """
|
| Compute error metrics between PIV and ground truth.
|
|
|
| Parameters
|
| ----------
|
| piv_plus : dict
|
| PIV profiles in wall units
|
| gt_plus : dict
|
| Ground truth profiles in wall units
|
| y_plus_range : tuple
|
| y+ range for comparison (exclude near-wall and centerline regions)
|
| """
|
|
|
| y_piv = piv_plus['y_plus']
|
| y_gt = gt_plus['y_plus']
|
|
|
|
|
| mask_piv = (y_piv >= y_plus_range[0]) & (y_piv <= y_plus_range[1])
|
| y_compare = y_piv[mask_piv]
|
|
|
| if len(y_compare) == 0:
|
| print(f" Warning: No PIV points in y+ range {y_plus_range}")
|
| return {}
|
|
|
| errors = {}
|
| for var in ['U_plus', 'V_plus', 'uu_plus', 'vv_plus', 'uv_plus']:
|
| piv_vals = piv_plus[var][mask_piv]
|
|
|
|
|
| gt_interp = interp1d(y_gt, gt_plus[var], kind='linear',
|
| bounds_error=False, fill_value=np.nan)
|
| gt_vals = gt_interp(y_compare)
|
|
|
|
|
| valid = ~np.isnan(piv_vals) & ~np.isnan(gt_vals)
|
| if valid.sum() == 0:
|
| continue
|
|
|
| piv_valid = piv_vals[valid]
|
| gt_valid = gt_vals[valid]
|
|
|
|
|
| diff = piv_valid - gt_valid
|
| rms_error = np.sqrt(np.mean(diff**2))
|
| mean_abs_error = np.mean(np.abs(diff))
|
|
|
|
|
| gt_range = np.ptp(gt_valid)
|
| rms_rel = (rms_error / gt_range * 100) if gt_range > 0 else np.nan
|
|
|
|
|
| corr = np.corrcoef(piv_valid, gt_valid)[0, 1]
|
|
|
|
|
| ss_res = np.sum(diff**2)
|
| ss_tot = np.sum((gt_valid - gt_valid.mean())**2)
|
| r2 = 1 - (ss_res / ss_tot) if ss_tot > 0 else np.nan
|
|
|
| errors[var] = {
|
| 'rms': rms_error,
|
| 'rms_rel': rms_rel,
|
| 'mae': mean_abs_error,
|
| 'corr': corr,
|
| 'r2': r2,
|
| 'n_points': valid.sum(),
|
| }
|
|
|
| return errors
|
|
|
|
|
| def plot_comparison(piv_plus, gt_plus, wall_units, errors, output_dir, window_label='16x16', show_fit_lines=False):
|
| """Generate comparison plots."""
|
| output_dir = Path(output_dir)
|
| output_dir.mkdir(parents=True, exist_ok=True)
|
|
|
| Re_tau = wall_units['Re_tau']
|
|
|
|
|
| has_ci = 'uu_plus_ci_lo' in gt_plus
|
|
|
|
|
| fig, ax = plt.subplots(figsize=(10, 7))
|
|
|
|
|
| if has_ci and 'U_plus_ci_lo' in gt_plus:
|
| plot_ci_band(ax, gt_plus['y_plus'], gt_plus['U_plus_ci_lo'],
|
| gt_plus['U_plus_ci_hi'], color='k', alpha=0.15, zorder=1)
|
| ax.semilogx(gt_plus['y_plus'], gt_plus['U_plus'], 'k-',
|
| linewidth=2, label='DNS (1px)', zorder=3)
|
|
|
|
|
| ax.semilogx(piv_plus['y_plus'], piv_plus['U_plus'], 'ro',
|
| markersize=4, alpha=0.7, label=f'PIV ({window_label})', zorder=2)
|
|
|
| if show_fit_lines:
|
| y_log = np.logspace(1, np.log10(Re_tau), 100)
|
| kappa, B = 0.41, 5.2
|
| ax.semilogx(y_log, (1/kappa)*np.log(y_log)+B, 'b--', linewidth=1, alpha=0.7,
|
| label=r'Log law: $U^+ = \frac{1}{\kappa}\ln(y^+) + B$')
|
| y_visc = np.linspace(0.1, 10, 50)
|
| ax.semilogx(y_visc, y_visc, 'g--', linewidth=1, alpha=0.7,
|
| label=r'Viscous sublayer: $U^+ = y^+$')
|
|
|
| ax.set_xlabel(r'$y^+$', fontsize=14)
|
| ax.set_ylabel(r'$U^+$', fontsize=14)
|
| ax.set_title(f'Mean Velocity Profile (Re$_\\tau$ = {Re_tau:.0f})', fontsize=16)
|
| ax.legend(fontsize=11)
|
| ax.set_xlim(1, Re_tau)
|
| ax.set_ylim(0, 25)
|
| ax.grid(True, alpha=0.3)
|
|
|
| if 'U_plus' in errors:
|
| ax.text(0.02, 0.98, f"R² = {errors['U_plus']['r2']:.4f}\n"
|
| f"RMS = {errors['U_plus']['rms_rel']:.1f}%",
|
| transform=ax.transAxes, fontsize=11, verticalalignment='top',
|
| bbox=dict(boxstyle='round', facecolor='white', alpha=0.8))
|
|
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'U_plus_profile.png', dpi=150)
|
| plt.close(fig)
|
|
|
|
|
| fig, axes = plt.subplots(1, 3, figsize=(15, 5))
|
|
|
|
|
| ax = axes[0]
|
| if has_ci:
|
| plot_ci_band(ax, gt_plus['y_plus'], gt_plus['uu_plus_ci_lo'],
|
| gt_plus['uu_plus_ci_hi'], color='k', zorder=1)
|
| ax.semilogx(gt_plus['y_plus'], gt_plus['uu_plus'], 'k-', linewidth=2, label='DNS')
|
| ax.semilogx(piv_plus['y_plus'], piv_plus['uu_plus'], 'ro', markersize=4,
|
| alpha=0.7, label='PIV')
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(r"$\overline{u'u'}^+$", fontsize=12)
|
| ax.set_title('Streamwise Normal Stress', fontsize=14)
|
| ax.legend()
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
| if 'uu_plus' in errors:
|
| ax.text(0.98, 0.98, f"R² = {errors['uu_plus']['r2']:.4f}",
|
| transform=ax.transAxes, fontsize=10, ha='right', va='top',
|
| bbox=dict(boxstyle='round', facecolor='white', alpha=0.8))
|
|
|
|
|
| ax = axes[1]
|
| if has_ci:
|
| plot_ci_band(ax, gt_plus['y_plus'], gt_plus['vv_plus_ci_lo'],
|
| gt_plus['vv_plus_ci_hi'], color='k', zorder=1)
|
| ax.semilogx(gt_plus['y_plus'], gt_plus['vv_plus'], 'k-', linewidth=2, label='DNS')
|
| ax.semilogx(piv_plus['y_plus'], piv_plus['vv_plus'], 'ro', markersize=4,
|
| alpha=0.7, label='PIV')
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(r"$\overline{v'v'}^+$", fontsize=12)
|
| ax.set_title('Wall-Normal Normal Stress', fontsize=14)
|
| ax.legend()
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
| if 'vv_plus' in errors:
|
| ax.text(0.98, 0.98, f"R² = {errors['vv_plus']['r2']:.4f}",
|
| transform=ax.transAxes, fontsize=10, ha='right', va='top',
|
| bbox=dict(boxstyle='round', facecolor='white', alpha=0.8))
|
|
|
|
|
| ax = axes[2]
|
| if has_ci:
|
| plot_ci_band(ax, gt_plus['y_plus'], gt_plus['uv_plus_ci_lo'],
|
| gt_plus['uv_plus_ci_hi'], sign=-1, color='k', zorder=1)
|
| ax.semilogx(gt_plus['y_plus'], -gt_plus['uv_plus'], 'k-', linewidth=2, label='DNS')
|
| ax.semilogx(piv_plus['y_plus'], -piv_plus['uv_plus'], 'ro', markersize=4,
|
| alpha=0.7, label='PIV')
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(r"$-\overline{u'v'}^+$", fontsize=12)
|
| ax.set_title('Reynolds Shear Stress', fontsize=14)
|
| ax.legend()
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
| if 'uv_plus' in errors:
|
| ax.text(0.98, 0.98, f"R² = {errors['uv_plus']['r2']:.4f}",
|
| transform=ax.transAxes, fontsize=10, ha='right', va='top',
|
| bbox=dict(boxstyle='round', facecolor='white', alpha=0.8))
|
|
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'reynolds_stresses.png', dpi=150)
|
| plt.close(fig)
|
|
|
|
|
| fig, ax = plt.subplots(figsize=(10, 7))
|
|
|
| if has_ci and 'V_plus_ci_lo' in gt_plus:
|
| plot_ci_band(ax, gt_plus['y_plus'], gt_plus['V_plus_ci_lo'],
|
| gt_plus['V_plus_ci_hi'], color='k', zorder=1)
|
| ax.plot(gt_plus['y_plus'], gt_plus['V_plus'], 'k-', linewidth=2, label='DNS')
|
| ax.plot(piv_plus['y_plus'], piv_plus['V_plus'], 'ro', markersize=4,
|
| alpha=0.7, label='PIV')
|
| ax.axhline(y=0, color='gray', linestyle='--', linewidth=0.5, alpha=0.7)
|
|
|
| ax.set_xlabel(r'$y^+$', fontsize=14)
|
| ax.set_ylabel(r'$V^+$', fontsize=14)
|
| ax.set_title(f'Mean Wall-Normal Velocity Profile (Re$_\\tau$ = {Re_tau:.0f})', fontsize=16)
|
| ax.legend(fontsize=11)
|
| ax.set_xscale('log')
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
| if 'V_plus' in errors:
|
| ax.text(0.02, 0.98, f"R² = {errors['V_plus']['r2']:.4f}\n"
|
| f"Corr = {errors['V_plus']['corr']:.4f}",
|
| transform=ax.transAxes, fontsize=11, verticalalignment='top',
|
| bbox=dict(boxstyle='round', facecolor='white', alpha=0.8))
|
|
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'V_plus_profile.png', dpi=150)
|
| plt.close(fig)
|
|
|
|
|
| fig, ax = plt.subplots(figsize=(10, 7))
|
|
|
| ax.plot(gt_plus['y_plus'], gt_plus['U_plus'], 'k-', linewidth=2, label='DNS U+')
|
| ax.plot(piv_plus['y_plus'], piv_plus['U_plus'], 'ko', markersize=3,
|
| alpha=0.5, label='PIV U+')
|
|
|
| ax.set_xlabel(r'$y^+$', fontsize=14)
|
| ax.set_ylabel(r'$U^+$', fontsize=14)
|
| ax.set_title('Mean Velocity Profile', fontsize=16)
|
| ax.legend(fontsize=11)
|
| ax.set_xscale('log')
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'U_plus_linear.png', dpi=150)
|
| plt.close(fig)
|
|
|
|
|
|
|
| fig, ax = plt.subplots(figsize=(10, 7))
|
|
|
| if has_ci and 'U_plus_ci_lo' in gt_plus:
|
| plot_ci_band(ax, gt_plus['y_plus'], gt_plus['U_plus_ci_lo'],
|
| gt_plus['U_plus_ci_hi'], color='k', zorder=1)
|
| ax.semilogx(gt_plus['y_plus'], gt_plus['U_plus'], 'k-',
|
| linewidth=2, label='DNS (1px)', zorder=3)
|
|
|
| ax.semilogx(piv_plus['y_plus'], piv_plus['U_plus'], 'ro',
|
| markersize=4, alpha=0.7, label=f'PIV ({window_label})', zorder=2)
|
|
|
| if show_fit_lines:
|
| y_log = np.logspace(1, np.log10(Re_tau), 100)
|
| kappa, B = 0.41, 5.2
|
| ax.semilogx(y_log, (1/kappa)*np.log(y_log)+B, 'b--', linewidth=1, alpha=0.7,
|
| label=r'Log law')
|
| y_visc = np.linspace(0.1, 10, 50)
|
| ax.semilogx(y_visc, y_visc, 'g--', linewidth=1, alpha=0.7, label=r'$U^+=y^+$')
|
|
|
| ax.set_xlabel(r'$y^+$', fontsize=14)
|
| ax.set_ylabel(r'$U^+$', fontsize=14)
|
| ax.set_title(f'Mean Velocity Profile - Smoothed ({window_label})', fontsize=16)
|
| ax.legend(fontsize=11)
|
| ax.set_xlim(1, Re_tau)
|
| ax.set_ylim(0, 25)
|
| ax.grid(True, alpha=0.3)
|
| if 'U_plus' in errors:
|
| ax.text(0.02, 0.98, f"R² = {errors['U_plus']['r2']:.4f}\n"
|
| f"RMS = {errors['U_plus']['rms_rel']:.1f}%",
|
| transform=ax.transAxes, fontsize=11, verticalalignment='top',
|
| bbox=dict(boxstyle='round', facecolor='white', alpha=0.8))
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'U_plus_profile_smooth.png', dpi=150)
|
| plt.close(fig)
|
|
|
|
|
| fig, axes = plt.subplots(1, 3, figsize=(15, 5))
|
|
|
| stress_configs = [
|
| ('uu_plus', r"$\overline{u'u'}^+$", 'Streamwise Normal Stress', 1),
|
| ('vv_plus', r"$\overline{v'v'}^+$", 'Wall-Normal Normal Stress', 1),
|
| ('uv_plus', r"$-\overline{u'v'}^+$", 'Reynolds Shear Stress', -1),
|
| ]
|
| for ax, (var, ylabel, title, sign) in zip(axes, stress_configs):
|
| gt_vals = sign * gt_plus[var]
|
| piv_vals = sign * piv_plus[var]
|
|
|
| ci_lo_key = f'{var}_ci_lo'
|
| ci_hi_key = f'{var}_ci_hi'
|
| if has_ci and ci_lo_key in gt_plus:
|
| plot_ci_band(ax, gt_plus['y_plus'], gt_plus[ci_lo_key],
|
| gt_plus[ci_hi_key], sign=sign, color='k', zorder=1)
|
| ax.semilogx(gt_plus['y_plus'], gt_vals, 'k-', linewidth=2, label='DNS')
|
| ax.semilogx(piv_plus['y_plus'], piv_vals, 'ro', markersize=4, alpha=0.7, label='PIV')
|
|
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(ylabel, fontsize=12)
|
| ax.set_title(title, fontsize=14)
|
| ax.legend()
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
| if var in errors:
|
| ax.text(0.98, 0.98, f"R² = {errors[var]['r2']:.4f}",
|
| transform=ax.transAxes, fontsize=10, ha='right', va='top',
|
| bbox=dict(boxstyle='round', facecolor='white', alpha=0.8))
|
|
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'reynolds_stresses_smooth.png', dpi=150)
|
| plt.close(fig)
|
|
|
|
|
| fig, axes = plt.subplots(1, 3, figsize=(16, 5))
|
|
|
|
|
| gt_trace = gt_plus['uu_plus'] + gt_plus['vv_plus']
|
| piv_trace = piv_plus['uu_plus'] + piv_plus['vv_plus']
|
|
|
|
|
| ax = axes[0]
|
| ax.semilogx(gt_plus['y_plus'], gt_plus['uu_plus'], 'k-', linewidth=2, label="DNS u'u'+")
|
| ax.semilogx(gt_plus['y_plus'], gt_plus['vv_plus'], 'k--', linewidth=2, label="DNS v'v'+")
|
| ax.semilogx(piv_plus['y_plus'], piv_plus['uu_plus'], 'ro', markersize=3, alpha=0.7, label="PIV u'u'+")
|
| ax.semilogx(piv_plus['y_plus'], piv_plus['vv_plus'], 'bs', markersize=3, alpha=0.7, label="PIV v'v'+")
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(r"Stress$^+$", fontsize=12)
|
| ax.set_title('Individual Normal Stresses', fontsize=14)
|
| ax.legend(fontsize=9)
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
|
|
| ax = axes[1]
|
| ax.semilogx(gt_plus['y_plus'], gt_trace, 'k-', linewidth=2, label='DNS')
|
| ax.semilogx(piv_plus['y_plus'], piv_trace, 'ro', markersize=4, alpha=0.7, label='PIV')
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(r"$\overline{u'u'}^+ + \overline{v'v'}^+$", fontsize=12)
|
| ax.set_title("Trace Invariant (u'u' + v'v')", fontsize=14)
|
| ax.legend(fontsize=11)
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
|
|
| ax = axes[2]
|
| gt_ratio = gt_plus['uu_plus'] / (gt_plus['vv_plus'] + 1e-10)
|
| piv_ratio = piv_plus['uu_plus'] / (piv_plus['vv_plus'] + 1e-10)
|
| ax.semilogx(gt_plus['y_plus'], gt_ratio, 'k-', linewidth=2, label='DNS')
|
| ax.semilogx(piv_plus['y_plus'], piv_ratio, 'ro', markersize=4, alpha=0.7, label='PIV')
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(r"$\overline{u'u'}^+ / \overline{v'v'}^+$", fontsize=12)
|
| ax.set_title("Stress Ratio (rotation indicator)", fontsize=14)
|
| ax.legend(fontsize=11)
|
| ax.set_xlim(1, Re_tau)
|
| ax.set_ylim(0, 10)
|
| ax.grid(True, alpha=0.3)
|
|
|
| fig.suptitle("Rotation Diagnostic: Trace is invariant under rotation", fontsize=14, y=1.02)
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'trace_invariant.png', dpi=150)
|
| plt.close(fig)
|
|
|
|
|
| fig, axes = plt.subplots(2, 3, figsize=(15, 10))
|
|
|
|
|
| gt_interp_fn = {}
|
| for var in ['U_plus', 'V_plus', 'uu_plus', 'vv_plus', 'uv_plus']:
|
| gt_interp_fn[var] = interp1d(gt_plus['y_plus'], gt_plus[var], kind='linear',
|
| bounds_error=False, fill_value=np.nan)
|
|
|
|
|
| vel_configs = [
|
| ('U_plus', r"$U^+_{\mathrm{PIV}} - U^+_{\mathrm{Ref}}$",
|
| 'Mean Streamwise Velocity Residual', 1),
|
| ('V_plus', r"$V^+_{\mathrm{PIV}} - V^+_{\mathrm{Ref}}$",
|
| 'Mean Wall-Normal Velocity Residual', 1),
|
| ]
|
| for ax, (var, ylabel, title, sign) in zip(axes[0, :2], vel_configs):
|
| gt_at_piv = gt_interp_fn[var](piv_plus['y_plus'])
|
| residual = sign * piv_plus[var] - sign * gt_at_piv
|
|
|
| ax.semilogx(piv_plus['y_plus'], residual, 'ro', markersize=3, alpha=0.5)
|
| yp_s, r_s = log_smooth(piv_plus['y_plus'], residual)
|
| ax.semilogx(yp_s, r_s, 'r-', linewidth=2, label=f'PIV ({window_label})')
|
| ax.axhline(y=0, color='k', linestyle='-', linewidth=1, alpha=0.5)
|
|
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(ylabel, fontsize=12)
|
| ax.set_title(title, fontsize=14)
|
| ax.legend()
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
| axes[0, 2].set_visible(False)
|
|
|
|
|
| stress_configs = [
|
| ('uu_plus', r"$\overline{u'u'}^+_{\mathrm{PIV}} - \overline{u'u'}^+_{\mathrm{Ref}}$",
|
| 'Streamwise Normal Stress Residual', 1),
|
| ('vv_plus', r"$\overline{v'v'}^+_{\mathrm{PIV}} - \overline{v'v'}^+_{\mathrm{Ref}}$",
|
| 'Wall-Normal Normal Stress Residual', 1),
|
| ('uv_plus', r"$-\overline{u'v'}^+_{\mathrm{PIV}} - (-\overline{u'v'}^+_{\mathrm{Ref}})$",
|
| 'Shear Stress Residual', -1),
|
| ]
|
| for ax, (var, ylabel, title, sign) in zip(axes[1, :], stress_configs):
|
| gt_at_piv = gt_interp_fn[var](piv_plus['y_plus'])
|
| residual = sign * piv_plus[var] - sign * gt_at_piv
|
|
|
| ax.semilogx(piv_plus['y_plus'], residual, 'ro', markersize=3, alpha=0.5)
|
| yp_s, r_s = log_smooth(piv_plus['y_plus'], residual)
|
| ax.semilogx(yp_s, r_s, 'r-', linewidth=2, label=f'PIV ({window_label})')
|
| ax.axhline(y=0, color='k', linestyle='-', linewidth=1, alpha=0.5)
|
|
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(ylabel, fontsize=12)
|
| ax.set_title(title, fontsize=14)
|
| ax.legend()
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'residuals.png', dpi=150)
|
| plt.close(fig)
|
|
|
|
|
| fig, axes = plt.subplots(1, 3, figsize=(16, 5))
|
|
|
|
|
| uu_residual = piv_plus['uu_plus'] - gt_interp_fn['uu_plus'](piv_plus['y_plus'])
|
| vv_residual = piv_plus['vv_plus'] - gt_interp_fn['vv_plus'](piv_plus['y_plus'])
|
| gradient_only = uu_residual - vv_residual
|
|
|
|
|
| ax = axes[0]
|
| ax.semilogx(piv_plus['y_plus'], vv_residual, 'bo', markersize=2, alpha=0.3)
|
| yp_s, r_s = log_smooth(piv_plus['y_plus'], vv_residual)
|
| ax.semilogx(yp_s, r_s, 'b-', linewidth=2.5, label=r"$v'v'$ residual (noise floor)")
|
| ax.axhline(y=0, color='k', linestyle='-', linewidth=1, alpha=0.5)
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(r"$\overline{v'v'}^+_{\mathrm{PIV}} - \overline{v'v'}^+_{\mathrm{Ref}}$", fontsize=12)
|
| ax.set_title('Noise Floor (isotropic)', fontsize=14)
|
| ax.legend(fontsize=10)
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
|
|
| ax = axes[1]
|
| ax.semilogx(piv_plus['y_plus'], gradient_only, 'ro', markersize=2, alpha=0.3)
|
| yp_s, r_s = log_smooth(piv_plus['y_plus'], gradient_only)
|
| ax.semilogx(yp_s, r_s, 'r-', linewidth=2.5,
|
| label=r"$(\overline{u'u'} - \overline{v'v'})_{\mathrm{PIV}} - (\overline{u'u'} - \overline{v'v'})_{\mathrm{Ref}}$")
|
| ax.axhline(y=0, color='k', linestyle='-', linewidth=1, alpha=0.5)
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(r"Gradient-only residual$^+$", fontsize=12)
|
| ax.set_title(r"Gradient Correction Residual ($u'u' - v'v'$ removes noise)", fontsize=14)
|
| ax.legend(fontsize=9)
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
|
|
| ax = axes[2]
|
| ax.semilogx(piv_plus['y_plus'], uu_residual, 'ro', markersize=2, alpha=0.15)
|
| yp_s_uu, r_s_uu = log_smooth(piv_plus['y_plus'], uu_residual)
|
| ax.semilogx(yp_s_uu, r_s_uu, 'r-', linewidth=2, label=r"$u'u'$ residual (total)")
|
|
|
| ax.semilogx(piv_plus['y_plus'], vv_residual, 'bo', markersize=2, alpha=0.15)
|
| yp_s_vv, r_s_vv = log_smooth(piv_plus['y_plus'], vv_residual)
|
| ax.semilogx(yp_s_vv, r_s_vv, 'b-', linewidth=2, label=r"$v'v'$ residual (noise floor)")
|
|
|
| yp_s_g, r_s_g = log_smooth(piv_plus['y_plus'], gradient_only)
|
| ax.semilogx(yp_s_g, r_s_g, 'g--', linewidth=2, label=r"$u'u' - v'v'$ residual (gradient only)")
|
|
|
| ax.axhline(y=0, color='k', linestyle='-', linewidth=1, alpha=0.5)
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(r"Residual$^+$", fontsize=12)
|
| ax.set_title('Decomposition: Total = Noise + Gradient', fontsize=14)
|
| ax.legend(fontsize=9)
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
| fig.suptitle(f'Noise Floor vs Gradient Correction ({window_label})', fontsize=14, y=1.02)
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'noise_gradient_decomposition.png', dpi=150)
|
| plt.close(fig)
|
|
|
| print(f"\nPlots saved to: {output_dir}")
|
|
|
|
|
| def plot_combined_stresses(piv_plus, gt_plus, wall_units, errors, output_dir, window_label='16x16'):
|
| """Plot uu+, vv+, -uv+ all on one axis."""
|
| output_dir = Path(output_dir)
|
| output_dir.mkdir(parents=True, exist_ok=True)
|
|
|
| Re_tau = wall_units['Re_tau']
|
|
|
| has_ci = 'uu_plus_ci_lo' in gt_plus
|
|
|
| fig, ax = plt.subplots(figsize=(12, 8))
|
|
|
|
|
| if has_ci:
|
| plot_ci_band(ax, gt_plus['y_plus'], gt_plus['uu_plus_ci_lo'],
|
| gt_plus['uu_plus_ci_hi'], color='k', alpha=0.12, zorder=1)
|
| plot_ci_band(ax, gt_plus['y_plus'], gt_plus['vv_plus_ci_lo'],
|
| gt_plus['vv_plus_ci_hi'], color='k', alpha=0.12, zorder=1)
|
| plot_ci_band(ax, gt_plus['y_plus'], gt_plus['uv_plus_ci_lo'],
|
| gt_plus['uv_plus_ci_hi'], sign=-1, color='k', alpha=0.12, zorder=1)
|
|
|
|
|
| ax.plot(gt_plus['y_plus'], gt_plus['uu_plus'], 'k-', linewidth=2,
|
| label=r"Ref $\overline{u'u'}^+$")
|
| ax.plot(gt_plus['y_plus'], gt_plus['vv_plus'], 'k--', linewidth=2,
|
| label=r"Ref $\overline{v'v'}^+$")
|
| ax.plot(gt_plus['y_plus'], -gt_plus['uv_plus'], 'k:', linewidth=2,
|
| label=r"Ref $-\overline{u'v'}^+$")
|
|
|
|
|
| marker_configs = [
|
| ('uu_plus', 1, 'r', 'o', r"PIV $\overline{u'u'}^+$"),
|
| ('vv_plus', 1, 'g', 's', r"PIV $\overline{v'v'}^+$"),
|
| ('uv_plus', -1, 'm', 'D', r"PIV $-\overline{u'v'}^+$"),
|
| ]
|
| for var, sign, col, mkr, label in marker_configs:
|
| piv_vals = sign * piv_plus[var]
|
| ax.plot(piv_plus['y_plus'], piv_vals, color=col, marker=mkr,
|
| markersize=4, alpha=0.7, linestyle='none', label=label, zorder=5)
|
|
|
| ax.set_xlabel(r'$y^+$', fontsize=14)
|
| ax.set_ylabel(r'Stress$^+$', fontsize=14)
|
| ax.set_title(f'Reynolds Stresses ({window_label}) - PIV vs Reference '
|
| f'(Re$_\\tau$ = {Re_tau:.0f})', fontsize=16)
|
| ax.legend(fontsize=10, ncol=2, loc='upper right')
|
| ax.set_xscale('log')
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'combined_stresses.png', dpi=150)
|
| plt.close(fig)
|
| print(f" Combined stresses plot saved to: {output_dir / 'combined_stresses.png'}")
|
|
|
|
|
| def main(mode='instantaneous', gt_dir=None, base_dir=None, ensemble_dir=None, num_frames=1000, output_dir_override=None, show_fit_lines=False):
|
| """Main benchmark comparison function.
|
|
|
| Parameters
|
| ----------
|
| mode : str
|
| 'instantaneous' or 'ensemble'
|
| gt_dir : Path
|
| Ground truth directory path (required)
|
| base_dir : Path, optional
|
| Base directory containing PIV results
|
| ensemble_dir : Path, optional
|
| Direct path to ensemble directory containing ensemble_result.mat and coordinates.mat.
|
| If provided, overrides base_dir for ensemble mode.
|
| num_frames : int
|
| Number of frames subdirectory (e.g. 1000 or 4000). Used in path construction.
|
| output_dir_override : Path, optional
|
| Custom output directory. If None, uses default naming.
|
| """
|
| if gt_dir is None:
|
| raise ValueError("gt_dir is required. Please provide the ground truth directory path.")
|
|
|
|
|
| script_dir = Path(__file__).parent
|
| gt_dir = Path(gt_dir)
|
|
|
| if mode == 'ensemble':
|
| if ensemble_dir is not None:
|
| ensemble_dir = Path(ensemble_dir)
|
| ensemble_path = ensemble_dir / 'ensemble_result.mat'
|
| coords_path = ensemble_dir / 'coordinates.mat'
|
| elif base_dir is not None:
|
| base_dir = Path(base_dir)
|
| ensemble_path = base_dir / f'calibrated_piv/{num_frames}/Cam1/ensemble/ensemble_result.mat'
|
| coords_path = base_dir / f'calibrated_piv/{num_frames}/Cam1/ensemble/coordinates.mat'
|
| else:
|
| raise ValueError("Either ensemble_dir or base_dir must be provided for ensemble mode.")
|
| output_dir = output_dir_override or (script_dir / 'benchmark_results_ensemble')
|
| else:
|
| if base_dir is None:
|
| raise ValueError("base_dir is required for instantaneous mode.")
|
| base_dir = Path(base_dir)
|
| stats_path = base_dir / f'statistics/{num_frames}/Cam1/instantaneous/mean_stats/mean_stats.mat'
|
| output_dir = output_dir_override or (script_dir / 'benchmark_results')
|
|
|
| print("=" * 70)
|
| print(f"PIV BENCHMARK COMPARISON ({mode.upper()})")
|
| print("=" * 70)
|
|
|
|
|
| print("\n[1] Loading wall units...")
|
| wall_units_file = gt_dir / 'wall_units.mat'
|
| if not wall_units_file.exists():
|
| wall_units_file = gt_dir / 'diagnostics.mat'
|
| if not wall_units_file.exists():
|
| wall_units_file = gt_dir / 'direct_stats.mat'
|
| wall_units = load_wall_units(wall_units_file)
|
| print(f" u_tau = {wall_units['u_tau']:.4f} mm/s")
|
| print(f" nu = {wall_units['nu']:.4f} mm²/s")
|
| print(f" delta_nu = {wall_units['delta_nu']:.4f} mm")
|
| print(f" Re_tau = {wall_units['Re_tau']:.0f}")
|
|
|
| print("\n[2] Loading ground truth...")
|
| profiles_file = gt_dir / 'profiles.mat'
|
| if not profiles_file.exists():
|
| profiles_file = gt_dir / 'ensemble_statistics_full.mat'
|
| if not profiles_file.exists():
|
| profiles_file = gt_dir / 'direct_stats.mat'
|
| gt = load_ground_truth(profiles_file, wall_units_path=wall_units_file)
|
| print(f" y+ range: {gt['y_plus'].min():.1f} to {gt['y_plus'].max():.1f}")
|
| print(f" U range: {gt['U'].min():.2f} to {gt['U'].max():.2f} mm/s")
|
|
|
| print(f"\n[3] Loading PIV statistics ({mode}, run 4)...")
|
| if mode == 'ensemble':
|
| piv = load_ensemble_statistics(ensemble_path, coords_path, run_idx=3)
|
| else:
|
| piv = load_piv_statistics(stats_path, run_idx=3)
|
| print(f" Grid size: {piv['ux'].shape}")
|
| print(f" ux range: {np.nanmin(piv['ux'])*1000:.2f} to {np.nanmax(piv['ux'])*1000:.2f} mm/s")
|
|
|
| print("\n[4] Computing x-averaged PIV profiles...")
|
| piv_profiles = compute_piv_profiles(piv, x_exclude_vectors=4)
|
| print(f" y range: {piv_profiles['y_mm'].min():.2f} to {piv_profiles['y_mm'].max():.2f} mm")
|
| print(f" U range: {np.nanmin(piv_profiles['U']):.2f} to {np.nanmax(piv_profiles['U']):.2f} mm/s")
|
|
|
| print("\n[5] Converting to wall units...")
|
|
|
|
|
| y_offset_mm = -piv_profiles['y_mm'].min()
|
| print(f" Applying y-offset: {y_offset_mm:.2f} mm (aligning y_min to wall)")
|
|
|
| piv_plus = convert_to_wall_units(piv_profiles, wall_units, y_offset_mm=y_offset_mm)
|
| piv_plus['y_plus'] = piv_plus['y_plus'] + 1.0
|
| print(f" Aligned y range: {piv_plus['y_mm'].min():.2f} to {piv_plus['y_mm'].max():.2f} mm")
|
| print(f" y+ range: {piv_plus['y_plus'].min():.1f} to {piv_plus['y_plus'].max():.1f} (y+ +1 applied)")
|
| print(f" U+ range: {np.nanmin(piv_plus['U_plus']):.2f} to {np.nanmax(piv_plus['U_plus']):.2f}")
|
|
|
|
|
| gt_plus = {
|
| 'y_plus': gt['y_plus'],
|
| 'U_plus': gt['U_plus'],
|
| 'V_plus': gt['V'] / wall_units['u_tau'],
|
| 'uu_plus': gt['uu_plus'],
|
| 'vv_plus': gt['vv_plus'],
|
| 'uv_plus': gt['uv_plus'],
|
| }
|
|
|
| for ci_key in ['U_plus_ci_lo', 'U_plus_ci_hi', 'V_plus_ci_lo', 'V_plus_ci_hi',
|
| 'uu_plus_ci_lo', 'uu_plus_ci_hi', 'vv_plus_ci_lo', 'vv_plus_ci_hi',
|
| 'uv_plus_ci_lo', 'uv_plus_ci_hi']:
|
| if ci_key in gt:
|
| gt_plus[ci_key] = gt[ci_key]
|
|
|
|
|
|
|
| y_mid_idx = len(piv_plus['y_plus']) // 4
|
| piv_v_sample = piv_plus['V_plus'][y_mid_idx]
|
| gt_v_idx = np.argmin(np.abs(gt_plus['y_plus'] - piv_plus['y_plus'][y_mid_idx]))
|
| gt_v_sample = gt['V'][gt_v_idx] / wall_units['u_tau']
|
|
|
| print(f"\n Sign check at y+ ≈ {piv_plus['y_plus'][y_mid_idx]:.0f}:")
|
| print(f" PIV V+ = {piv_v_sample:+.4f}")
|
| print(f" DNS V+ = {gt_v_sample:+.4f}")
|
|
|
| v_sign_match = np.sign(piv_v_sample) == np.sign(gt_v_sample) or abs(gt_v_sample) < 0.01
|
| if v_sign_match:
|
| print(" => V sign MATCHES ✓ (no flip needed)")
|
| else:
|
| print(" => V sign MISMATCH ✗ (PIV pipeline may still have sign issue)")
|
|
|
|
|
|
|
|
|
| print("\n[6] Computing error metrics (y+ = 10-500)...")
|
| errors = compute_errors(piv_plus, gt_plus, y_plus_range=(10, 500))
|
|
|
| print("\n" + "=" * 70)
|
| print("BENCHMARK RESULTS")
|
| print("=" * 70)
|
|
|
| for var, err in errors.items():
|
| var_name = {
|
| 'U_plus': 'Mean Streamwise Velocity (U+)',
|
| 'V_plus': 'Mean Wall-normal Velocity (V+)',
|
| 'uu_plus': 'Streamwise Stress (uu+)',
|
| 'vv_plus': 'Wall-normal Stress (vv+)',
|
| 'uv_plus': 'Shear Stress (uv+)',
|
| }.get(var, var)
|
|
|
| print(f"\n{var_name}:")
|
| print(f" RMS Error: {err['rms']:.4f} ({err['rms_rel']:.1f}% of range)")
|
| print(f" MAE: {err['mae']:.4f}")
|
| print(f" R²: {err['r2']:.4f}")
|
| print(f" Correlation: {err['corr']:.4f}")
|
| print(f" Points compared: {err['n_points']}")
|
|
|
| print("\n[7] Generating plots...")
|
| plot_comparison(piv_plus, gt_plus, wall_units, errors, output_dir,
|
| show_fit_lines=show_fit_lines)
|
| plot_combined_stresses(piv_plus, gt_plus, wall_units, errors, output_dir)
|
|
|
| print("\n" + "=" * 70)
|
| print("BENCHMARK COMPLETE")
|
| print("=" * 70)
|
|
|
|
|
| def plot_combined_comparison(all_results, gt_plus, wall_units, output_dir, show_fit_lines=False):
|
| """
|
| Generate combined comparison plots with all window sizes on one figure.
|
|
|
| Parameters
|
| ----------
|
| all_results : list of dict
|
| List of dicts with keys: 'piv_plus', 'errors', 'window_label', 'window_size'
|
| gt_plus : dict
|
| Ground truth profiles in wall units
|
| wall_units : dict
|
| Wall unit parameters
|
| output_dir : Path
|
| Output directory for plots
|
| """
|
| output_dir = Path(output_dir)
|
| output_dir.mkdir(parents=True, exist_ok=True)
|
|
|
| Re_tau = wall_units['Re_tau']
|
|
|
|
|
| colors = ['#e41a1c', '#377eb8', '#4daf4a', '#984ea3', '#ff7f00', '#a65628']
|
| markers = ['o', 's', '^', 'D', 'v', 'p']
|
|
|
|
|
| has_ci = 'uu_plus_ci_lo' in gt_plus
|
|
|
|
|
|
|
|
|
| fig, ax = plt.subplots(figsize=(12, 8))
|
|
|
|
|
| if has_ci and 'U_plus_ci_lo' in gt_plus:
|
| plot_ci_band(ax, gt_plus['y_plus'], gt_plus['U_plus_ci_lo'],
|
| gt_plus['U_plus_ci_hi'], color='k', alpha=0.15, zorder=1)
|
| ax.semilogx(gt_plus['y_plus'], gt_plus['U_plus'], 'k-',
|
| linewidth=2.5, label='DNS (1px)', zorder=10)
|
|
|
|
|
| for i, res in enumerate(all_results):
|
| piv_plus = res['piv_plus']
|
| label = res['window_label']
|
| ax.semilogx(piv_plus['y_plus'], piv_plus['U_plus'],
|
| color=colors[i % len(colors)], marker=markers[i % len(markers)],
|
| markersize=4, alpha=0.7, linestyle='none',
|
| label=f'PIV ({label})', zorder=5-i*0.1)
|
|
|
| if show_fit_lines:
|
| y_log = np.logspace(1, np.log10(Re_tau), 100)
|
| kappa, B = 0.41, 5.2
|
| ax.semilogx(y_log, (1/kappa)*np.log(y_log)+B, 'b--', linewidth=1.5, alpha=0.5,
|
| label=r'Log law: $U^+ = \frac{1}{\kappa}\ln(y^+) + B$')
|
| y_visc = np.linspace(0.1, 10, 50)
|
| ax.semilogx(y_visc, y_visc, 'g--', linewidth=1.5, alpha=0.5,
|
| label=r'Viscous sublayer: $U^+ = y^+$')
|
|
|
| ax.set_xlabel(r'$y^+$', fontsize=14)
|
| ax.set_ylabel(r'$U^+$', fontsize=14)
|
| ax.set_title(f'Mean Velocity Profile - All Window Sizes (Re$_\\tau$ = {Re_tau:.0f})', fontsize=16)
|
| ax.legend(fontsize=10, loc='upper left')
|
| ax.set_xlim(1, Re_tau)
|
| ax.set_ylim(0, 25)
|
| ax.grid(True, alpha=0.3)
|
|
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'U_plus_profile_combined.png', dpi=150)
|
| plt.close(fig)
|
|
|
|
|
|
|
|
|
| fig, axes = plt.subplots(1, 3, figsize=(18, 6))
|
|
|
|
|
| ax = axes[0]
|
| if has_ci:
|
| plot_ci_band(ax, gt_plus['y_plus'], gt_plus['uu_plus_ci_lo'],
|
| gt_plus['uu_plus_ci_hi'], color='k', zorder=1)
|
| ax.plot(gt_plus['y_plus'], gt_plus['uu_plus'], 'k-', linewidth=2.5, label='DNS', zorder=10)
|
| for i, res in enumerate(all_results):
|
| piv_plus = res['piv_plus']
|
| label = res['window_label']
|
| ax.plot(piv_plus['y_plus'], piv_plus['uu_plus'],
|
| color=colors[i % len(colors)], marker=markers[i % len(markers)],
|
| markersize=3, alpha=0.7, linestyle='none', label=f'PIV ({label})')
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(r"$\overline{u'u'}^+$", fontsize=12)
|
| ax.set_title('Streamwise Normal Stress', fontsize=14)
|
| ax.legend(fontsize=9)
|
| ax.set_xscale('log')
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
|
|
| ax = axes[1]
|
| if has_ci:
|
| plot_ci_band(ax, gt_plus['y_plus'], gt_plus['vv_plus_ci_lo'],
|
| gt_plus['vv_plus_ci_hi'], color='k', zorder=1)
|
| ax.plot(gt_plus['y_plus'], gt_plus['vv_plus'], 'k-', linewidth=2.5, label='DNS', zorder=10)
|
| for i, res in enumerate(all_results):
|
| piv_plus = res['piv_plus']
|
| label = res['window_label']
|
| ax.plot(piv_plus['y_plus'], piv_plus['vv_plus'],
|
| color=colors[i % len(colors)], marker=markers[i % len(markers)],
|
| markersize=3, alpha=0.7, linestyle='none', label=f'PIV ({label})')
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(r"$\overline{v'v'}^+$", fontsize=12)
|
| ax.set_title('Wall-Normal Normal Stress', fontsize=14)
|
| ax.legend(fontsize=9)
|
| ax.set_xscale('log')
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
|
|
| ax = axes[2]
|
| if has_ci:
|
| plot_ci_band(ax, gt_plus['y_plus'], gt_plus['uv_plus_ci_lo'],
|
| gt_plus['uv_plus_ci_hi'], sign=-1, color='k', zorder=1)
|
| ax.plot(gt_plus['y_plus'], -gt_plus['uv_plus'], 'k-', linewidth=2.5, label='DNS', zorder=10)
|
| for i, res in enumerate(all_results):
|
| piv_plus = res['piv_plus']
|
| label = res['window_label']
|
| ax.plot(piv_plus['y_plus'], -piv_plus['uv_plus'],
|
| color=colors[i % len(colors)], marker=markers[i % len(markers)],
|
| markersize=3, alpha=0.7, linestyle='none', label=f'PIV ({label})')
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(r"$-\overline{u'v'}^+$", fontsize=12)
|
| ax.set_title('Reynolds Shear Stress', fontsize=14)
|
| ax.legend(fontsize=9)
|
| ax.set_xscale('log')
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'reynolds_stresses_combined.png', dpi=150)
|
| plt.close(fig)
|
|
|
|
|
|
|
|
|
| fig, ax = plt.subplots(figsize=(12, 8))
|
|
|
| if has_ci and 'V_plus_ci_lo' in gt_plus:
|
| plot_ci_band(ax, gt_plus['y_plus'], gt_plus['V_plus_ci_lo'],
|
| gt_plus['V_plus_ci_hi'], color='k', zorder=1)
|
| ax.plot(gt_plus['y_plus'], gt_plus['V_plus'], 'k-', linewidth=2.5, label='DNS', zorder=10)
|
| for i, res in enumerate(all_results):
|
| piv_plus = res['piv_plus']
|
| label = res['window_label']
|
| ax.plot(piv_plus['y_plus'], piv_plus['V_plus'],
|
| color=colors[i % len(colors)], marker=markers[i % len(markers)],
|
| markersize=4, alpha=0.7, linestyle='none', label=f'PIV ({label})')
|
| ax.axhline(y=0, color='gray', linestyle='--', linewidth=0.5, alpha=0.7)
|
|
|
| ax.set_xlabel(r'$y^+$', fontsize=14)
|
| ax.set_ylabel(r'$V^+$', fontsize=14)
|
| ax.set_title(f'Mean Wall-Normal Velocity Profile - All Window Sizes (Re$_\\tau$ = {Re_tau:.0f})', fontsize=16)
|
| ax.legend(fontsize=10)
|
| ax.set_xscale('log')
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'V_plus_profile_combined.png', dpi=150)
|
| plt.close(fig)
|
|
|
|
|
|
|
|
|
| fig, ax = plt.subplots(figsize=(12, 8))
|
|
|
| ax.plot(gt_plus['y_plus'], gt_plus['U_plus'], 'k-', linewidth=2.5, label='DNS U+', zorder=10)
|
| for i, res in enumerate(all_results):
|
| piv_plus = res['piv_plus']
|
| label = res['window_label']
|
| ax.plot(piv_plus['y_plus'], piv_plus['U_plus'],
|
| color=colors[i % len(colors)], marker=markers[i % len(markers)],
|
| markersize=3, alpha=0.6, linestyle='none', label=f'PIV ({label})')
|
|
|
| ax.set_xlabel(r'$y^+$', fontsize=14)
|
| ax.set_ylabel(r'$U^+$', fontsize=14)
|
| ax.set_title('Mean Velocity Profile - All Window Sizes', fontsize=16)
|
| ax.legend(fontsize=10)
|
| ax.set_xscale('log')
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'U_plus_linear_combined.png', dpi=150)
|
| plt.close(fig)
|
|
|
|
|
|
|
|
|
| fig, ax = plt.subplots(figsize=(12, 8))
|
|
|
| if has_ci and 'U_plus_ci_lo' in gt_plus:
|
| plot_ci_band(ax, gt_plus['y_plus'], gt_plus['U_plus_ci_lo'],
|
| gt_plus['U_plus_ci_hi'], color='k', alpha=0.15, zorder=1)
|
| ax.semilogx(gt_plus['y_plus'], gt_plus['U_plus'], 'k-',
|
| linewidth=2.5, label='DNS (1px)', zorder=10)
|
|
|
| for i, res in enumerate(all_results):
|
| piv_plus = res['piv_plus']
|
| label = res['window_label']
|
| c = colors[i % len(colors)]
|
| ax.semilogx(piv_plus['y_plus'], piv_plus['U_plus'],
|
| color=c, marker=markers[i % len(markers)],
|
| markersize=4, alpha=0.7, linestyle='none',
|
| label=f'PIV ({label})', zorder=5-i*0.1)
|
|
|
| if show_fit_lines:
|
| y_log = np.logspace(1, np.log10(Re_tau), 100)
|
| kappa, B = 0.41, 5.2
|
| ax.semilogx(y_log, (1/kappa)*np.log(y_log)+B, 'b--', linewidth=1.5, alpha=0.5,
|
| label='Log law')
|
| y_visc = np.linspace(0.1, 10, 50)
|
| ax.semilogx(y_visc, y_visc, 'g--', linewidth=1.5, alpha=0.5, label=r'$U^+=y^+$')
|
|
|
| ax.set_xlabel(r'$y^+$', fontsize=14)
|
| ax.set_ylabel(r'$U^+$', fontsize=14)
|
| ax.set_title(f'Mean Velocity Profile - Smoothed (Re$_\\tau$ = {Re_tau:.0f})', fontsize=16)
|
| ax.legend(fontsize=10, loc='upper left')
|
| ax.set_xlim(1, Re_tau)
|
| ax.set_ylim(0, 25)
|
| ax.grid(True, alpha=0.3)
|
|
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'U_plus_profile_combined_smooth.png', dpi=150)
|
| plt.close(fig)
|
|
|
|
|
|
|
|
|
| fig, axes = plt.subplots(1, 3, figsize=(18, 6))
|
|
|
| stress_configs = [
|
| ('uu_plus', r"$\overline{u'u'}^+$", 'Streamwise Normal Stress', 1),
|
| ('vv_plus', r"$\overline{v'v'}^+$", 'Wall-Normal Normal Stress', 1),
|
| ('uv_plus', r"$-\overline{u'v'}^+$", 'Reynolds Shear Stress', -1),
|
| ]
|
| for ax, (var, ylabel, title, sign) in zip(axes, stress_configs):
|
| gt_vals = sign * gt_plus[var]
|
| ci_lo_key = f'{var}_ci_lo'
|
| ci_hi_key = f'{var}_ci_hi'
|
| if has_ci and ci_lo_key in gt_plus:
|
| plot_ci_band(ax, gt_plus['y_plus'], gt_plus[ci_lo_key],
|
| gt_plus[ci_hi_key], sign=sign, color='k', zorder=1)
|
| ax.plot(gt_plus['y_plus'], gt_vals, 'k-', linewidth=2.5, label='DNS', zorder=10)
|
|
|
| for i, res in enumerate(all_results):
|
| piv_plus = res['piv_plus']
|
| label = res['window_label']
|
| c = colors[i % len(colors)]
|
| piv_vals = sign * piv_plus[var]
|
| ax.plot(piv_plus['y_plus'], piv_vals,
|
| color=c, marker=markers[i % len(markers)],
|
| markersize=4, alpha=0.7, linestyle='none',
|
| label=f'PIV ({label})', zorder=5-i*0.1)
|
|
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(ylabel, fontsize=12)
|
| ax.set_title(title, fontsize=14)
|
| ax.legend(fontsize=9)
|
| ax.set_xscale('log')
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'reynolds_stresses_combined_smooth.png', dpi=150)
|
| plt.close(fig)
|
|
|
|
|
|
|
|
|
| fig, axes = plt.subplots(1, 2, figsize=(14, 6))
|
|
|
|
|
| gt_trace = gt_plus['uu_plus'] + gt_plus['vv_plus']
|
|
|
|
|
| ax = axes[0]
|
| ax.semilogx(gt_plus['y_plus'], gt_trace, 'k-', linewidth=2.5, label='DNS', zorder=10)
|
| for i, res in enumerate(all_results):
|
| piv_plus = res['piv_plus']
|
| label = res['window_label']
|
| piv_trace = piv_plus['uu_plus'] + piv_plus['vv_plus']
|
| ax.semilogx(piv_plus['y_plus'], piv_trace,
|
| color=colors[i % len(colors)], marker=markers[i % len(markers)],
|
| markersize=4, alpha=0.7, linestyle='none', label=f'PIV ({label})')
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(r"$\overline{u'u'}^+ + \overline{v'v'}^+$", fontsize=12)
|
| ax.set_title("Trace Invariant (rotation-invariant)", fontsize=14)
|
| ax.legend(fontsize=10)
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
|
|
| ax = axes[1]
|
| gt_ratio = gt_plus['uu_plus'] / (gt_plus['vv_plus'] + 1e-10)
|
| ax.semilogx(gt_plus['y_plus'], gt_ratio, 'k-', linewidth=2.5, label='DNS', zorder=10)
|
| for i, res in enumerate(all_results):
|
| piv_plus = res['piv_plus']
|
| label = res['window_label']
|
| piv_ratio = piv_plus['uu_plus'] / (piv_plus['vv_plus'] + 1e-10)
|
| ax.semilogx(piv_plus['y_plus'], piv_ratio,
|
| color=colors[i % len(colors)], marker=markers[i % len(markers)],
|
| markersize=4, alpha=0.7, linestyle='none', label=f'PIV ({label})')
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(r"$\overline{u'u'}^+ / \overline{v'v'}^+$", fontsize=12)
|
| ax.set_title("Stress Ratio (rotation indicator)", fontsize=14)
|
| ax.legend(fontsize=10)
|
| ax.set_xlim(1, Re_tau)
|
| ax.set_ylim(0, 10)
|
| ax.grid(True, alpha=0.3)
|
|
|
| fig.suptitle("Rotation Diagnostic: If trace matches but ratio differs, rotation problem exists", fontsize=12, y=1.02)
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'trace_invariant_combined.png', dpi=150)
|
| plt.close(fig)
|
|
|
|
|
|
|
|
|
| fig, axes = plt.subplots(2, 3, figsize=(18, 12))
|
|
|
|
|
| gt_interp_fn = {}
|
| for var in ['U_plus', 'V_plus', 'uu_plus', 'vv_plus', 'uv_plus']:
|
| gt_interp_fn[var] = interp1d(gt_plus['y_plus'], gt_plus[var], kind='linear',
|
| bounds_error=False, fill_value=np.nan)
|
|
|
|
|
| vel_configs = [
|
| ('U_plus', r"$U^+_{\mathrm{PIV}} - U^+_{\mathrm{Ref}}$",
|
| 'Mean Streamwise Velocity Residual', 1),
|
| ('V_plus', r"$V^+_{\mathrm{PIV}} - V^+_{\mathrm{Ref}}$",
|
| 'Mean Wall-Normal Velocity Residual', 1),
|
| ]
|
| for ax, (var, ylabel, title, sign) in zip(axes[0, :2], vel_configs):
|
| ax.axhline(y=0, color='k', linestyle='-', linewidth=1, alpha=0.5)
|
| for i, res in enumerate(all_results):
|
| piv_plus = res['piv_plus']
|
| label = res['window_label']
|
| c = colors[i % len(colors)]
|
| gt_at_piv = gt_interp_fn[var](piv_plus['y_plus'])
|
| residual = sign * piv_plus[var] - sign * gt_at_piv
|
| ax.plot(piv_plus['y_plus'], residual,
|
| color=c, marker=markers[i % len(markers)],
|
| markersize=2, alpha=0.15, linestyle='none', zorder=2)
|
| yp_s, r_s = log_smooth(piv_plus['y_plus'], residual)
|
| ax.plot(yp_s, r_s, color=c, linewidth=2,
|
| label=f'PIV ({label})', zorder=5-i*0.1)
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(ylabel, fontsize=12)
|
| ax.set_title(title, fontsize=14)
|
| ax.legend(fontsize=9)
|
| ax.set_xscale('log')
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
| axes[0, 2].set_visible(False)
|
|
|
|
|
| stress_configs = [
|
| ('uu_plus', r"$\overline{u'u'}^+_{\mathrm{PIV}} - \overline{u'u'}^+_{\mathrm{Ref}}$",
|
| 'Streamwise Normal Stress Residual', 1),
|
| ('vv_plus', r"$\overline{v'v'}^+_{\mathrm{PIV}} - \overline{v'v'}^+_{\mathrm{Ref}}$",
|
| 'Wall-Normal Normal Stress Residual', 1),
|
| ('uv_plus', r"$-\overline{u'v'}^+_{\mathrm{PIV}} - (-\overline{u'v'}^+_{\mathrm{Ref}})$",
|
| 'Shear Stress Residual', -1),
|
| ]
|
| for ax, (var, ylabel, title, sign) in zip(axes[1, :], stress_configs):
|
| ax.axhline(y=0, color='k', linestyle='-', linewidth=1, alpha=0.5)
|
| for i, res in enumerate(all_results):
|
| piv_plus = res['piv_plus']
|
| label = res['window_label']
|
| c = colors[i % len(colors)]
|
| gt_at_piv = gt_interp_fn[var](piv_plus['y_plus'])
|
| residual = sign * piv_plus[var] - sign * gt_at_piv
|
| ax.plot(piv_plus['y_plus'], residual,
|
| color=c, marker=markers[i % len(markers)],
|
| markersize=2, alpha=0.15, linestyle='none', zorder=2)
|
| yp_s, r_s = log_smooth(piv_plus['y_plus'], residual)
|
| ax.plot(yp_s, r_s, color=c, linewidth=2,
|
| label=f'PIV ({label})', zorder=5-i*0.1)
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(ylabel, fontsize=12)
|
| ax.set_title(title, fontsize=14)
|
| ax.legend(fontsize=9)
|
| ax.set_xscale('log')
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'residuals_combined.png', dpi=150)
|
| plt.close(fig)
|
|
|
|
|
|
|
|
|
| fig, axes = plt.subplots(1, 3, figsize=(18, 6))
|
|
|
|
|
| ax = axes[0]
|
| ax.axhline(y=0, color='k', linestyle='-', linewidth=1, alpha=0.5)
|
| for i, res in enumerate(all_results):
|
| piv_plus = res['piv_plus']
|
| label = res['window_label']
|
| c = colors[i % len(colors)]
|
| vv_res = piv_plus['vv_plus'] - gt_interp_fn['vv_plus'](piv_plus['y_plus'])
|
| ax.plot(piv_plus['y_plus'], vv_res,
|
| color=c, marker=markers[i % len(markers)],
|
| markersize=2, alpha=0.15, linestyle='none', zorder=2)
|
| yp_s, r_s = log_smooth(piv_plus['y_plus'], vv_res)
|
| ax.plot(yp_s, r_s, color=c, linewidth=2,
|
| label=f'PIV ({label})', zorder=5-i*0.1)
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(r"$\overline{v'v'}^+_{\mathrm{PIV}} - \overline{v'v'}^+_{\mathrm{Ref}}$", fontsize=12)
|
| ax.set_title('Noise Floor (isotropic)', fontsize=14)
|
| ax.legend(fontsize=9)
|
| ax.set_xscale('log')
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
|
|
| ax = axes[1]
|
| ax.axhline(y=0, color='k', linestyle='-', linewidth=1, alpha=0.5)
|
| for i, res in enumerate(all_results):
|
| piv_plus = res['piv_plus']
|
| label = res['window_label']
|
| c = colors[i % len(colors)]
|
| uu_res = piv_plus['uu_plus'] - gt_interp_fn['uu_plus'](piv_plus['y_plus'])
|
| vv_res = piv_plus['vv_plus'] - gt_interp_fn['vv_plus'](piv_plus['y_plus'])
|
| grad_only = uu_res - vv_res
|
| ax.plot(piv_plus['y_plus'], grad_only,
|
| color=c, marker=markers[i % len(markers)],
|
| markersize=2, alpha=0.15, linestyle='none', zorder=2)
|
| yp_s, r_s = log_smooth(piv_plus['y_plus'], grad_only)
|
| ax.plot(yp_s, r_s, color=c, linewidth=2,
|
| label=f'PIV ({label})', zorder=5-i*0.1)
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(r"Gradient-only residual$^+$", fontsize=12)
|
| ax.set_title(r"Gradient Correction Residual ($u'u' - v'v'$ removes noise)", fontsize=14)
|
| ax.legend(fontsize=9)
|
| ax.set_xscale('log')
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
|
|
| ax = axes[2]
|
| finest = all_results[-1]
|
| piv_plus = finest['piv_plus']
|
| label = finest['window_label']
|
| uu_res = piv_plus['uu_plus'] - gt_interp_fn['uu_plus'](piv_plus['y_plus'])
|
| vv_res = piv_plus['vv_plus'] - gt_interp_fn['vv_plus'](piv_plus['y_plus'])
|
| grad_only = uu_res - vv_res
|
|
|
| ax.plot(piv_plus['y_plus'], uu_res, 'ro', markersize=2, alpha=0.1)
|
| yp_s, r_s = log_smooth(piv_plus['y_plus'], uu_res)
|
| ax.plot(yp_s, r_s, 'r-', linewidth=2, label=r"$u'u'$ residual (total)")
|
|
|
| ax.plot(piv_plus['y_plus'], vv_res, 'bo', markersize=2, alpha=0.1)
|
| yp_s, r_s = log_smooth(piv_plus['y_plus'], vv_res)
|
| ax.plot(yp_s, r_s, 'b-', linewidth=2, label=r"$v'v'$ residual (noise floor)")
|
|
|
| yp_s, r_s = log_smooth(piv_plus['y_plus'], grad_only)
|
| ax.plot(yp_s, r_s, 'g--', linewidth=2, label=r"$u'u' - v'v'$ residual (gradient only)")
|
|
|
| ax.axhline(y=0, color='k', linestyle='-', linewidth=1, alpha=0.5)
|
| ax.set_xlabel(r'$y^+$', fontsize=12)
|
| ax.set_ylabel(r"Residual$^+$", fontsize=12)
|
| ax.set_title(f'Decomposition ({label}): Total = Noise + Gradient', fontsize=14)
|
| ax.legend(fontsize=9)
|
| ax.set_xscale('log')
|
| ax.set_xlim(1, Re_tau)
|
| ax.grid(True, alpha=0.3)
|
|
|
| fig.tight_layout()
|
| fig.savefig(output_dir / 'noise_gradient_decomposition_combined.png', dpi=150)
|
| plt.close(fig)
|
|
|
| print(f"\nCombined plots saved to: {output_dir}")
|
|
|
|
|
| def main_multi_run(mode='ensemble', run_indices=None, window_sizes=None, run_labels=None, gt_dir=None, base_dir=None, ensemble_dir=None, y_plus_offset=0.0, num_frames=1000, output_dir_override=None, show_fit_lines=False):
|
| """
|
| Main benchmark comparison function for multiple runs/window sizes.
|
|
|
| Parameters
|
| ----------
|
| mode : str
|
| 'instantaneous' or 'ensemble'
|
| run_indices : list of int
|
| List of run indices (0-based) to process
|
| window_sizes : list of int
|
| Corresponding window sizes for labels (e.g., [16, 8, 6, 4])
|
| run_labels : list of str, optional
|
| Custom labels for output folders (e.g., ['run_1', 'run_2', 'run_3'])
|
| gt_dir : Path, optional
|
| Ground truth directory. Defaults to script_dir/ground_truth/ensemble_statistics
|
| base_dir : Path, optional
|
| Base directory containing PIV results. Defaults to window_validation folder.
|
| ensemble_dir : Path, optional
|
| Direct path to ensemble directory containing ensemble_result.mat and coordinates.mat.
|
| If provided, overrides base_dir for ensemble mode.
|
| y_plus_offset : float, optional
|
| Offset to add to y+ coordinates (for calibration correction)
|
| """
|
|
|
| script_dir = Path(__file__).parent
|
| if gt_dir is None:
|
| raise ValueError("gt_dir is required. Please provide the ground truth directory path.")
|
| gt_dir = Path(gt_dir)
|
|
|
| if mode == 'ensemble':
|
| if ensemble_dir is not None:
|
| ensemble_dir = Path(ensemble_dir)
|
| ensemble_path = ensemble_dir / 'ensemble_result.mat'
|
| coords_path = ensemble_dir / 'coordinates.mat'
|
| elif base_dir is not None:
|
| base_dir = Path(base_dir)
|
| ensemble_path = base_dir / f'calibrated_piv/{num_frames}/Cam1/ensemble/ensemble_result.mat'
|
| coords_path = base_dir / f'calibrated_piv/{num_frames}/Cam1/ensemble/coordinates.mat'
|
| else:
|
| raise ValueError("Either ensemble_dir or base_dir must be provided for ensemble mode.")
|
| output_dir = output_dir_override or (script_dir / 'benchmark_results_ensemble')
|
| else:
|
| if base_dir is None:
|
| raise ValueError("base_dir is required for instantaneous mode.")
|
| base_dir = Path(base_dir)
|
| stats_path = base_dir / f'statistics/{num_frames}/Cam1/instantaneous/mean_stats/mean_stats.mat'
|
| output_dir = output_dir_override or (script_dir / 'benchmark_results')
|
|
|
| print("=" * 70)
|
| print(f"PIV BENCHMARK COMPARISON ({mode.upper()}) - MULTI-RUN")
|
| print("=" * 70)
|
| print(f"Processing runs: {run_indices}")
|
| print(f"Window sizes: {window_sizes}")
|
|
|
|
|
| print("\n[1] Loading wall units...")
|
| wall_units_file = gt_dir / 'wall_units.mat'
|
| if not wall_units_file.exists():
|
| wall_units_file = gt_dir / 'diagnostics.mat'
|
| if not wall_units_file.exists():
|
| wall_units_file = gt_dir / 'direct_stats.mat'
|
| wall_units = load_wall_units(wall_units_file)
|
| print(f" u_tau = {wall_units['u_tau']:.4f} mm/s")
|
| print(f" nu = {wall_units['nu']:.4f} mm²/s")
|
| print(f" delta_nu = {wall_units['delta_nu']:.4f} mm")
|
| print(f" Re_tau = {wall_units['Re_tau']:.0f}")
|
|
|
| print("\n[2] Loading ground truth...")
|
| profiles_file = gt_dir / 'profiles.mat'
|
| if not profiles_file.exists():
|
| profiles_file = gt_dir / 'ensemble_statistics_full.mat'
|
| if not profiles_file.exists():
|
| profiles_file = gt_dir / 'direct_stats.mat'
|
| gt = load_ground_truth(profiles_file, wall_units_path=wall_units_file)
|
| print(f" y+ range: {gt['y_plus'].min():.1f} to {gt['y_plus'].max():.1f}")
|
|
|
|
|
| gt_plus = {
|
| 'y_plus': gt['y_plus'],
|
| 'U_plus': gt['U_plus'],
|
| 'V_plus': gt['V'] / wall_units['u_tau'],
|
| 'uu_plus': gt['uu_plus'],
|
| 'vv_plus': gt['vv_plus'],
|
| 'uv_plus': gt['uv_plus'],
|
| }
|
|
|
| for ci_key in ['U_plus_ci_lo', 'U_plus_ci_hi', 'V_plus_ci_lo', 'V_plus_ci_hi',
|
| 'uu_plus_ci_lo', 'uu_plus_ci_hi', 'vv_plus_ci_lo', 'vv_plus_ci_hi',
|
| 'uv_plus_ci_lo', 'uv_plus_ci_hi']:
|
| if ci_key in gt:
|
| gt_plus[ci_key] = gt[ci_key]
|
|
|
|
|
| all_results = []
|
| if run_labels is None:
|
| run_labels = [f'{ws}x{ws}' for ws in window_sizes]
|
| for i, (run_idx, win_size) in enumerate(zip(run_indices, window_sizes)):
|
| window_label = f'{win_size}x{win_size}'
|
| run_output_dir = output_dir / run_labels[i]
|
|
|
| print(f"\n{'='*70}")
|
| print(f"Processing Run {run_idx+1} (Window: {window_label})")
|
| print('='*70)
|
|
|
| try:
|
| if mode == 'ensemble':
|
| piv = load_ensemble_statistics(ensemble_path, coords_path, run_idx=run_idx)
|
| else:
|
| piv = load_piv_statistics(stats_path, run_idx=run_idx)
|
|
|
| print(f" Grid size: {piv['ux'].shape}")
|
| print(f" ux range: {np.nanmin(piv['ux'])*1000:.2f} to {np.nanmax(piv['ux'])*1000:.2f} mm/s")
|
|
|
|
|
| piv_profiles = compute_piv_profiles(piv, x_exclude_vectors=4)
|
| print(f" y range: {piv_profiles['y_mm'].min():.2f} to {piv_profiles['y_mm'].max():.2f} mm")
|
|
|
|
|
| y_offset_mm = -piv_profiles['y_mm'].min()
|
| piv_plus = convert_to_wall_units(piv_profiles, wall_units, y_offset_mm=y_offset_mm)
|
| piv_plus['y_plus'] = piv_plus['y_plus'] + 1.0
|
|
|
| if y_plus_offset != 0.0:
|
| piv_plus['y_plus'] = piv_plus['y_plus'] + y_plus_offset
|
| print(f" y+ offset applied: {y_plus_offset:+.1f}")
|
| print(f" y+ range: {piv_plus['y_plus'].min():.1f} to {piv_plus['y_plus'].max():.1f} (y+ +1 applied)")
|
|
|
|
|
| errors = compute_errors(piv_plus, gt_plus, y_plus_range=(10, 500))
|
|
|
|
|
| if 'U_plus' in errors:
|
| print(f" U+ R² = {errors['U_plus']['r2']:.4f}, RMS = {errors['U_plus']['rms_rel']:.1f}%")
|
| if 'uu_plus' in errors:
|
| print(f" uu+ R² = {errors['uu_plus']['r2']:.4f}")
|
|
|
|
|
| plot_comparison(piv_plus, gt_plus, wall_units, errors, run_output_dir,
|
| window_label=window_label, show_fit_lines=show_fit_lines)
|
| plot_combined_stresses(piv_plus, gt_plus, wall_units, errors, run_output_dir,
|
| window_label=window_label)
|
|
|
|
|
| all_results.append({
|
| 'piv_plus': piv_plus,
|
| 'errors': errors,
|
| 'window_label': window_label,
|
| 'window_size': win_size,
|
| })
|
|
|
| except Exception as e:
|
| print(f" ERROR processing run {run_idx}: {e}")
|
| import traceback
|
| traceback.print_exc()
|
|
|
|
|
| if len(all_results) > 1:
|
| print(f"\n{'='*70}")
|
| print("Generating combined comparison plots...")
|
| print('='*70)
|
| plot_combined_comparison(all_results, gt_plus, wall_units, output_dir,
|
| show_fit_lines=show_fit_lines)
|
|
|
|
|
| print("\n" + "=" * 70)
|
| print("BENCHMARK SUMMARY")
|
| print("=" * 70)
|
| print(f"\n{'Window':<12} {'U+ R²':<10} {'U+ RMS%':<10} {'uu+ R²':<10} {'vv+ R²':<10} {'-uv+ R²':<10}")
|
| print("-" * 62)
|
| for res in all_results:
|
| errs = res['errors']
|
| u_r2 = errs.get('U_plus', {}).get('r2', np.nan)
|
| u_rms = errs.get('U_plus', {}).get('rms_rel', np.nan)
|
| uu_r2 = errs.get('uu_plus', {}).get('r2', np.nan)
|
| vv_r2 = errs.get('vv_plus', {}).get('r2', np.nan)
|
| uv_r2 = errs.get('uv_plus', {}).get('r2', np.nan)
|
| print(f"{res['window_label']:<12} {u_r2:<10.4f} {u_rms:<10.1f} {uu_r2:<10.4f} {vv_r2:<10.4f} {uv_r2:<10.4f}")
|
|
|
| print("\n" + "=" * 70)
|
| print("BENCHMARK COMPLETE")
|
| print("=" * 70)
|
|
|
|
|
| if __name__ == '__main__':
|
| import argparse
|
| parser = argparse.ArgumentParser(description='PIV Benchmark Comparison')
|
| parser.add_argument('--mode', '-m', choices=['instantaneous', 'ensemble'],
|
| default='instantaneous', help='PIV mode (default: instantaneous)')
|
| parser.add_argument('--runs', '-r', type=str, default=None,
|
| help='Comma-separated run indices (0-based), e.g., "0,1,2"')
|
| parser.add_argument('--windows', '-w', type=str, default=None,
|
| help='Comma-separated window sizes for labels, e.g., "32,8,8"')
|
| parser.add_argument('--labels', '-l', type=str, default=None,
|
| help='Comma-separated output folder labels, e.g., "run_1,run_2,run_3"')
|
| parser.add_argument('--gt-dir', '-g', type=str, required=True,
|
| help='Ground truth directory path (required)')
|
| parser.add_argument('--base-dir', '-b', type=str, default=None,
|
| help='Base directory containing PIV results')
|
| parser.add_argument('--ensemble-dir', '-e', type=str, default=None,
|
| help='Direct path to ensemble directory containing ensemble_result.mat and coordinates.mat')
|
| parser.add_argument('--y-plus-offset', '-y', type=float, default=0.0,
|
| help='Offset to add to y+ coordinates (calibration correction)')
|
| parser.add_argument('--num-frames', '-n', type=int, default=1000,
|
| help='Frame count subdirectory in paths (default: 1000)')
|
| parser.add_argument('--output-dir', '-o', type=str, default=None,
|
| help='Custom output directory for results')
|
| parser.add_argument('--show-fit-lines', action='store_true', default=False,
|
| help='Show log-law and viscous sublayer reference lines on U+ plots')
|
| args = parser.parse_args()
|
|
|
| gt_dir = Path(args.gt_dir)
|
| base_dir = Path(args.base_dir) if args.base_dir else None
|
| ensemble_dir = Path(args.ensemble_dir) if args.ensemble_dir else None
|
| output_dir_override = Path(args.output_dir) if args.output_dir else None
|
|
|
| if args.runs and args.windows:
|
| run_indices = [int(r) for r in args.runs.split(',')]
|
| window_sizes = [int(w) for w in args.windows.split(',')]
|
| run_labels = args.labels.split(',') if args.labels else None
|
| main_multi_run(mode=args.mode, run_indices=run_indices, window_sizes=window_sizes,
|
| run_labels=run_labels, gt_dir=gt_dir, base_dir=base_dir,
|
| ensemble_dir=ensemble_dir, y_plus_offset=args.y_plus_offset,
|
| num_frames=args.num_frames, output_dir_override=output_dir_override,
|
| show_fit_lines=args.show_fit_lines)
|
| else:
|
| main(mode=args.mode, gt_dir=gt_dir, base_dir=base_dir, ensemble_dir=ensemble_dir,
|
| num_frames=args.num_frames, output_dir_override=output_dir_override,
|
| show_fit_lines=args.show_fit_lines)
|
|
|
