import sys import os import numpy as np import plotly.graph_objects as go sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__)))) import config BASE_DIR = os.path.dirname(os.path.dirname(os.path.abspath(__file__))) FDM_ANIM_DIR = os.path.join(BASE_DIR, 'animations', 'fdm') def _next_path(base_dir, prefix, ext): i = 1 while True: path = os.path.join(base_dir, f'{prefix}_{i:03d}{ext}') if not os.path.exists(path): return path i += 1 def visualize_fdm(T_matrix, x_vals, t_vals): """Produce three HTML visualisations for the FDM solver output. Parameters ---------- T_matrix : np.ndarray, shape (NX, NT) Temperature field: T_matrix[i, n] = T(x_i, t_n). x_vals : np.ndarray, shape (NX,) Spatial node positions. t_vals : np.ndarray, shape (NT,) Time values. """ os.makedirs(FDM_ANIM_DIR, exist_ok=True) # ------------------------------------------------------------------ # 1. Heatmap # ------------------------------------------------------------------ zmax = float(np.max(np.abs(T_matrix - config.T0))) # Use symmetric range centred on T0 if there is any variation, # otherwise fall back to the raw range. z_data = T_matrix.T # shape (NT, NX) — rows=time, cols=space if zmax > 0: z_center = float(np.mean(T_matrix)) z_abs = float(np.max(np.abs(T_matrix - z_center))) zmin_sym = z_center - z_abs zmax_sym = z_center + z_abs else: zmin_sym = float(np.min(T_matrix)) zmax_sym = float(np.max(T_matrix)) fig_heatmap = go.Figure(go.Heatmap( z=z_data, x=x_vals, y=t_vals, colorscale='RdBu_r', zmin=zmin_sym, zmax=zmax_sym, colorbar=dict(title='T [°C]'), )) fig_heatmap.update_layout( title='FDM — Heat Equation T(x,t)', xaxis_title='x [m]', yaxis_title='t [s]', height=500, ) heatmap_path = _next_path(FDM_ANIM_DIR, 'heatmap', '.html') fig_heatmap.write_html(heatmap_path) print(f"Heatmap saved → {heatmap_path}") # ------------------------------------------------------------------ # 2. Animated profile T(x) evolving in time # ------------------------------------------------------------------ L = config.L n_frames = len(t_vals) # Subsample frames for a manageable animation (max ~200 frames) max_frames = 200 step = max(1, n_frames // max_frames) frame_indices = list(range(0, n_frames, step)) y_min = float(np.min(T_matrix)) - 1.0 y_max = float(np.max(T_matrix)) + 1.0 vline_shapes = [ dict(type='line', x0=0, x1=0, y0=y_min, y1=y_max, line=dict(color='grey', dash='dash', width=1)), dict(type='line', x0=L, x1=L, y0=y_min, y1=y_max, line=dict(color='grey', dash='dash', width=1)), ] frames = [] for idx in frame_indices: frames.append(go.Frame( data=[go.Scatter( x=x_vals, y=T_matrix[:, idx], mode='lines', line=dict(color='royalblue', width=2), name='FDM', )], name=str(idx), layout=go.Layout( title_text=f'FDM | t = {t_vals[idx]:.3f} s', ), )) fig_anim = go.Figure( data=[go.Scatter( x=x_vals, y=T_matrix[:, frame_indices[0]], mode='lines', line=dict(color='royalblue', width=2), name='FDM', )], layout=go.Layout( title=f'FDM | t = {t_vals[frame_indices[0]]:.3f} s', xaxis=dict(title='x [m]', range=[-0.02 * L, 1.02 * L]), yaxis=dict(title='T [°C]', range=[y_min, y_max]), shapes=vline_shapes, updatemenus=[dict( type='buttons', showactive=False, y=1.15, x=0.5, xanchor='center', buttons=[ dict( label='▶ Play', method='animate', args=[None, dict( frame=dict(duration=40, redraw=False), fromcurrent=True, mode='immediate', )], ), dict( label='⏸ Pause', method='animate', args=[[None], dict( frame=dict(duration=0, redraw=False), mode='immediate', )], ), ], )], sliders=[dict( steps=[ dict( method='animate', args=[[str(idx)], dict( mode='immediate', frame=dict(duration=0, redraw=False), )], label=f'{t_vals[idx]:.2f}', ) for idx in frame_indices ], transition=dict(duration=0), x=0.05, y=0, len=0.9, currentvalue=dict(prefix='t = ', font=dict(size=14)), )], ), frames=frames, ) anim_path = _next_path(FDM_ANIM_DIR, 'animation', '.html') fig_anim.write_html(anim_path) print(f"Animation saved → {anim_path}") # ------------------------------------------------------------------ # 3. Time evolution at fixed spatial points # ------------------------------------------------------------------ fixed_fractions = [0.0, 0.25, 0.5, 0.75, 1.0] colors = ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd'] fig_ts = go.Figure() for frac, color in zip(fixed_fractions, colors): x_target = frac * L idx_x = int(np.argmin(np.abs(x_vals - x_target))) label = f'x = {x_vals[idx_x]:.2f} m' fig_ts.add_trace(go.Scatter( x=t_vals, y=T_matrix[idx_x, :], mode='lines', name=label, line=dict(color=color, width=2), )) # "Heat ON" vertical dashed line at t = T_STEP t_step = config.T_STEP t_min_val = float(np.min(t_vals)) t_max_val = float(np.max(t_vals)) T_min_val = float(np.min(T_matrix)) - 1.0 T_max_val = float(np.max(T_matrix)) + 1.0 fig_ts.add_shape( type='line', x0=t_step, x1=t_step, y0=T_min_val, y1=T_max_val, line=dict(color='red', dash='dash', width=1.5), ) fig_ts.add_annotation( x=t_step, y=T_max_val, text='Heat ON', showarrow=False, yanchor='top', font=dict(color='red', size=11), ) fig_ts.update_layout( title='FDM — Temperature evolution at fixed points', xaxis=dict(title='t [s]', range=[t_min_val, t_max_val]), yaxis=dict(title='T [°C]', range=[T_min_val, T_max_val]), legend=dict(x=0.01, y=0.99), height=480, ) ts_path = _next_path(FDM_ANIM_DIR, 'time_series', '.html') fig_ts.write_html(ts_path) print(f"Time-series saved → {ts_path}")