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