一维杆移动热源热扩散模拟中不同维度数组插值问题及TypeError报错排查

Let's work through your problem step by step—there are a few key issues in your code causing the mismatches, TypeError, and incorrect heat source application. Here's how to fix everything and create a flexible solution that works for any time-position function:

1. Fix the Heat Source Position Function (wf_pos) #

Your original wf_pos has a critical logic error: you're trying to create an interp1d object using a scalar t and scalar position, which doesn't make sense. For your square-root position function (an analytical formula), you don't even need interpolation—just compute the position directly. For non-analytical functions, precompute positions over your time grid first, then create an interpolation function.

Option A: Analytical Position Function (your case)

def wf_pos(t):
    """Calculate heat source position (meters) for scalar or array input t"""
    return np.sqrt(t * dt)

Option B: Generic Non-Analytical Position Function

If you later switch to a position function that can't be computed directly, precompute positions for all your evaluation times first:

# Precompute positions for all time points in your evaluation grid
t_all = t_eval  # Use your existing time evaluation array
pos_all = your_custom_position_function(t_all)  # Replace with your function
wf_pos_interp = interp1d(t_all, pos_all, kind='linear', fill_value="extrapolate")

# Now call wf_pos_interp(t) to get the position at any time t

2. Fix the Floating-Point Mismatch Between Source Position and Grid #

Using np.where(x_points == wf_start) will almost never work due to floating-point precision errors. Instead, find the nearest grid index to your target position:

def get_nearest_grid_index(x_grid, target_pos):
    """Find the index of the grid point closest to target_pos"""
    return np.argmin(np.abs(x_grid - target_pos))

Use this function in your plotting code to get valid start/end indices:

for k in range(5):
    # Calculate start/end times for this 3-minute segment
    start_time = t[(k)*t_seg]
    end_time = t[(k+1)*t_seg]
    
    # Get source positions at start/end of the segment
    wf_start = wf_pos(start_time)  # Or wf_pos_interp(start_time) for non-analytical
    wf_end = wf_pos(end_time)
    
    # Find nearest grid indices
    idx_start = get_nearest_grid_index(x_points, wf_start)
    idx_end = get_nearest_grid_index(x_points, wf_end)
    
    # Ensure idx_end is greater than idx_start (in case source moves backward)
    if idx_end < idx_start:
        idx_start, idx_end = idx_end, idx_start
    
    # Plot the temperature segment (average over the time segment for clarity)
    ax[k].plot(x_points[idx_start:idx_end], u[(k)*t_seg : (k+1)*t_seg, idx_start:idx_end].mean(axis=0), 
               label=r'$T_{\mathrm{bed}}(x)$', color='C3', linewidth=1.5)
    ax[k].set_ylabel(r'$T_{\mathrm{bed}}$ (°C)')
    ax[k].set_xlabel(r'Position along the bed (x)')
    ax[k].set_title(f'Bed temperature: {k*3} to {(k+1)*3} minutes')
    ax[k].legend()
    ax[k].grid(True)

3. Fix the TypeError and Incorrect Heat Source Application in the ODE #

Your TypeError: object of type 'float' has no len() comes from two issues:

• The broken wf_pos function returning an invalid object
• Overwriting the x parameter (your spatial grid) inside the ode function with the source position

Plus, your original ODE applies the heat source to every grid point (Tp += Q_val)—that's wrong! You only want to add the heat to the grid point where the source is located. Here's the fixed ODE:

def ode(t, T, Nx, x_grid, dx):
    """Fixed ODE form of the spatially discretized PDE"""
    NX = len(T)
    Tp = np.zeros(NX)
    
    # Compute finite difference Laplacian
    for i in range(1, NX-1):
        Tp[i] = (T[i-1] - 2 * T[i] + T[i+1])
    
    # Get current source position and corresponding grid index
    source_pos = wf_pos(t)  # Or wf_pos_interp(t)
    source_idx = get_nearest_grid_index(x_grid, source_pos)
    
    # Get heat source value and apply it to the correct grid point
    lindex = lindex_func(source_pos)
    Q_val = Qi_func(lindex)
    Tp[source_idx] += Q_val
    
    # Apply diffusion coefficient and divide by rho*Cp
    coef = k / (dx**2)
    Tp = coef * Tp
    Tp /= rhoCp
    
    # Apply boundary conditions (zero gradient)
    Tp[0] = Tp[1]
    Tp[NX-1] = Tp[NX-2]
    
    return Tp

Don't forget to update your args to avoid variable name conflicts:

args = (Nx, x_points, dx)  # Use x_points instead of x here

4. Generalize for Any Time-Position Function #

To make this work for any future position function:

1. Precompute positions for all your evaluation times (if non-analytical)
2. Use interp1d to create a smooth interpolation function
3. Use get_nearest_grid_index to map the continuous position to your discrete grid
4. Ensure the ODE only applies the heat source to the correct grid point

These changes will eliminate your TypeError, fix the position-grid mismatch, and make your code flexible enough to handle any heat source movement pattern.

内容的提问来源于stack exchange，提问作者user30517380