该代码使用热方程模拟了48小时内土壤中的温度演变，总结如下：
它导入必要的库：numpy用于数值计算，matplotlib用于绘图。
它定义了模拟中使用的常量：D（土壤的热扩散率）、深度（土壤的深度）、time_start（以秒为单位的开始时间）、time_end（以秒为单位的结束时间）和delta_t（以秒为单位的时间步长）。
它通过定义delta_x（减小的空间步长）来执行离散化，并基于给定的深度和时间参数来计算空间和时间步长的数量。
它用零初始化一个名为temperature的数组，该数组将存储不同深度和时间的温度值。
它设置温度阵列的初始条件，其中所有深度的初始温度为22.5摄氏度。
它根据给定的参数在曲面（x = 0）处设置边界条件：To（平均外部温度）和Tm（外部温度变化的幅度）。边界条件使用余弦函数随时间变化。
它对提供的真实的温度值进行插值，以匹配模拟中的时间步长。这允许在模拟温度和真实的温度之间进行比较。
它使用所提供的公式基于深度计算相移、移相。
其确定对应于4cm深度的深度指数。
它使用嵌套循环求解热方程。外部循环在时间步长上迭代，内部循环在空间步长上迭代。使用热方程公式更新每个深度和时间处的温度值。
它通过将边界条件添加到该深度的温度值来计算4 cm深度的温度（temperature_4cm）。
它使用matplotlib绘制了4cm深度处的真实的温度值和模拟温度随时间的演变。
总的来说，该代码模拟了土壤中的温度随时间的变化，并将其与提供的真实的温度值进行比较。

real_temperature_values= [22.50, 22.50, 22.30, 22.30, 22.20, 22.20, 22.10, 22.10, 22.10, 22.10, 22.10, 22.10, 22.10, 22.20, 22.30, 22.40,
22.50, 22.60, 22.70, 23.00, 23.20, 23.40, 23.70, 23.90, 24.00, 24.20, 24.40, 24.60, 24.70, 24.90, 25.10, 25.30,
25.60, 26.10, 26.60, 27.30, 28.20, 29.10, 30.00, 30.70, 31.50, 32.40, 33.20, 34.00, 34.90, 35.70, 36.50, 37.20,
37.90, 38.40, 38.90, 39.20, 39.20, 38.90, 38.50, 37.90, 37.40, 36.90, 36.40, 35.90, 35.40, 35.00, 34.50, 34.10,
33.80, 33.40, 33.10, 32.80, 32.50, 32.20, 32.00, 31.80, 31.50, 31.30, 31.00, 30.80, 30.60, 30.40, 30.10, 29.90,
29.70, 29.40, 29.20, 29.00, 28.80, 28.60, 28.40, 28.20, 28.10, 27.90, 27.70, 27.50, 27.40, 27.20, 27.10, 27.00,
26.80, 26.70, 26.60, 26.50, 26.40, 26.30, 26.20, 26.10, 26.00, 25.80, 25.80, 25.60, 25.60, 25.50, 25.40, 25.30,
25.20, 25.10, 25.00, 25.00, 24.90, 24.80, 24.70, 24.60, 24.60, 24.50, 24.50, 24.40, 24.40, 24.40, 24.30, 24.20,
24.20, 24.20, 24.20, 24.10, 24.00, 24.00, 24.00, 24.00, 23.90, 23.90, 23.80, 23.80, 23.80, 23.70, 23.60, 23.60,
23.60, 23.50, 23.50, 23.40, 23.40, 23.40, 23.40, 23.40, 23.40, 23.50, 23.50, 23.50, 23.50, 23.60, 23.60, 23.80,
23.90, 24.00, 24.20, 24.40, 24.60, 24.80, 25.00, 25.20, 25.50, 25.60, 25.80, 26.00, 26.20, 26.40, 26.60, 26.90,
27.10, 27.40, 27.90, 28.50, 29.10, 30.00, 30.60, 31.20, 31.90, 32.60, 33.40, 34.00, 34.60, 35.00, 35.20, 35.10,
35.00, 34.60, 34.30, 34.00, 34.10, 34.50, 35.10, 35.70, 36.20, 36.50, 36.90, 37.10, 37.40, 37.50, 37.50, 37.50,
37.30, 37.20, 37.10, 36.90, 36.50, 36.10, 35.70, 35.20, 34.90, 34.60, 34.40, 34.00, 33.60, 33.30, 32.90, 32.50,
32.20, 31.80, 31.50, 31.10, 30.80, 30.50, 30.10, 29.90, 29.70, 29.40, 29.20, 29.00, 28.80, 28.60, 28.40, 28.20,
28.10, 27.90, 27.70, 27.50, 27.40, 27.20, 27.00, 26.80, 26.70, 26.50, 26.40, 26.20, 26.10, 26.00, 25.80, 25.80,
25.60, 25.50, 25.40, 25.30, 25.20, 25.10, 25.00, 25.00, 24.90, 24.80, 24.70, 24.60, 24.50, 24.40, 24.40, 24.40,
24.20, 24.20, 24.20, 24.10, 24.00, 24.00, 24.00, 24.00, 23.90, 23.90, 23.80, 23.80, 23.70, 23.60, 23.60, 23.60]
import numpy as np
import matplotlib.pyplot as plt

# Constants
D = 4e-7  # Thermal diffusivity of the soil (units: m^2/s)
depth = 0.04  # Depth in m
time_start = 6 * 60 * 60 + 50 * 60  # Start time in seconds (6:50 am)
time_end = time_start + 48 * 60 * 60  # End time in seconds (next day 6:50 am)
delta_t = 60  # Time step size in seconds

# Discretization
delta_x = 0.001  # Reduced spatial step size in m

# Calculate the number of spatial and temporal steps
num_x_steps = int(depth / delta_x) + 1
num_t_steps = int((time_end - time_start) / delta_t) + 1

# Initialize temperature array
temperature = np.zeros((num_x_steps, num_t_steps))

# Set the initial conditions
temperature[:, 0] = 22.5  # Initial temperature at all depths (units: Celsius)

# Set the boundary condition at x = 0 (surface)
To = 29.364  # Average external temperature
Tm = 57.9 - 19.9  # Amplitude of external temperature variation (units: Celsius)
w = 2 * np.pi / (24 * 60 * 60)  # Angular frequency of external temperature variation     (units: rad/s)
boundary_condition = To + Tm * np.cos(w * np.linspace(time_start, time_end, num_t_steps))

# Real temperature values
real_temperature_values = np.interp(
    np.linspace(time_start, time_end, num_t_steps),
    np.linspace(time_start, time_end, len(real_temperature_values)),
    real_temperature_values)

# Calculate the phase shift based on depth
dephasage = (1.38 * np.sqrt(D) * np.arange(num_x_steps)) / depth

# Calculate the depth index
depth_4cm_index = int(0.04 / delta_x)  # Index corresponding to the depth of 4 cm

# Solve the heat equation
for t in range(1, num_t_steps):
    temperature[0, t] = boundary_condition[t] * np.exp(-dephasage[0])  # Update the     boundary condition at x = 0 (surface)
    for x in range(1, num_x_steps - 1):
        temperature[x, t] = temperature[x, t - 1] + (D * delta_t / (delta_x ** 2)) * (
            temperature[x + 1, t - 1] - 2 * temperature[x, t - 1] + temperature[x - 1, t - 1])

# Calculate the temperature at 4 cm depth
temperature_4cm = temperature[depth_4cm_index, :] + boundary_condition

    # Plot the temperature evolution
time = np.linspace(time_start, time_end, num_t_steps)
plt.plot(time, real_temperature_values, 'b-', label='Real Temperature')
plt.plot(time, temperature_4cm, 'r-', label='Simulated Temperature at 4 cm depth')
plt.xlabel('Time (s)')
plt.ylabel('Temperature (°C)')
plt.legend()
plt.title('Temperature Evolution')

plt.show()

出现错误消息“RuntimeWarning：double_scalars中遇到无效值temperature[x，t] = temperature[x，t - 1] +（D * delta_t /（delta_x**2））*（“
有谁知道如何修复错误消息？如果我把D改为10 e-20，代码可以工作，但我想使用D = 4 e-7
在讨论这些问题时，如果有人擅长物理，我会介意一些帮助，用热方程来重建真实的的温度值