阶段性练习：二维温度场可视化

阶段性练习：二维温度场可视化

项目目标

在 \(1\text{m} \times 1\text{m}\) 的二维薄板上，构造一个中心高温、四周低温的温度场：

\[ T(x,y) = 20+ 80\exp\left[ -\frac{(x-0.5)^2+(y-0.5)^2}{2\sigma^2} \right] \]

取：

\(\sigma = 0.15\)

解答

import numpy as np
import matplotlib.pyplot as plt


x_lenth = 1
y_lenth = 1
nx = 200
ny = 200
x = np.linspace(0,x_lenth,nx)
y = np.linspace(0,y_lenth,ny)

X,Y = np.meshgrid(x,y)

temperature = (
    20 + 80 * np.exp(
        -(
            (
                (X-0.5)**2 + (Y-0.5)**2
            )/(2*0.15**2)
        )
    )
)

fig , ax = plt.subplots()

image = ax.imshow(
    temperature,
    extent = [0,x_lenth,0,y_lenth],
    vmin = 20,
    vmax = 100,
    origin = "lower",
)

fig.colorbar(
    image,
    ax = ax,
    label = 'Temperature',
)

ax.set_title("2D Temperature Field")
ax.set_xlabel("x(m)")
ax.set_ylabel("y(m)")


plt.show()