给每一行做注释 import matplotlib.pyplot as plt import numpy as np a = 1.5 L = 1.0 T = 1.0 N = 32 dx = 2 / N alpha = 0.1 dt = alpha * dx art_visc_coeff = 0.6 u_prev = np.zeros(N) u = np.zeros(N) u_prev[0:int(N/2)] = 1.0 u_prev[int(N/2):N] = -1.0 t = 0.0 fig = plt.figure() plt.plot(u_prev) BC = 1 k = 0 while t < T: for i in range(1,N-1): visc_term = art_visc_coeff*dt*abs(a)/dx*(u_prev[i+1]-2*u_prev[i] +u_prev[i-1]) u[i] = u_prev[i] - dt*a * ( u_prev[i+1]- u_prev[i-1])/(2*dx) +visc_term if BC == 1: u[0] = 1.0 u[N-1] = -1. elif BC == 2: u[N-1] = u[N-2] u[0] = 1 elif BC == 3: u[0] = 1 u[N-1] = 2*u[N-2] - u[N-3] elif BC == 4: u[N-1] = u_prev[N-1] - dt*a * ( u_prev[N-1]- u_prev[N-2])/dx u[0] = 1 plt.plot(u) for j in range(N): u_prev[j] = u[j] t = t + dt k = k + 1 plt.show()
时间: 2024-04-09 09:27:31 浏览: 0
这段代码是用于模拟一维扩散方程的数值解。下面是对每一行代码的注释:
```python
import matplotlib.pyplot as plt # 导入绘图库matplotlib
import numpy as np # 导入数值计算库numpy
a = 1.5 # 扩散系数
L = 1.0 # 区域长度
T = 1.0 # 总时间
N = 32 # 空间网格数
dx = 2 / N # 空间步长
alpha = 0.1 # 数值稳定性参数
dt = alpha * dx # 时间步长
art_visc_coeff = 0.6 # 人工粘性系数
u_prev = np.zeros(N) # 上一时刻的解向量
u = np.zeros(N) # 当前时刻的解向量
u_prev[0:int(N/2)] = 1.0 # 设置初始条件,前一半位置的值为1.0
u_prev[int(N/2):N] = -1.0 # 设置初始条件,后一半位置的值为-1.0
t = 0.0 # 初始时间
fig = plt.figure() # 创建绘图窗口
plt.plot(u_prev) # 绘制初始条件下的图像
BC = 1 # 边界条件类型
k = 0 # 迭代次数
while t < T: # 时间循环
for i in range(1, N-1): # 空间循环,计算每个位置的解
visc_term = art_visc_coeff * dt * abs(a) / dx * (u_prev[i+1] - 2*u_prev[i] + u_prev[i-1]) # 人工粘性项
u[i] = u_prev[i] - dt * a * (u_prev[i+1] - u_prev[i-1]) / (2*dx) + visc_term # 更新解
if BC == 1: # 边界条件类型1
u[0] = 1.0
u[N-1] = -1.0
elif BC == 2: # 边界条件类型2
u[N-1] = u[N-2]
u[0] = 1.0
elif BC == 3: # 边界条件类型3
u[0] = 1.0
u[N-1] = 2*u[N-2] - u[N-3]
elif BC == 4: # 边界条件类型4
u[N-1] = u_prev[N-1] - dt * a * (u_prev[N-1] - u_prev[N-2]) / dx
u[0] = 1.0
plt.plot(u) # 绘制当前时刻的解图像
for j in range(N): # 更新上一时刻的解向量
u_prev[j] = u[j]
t = t + dt # 更新时间
k = k + 1 # 更新迭代次数
plt.show() # 显示图像
```
这段代码使用显式差分法对一维扩散方程进行数值求解,并根据不同的边界条件绘制了解的演化过程。