给我一段标准的LBM MRT的python代码

下面是一个标准的LBM MRT的Python代码示例，其中使用了numpy和numba库以加速计算过程：

import numpy as np
from numba import jit

# 定义LBM参数
Lx, Ly = 100, 50
q = 9
dx = 1.0
dt = 1.0
nu = 0.1
omega = 1.0 / (3.0 * nu + 0.5)

# 定义流体初始状态
rho0 = 1.0
u0 = np.zeros((2,))
f0 = np.zeros((Lx, Ly, q))
for i in range(Lx):
    for j in range(Ly):
        for k in range(q):
            w = np.array([4/9, 1/9, 1/9, 1/9, 1/9, 1/36, 1/36, 1/36, 1/36])
            c = np.array([[0,0], [1,0], [0,1], [-1,0], [0,-1], [1,1], [-1,1], [-1,-1], [1,-1]])
            f0[i, j, k] = w[k] * rho0 * (1.0 + 3.0 * np.dot(c[k], u0) + 4.5 * np.dot(c[k], u0)**2 - 1.5 * np.dot(u0, u0))

# 定义MRT参数
S = np.array([[1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0],
              [-4.0, -1.0, -1.0, -1.0, -1.0, 2.0, 2.0, 2.0, 2.0],
              [4.0, -2.0, -2.0, -2.0, -2.0, 1.0, 1.0, 1.0, 1.0],
              [0.0, 1.0, 0.0, -1.0, 0.0, 1.0, -1.0, -1.0, 1.0],
              [0.0, -2.0, 0.0, 2.0, 0.0, 1.0, -1.0, -1.0, 1.0],
              [0.0, 0.0, 1.0, 0.0, -1.0, 1.0, 1.0, -1.0, -1.0],
              [0.0, 0.0, -2.0, 0.0, 2.0, 1.0, 1.0, -1.0, -1.0],
              [0.0, 1.0, -1.0, 1.0, -1.0, 0.0, 0.0, 0.0, 0.0],
              [0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -1.0, 1.0, -1.0]])
Sinv = np.linalg.inv(S)
M = np.diag([2/3, -1/6, -1/6, 0.0, 0.0, 0.0, 1/6, 1/6, 1/6])
Minv = np.linalg.inv(M)

# 定义速度和密度变换函数
@jit(nopython=True)
def f2rho(f):
    rho = np.sum(f, axis=-1)
    return rho

@jit(nopython=True)
def rho2u(rho, f):
    u = np.zeros((2,))
    for k in range(q):
        c = np.array([[0,0], [1,0], [0,1], [-1,0], [0,-1], [1,1], [-1,1], [-1,-1], [1,-1]])
        u += f[..., k] * c[k] / rho[..., np.newaxis]
    return u

@jit(nopython=True)
def u2f(u, rho):
    f = np.zeros((Lx, Ly, q))
    for k in range(q):
        w = np.array([4/9, 1/9, 1/9, 1/9, 1/9, 1/36, 1/36, 1/36, 1/36])
        c = np.array([[0,0], [1,0], [0,1], [-1,0], [0,-1], [1,1], [-1,1], [-1,-1], [1,-1]])
        cu = np.dot(c[k], u)
        uu = np.dot(u, u)
        f[..., k] = rho * w[k] * (1.0 + 3.0 * cu + 4.5 * cu**2 - 1.5 * uu)
    return f

# 定义MRT函数
@jit(nopython=True)
def mrt(f, Sinv, M, Minv, rho0, u0, omega, dx, dt):
    rho = f2rho(f)
    u = rho2u(rho, f)
    f_eq = u2f(u, rho)

    m = np.matmul(Sinv, np.matmul(M, f - f_eq))
    m_star = m - omega * (m - np.matmul(M, m))
    f_star = np.matmul(Minv, np.matmul(S, m_star)) + f_eq

    rho_star = f2rho(f_star)
    u_star = rho2u(rho_star, f_star)
    f_new = u2f(u_star, rho_star)

    for i in range(Lx):
        for j in range(Ly):
            for k in range(q):
                f[i, j, k] = f[i, j, k] + (f_star[i, j, k] - f_new[i, j, k]) * np.exp(-dt / tau[k])

    return f

# 运行模拟
tau = np.array([3.0 * nu + 0.5, nu + 0.5, nu + 0.5, nu, nu, nu, nu, nu, nu])
f = f0.copy()

for iter in range(1000):
    f = mrt(f, Sinv, M, Minv, rho0, u0, omega, dx, dt)

需要注意的是，这段代码只是一个简单的示例，具体的模拟过程和参数设置需要根据具体的问题进行调整。