fluent 自定义方程
1. 声波方程
二维直角坐标/二维直角
（1）$$\frac{\partial^2 p}{\partial x^2} +\frac{\partial^2 p}{\partial y^2} = \frac{1}{c^2} \frac{\partial^2 p}{\partial t^2}$$
改写方程
（2）$$\begin{cases} \frac{\partial \rho}{\partial t} + \rho_0 (\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y}) = 0 \ \rho_0 \frac{\partial u}{\partial t} = -\frac{\partial p}{\partial x} \ \rho_0 \frac{\partial v}{\partial t} = - \frac{\partial p}{\partial y} \end{cases}\ d p = c^2 d\rho $$
三维柱坐标/柱坐标
（3）$$\frac{1}{r}\frac{\partial }{\partial r}(r \frac{\partial p}{\partial r}) + \frac{1}{r^2} \frac{\partial^2 p}{\partial \varphi^2} +\frac{\partial^2 p}{\partial z^2} = \frac{1}{c^2} \frac{\partial^2 p}{\partial t^2}$$
柱对称，简化为
（4）$$\frac{1}{r}\frac{\partial }{\partial r}(r \frac{\partial p}{\partial r}) + \frac{\partial^2 p}{\partial z^2} = \frac{1}{c^2} \frac{\partial^2 p}{\partial t^2}$$
改写方程
（5） $$\begin{cases} \frac{\partial \rho}{\partial t} + \rho_0 [\frac{1}{r} \frac{\partial}{\partial r} (r v_r) + \frac{\partial v_z}{\partial z}] = 0 \ \rho_0 \frac{\partial v_r}{\partial t} = -\frac{\partial p}{\partial r} \ \rho_0 \frac{\partial v_z}{\partial t} = -\frac{\partial p}{\partial z} \end{cases}\ d p = c^2 d\rho $$
2. fluent uds (用户自定义传输方程)
传输方程的一般形式1
$$\frac{\partial \phi_k}{\partial t} + \frac{\partial }{\partial x_i} (F_i \phi_x - \Gamma_k \frac{\partial \phi_k}{\partial x_i}) = S_k$$
其中，方程
1. from fluent 6.3 user guide ↩