我有一个 1 个空间维度的耦合非线性 PDE 系统，我想使用 FiPy 来解决这个问题。因变量是和： $n$$T$

$$\begin{align} \frac{\partial n}{\partial t} \,&=\, D\,\frac{\partial^2 n}{\partial x^2} \\ \frac{\partial T}{\partial t} \,&=\, \frac{D}{\zeta}\,\frac{\partial^2 T}{\partial x^2} \,+\, \left(\frac{\zeta + 1}{\zeta}\right) \frac{D}{n} \, \frac{\partial n}{\partial x} \, \frac{\partial T}{\partial x} \end{align}$$

到目前为止，和都是简单的数值参数。$D$$\zeta$

我在表示方程中的第二项时遇到了严重的麻烦，因为似乎没有很好的写法。它应该写成对流项还是源项？$\frac{\partial T}{\partial t}$

这是到目前为止的代码，省略了一些内容：

L = 5.0
nx = 100
mesh = Grid1D(nx=nx, dx=L/nx)
x = mesh.cellCenters[0]

density = CellVariable(name=r"$n$", mesh=mesh)     # The n dependent variable
temperature = CellVariable(name=r"$T$", mesh=mesh) # The T dependent variable

D = 5.0
zeta = 0.5

density_equation = TransientTerm(var=density) == \
                    DiffusionTerm(coeff=D, var=density)

temp_equation = TransientTerm(var=temperature) == \
                 DiffusionTerm(coeff= D / zeta, var=temperature) \
                          + S_T    # <- What should be filled in for this?

semifull_eq = density_equation & temp_equation

if __name__ == '__main__':
    viewer = Viewer((density, temperature))

timeStepDuration = dx**2 / (2*diffusivity)
for steps in range(100):
    semifull_eq.solve(dt=timeStepDuration)
    if __name__ == '__main__':
        viewer.plot()

为简洁起见，我省略了边界和初始条件。