$$\alpha = \frac{k \cdot E_x}{u^2}, \quad P_e = \frac{u \cdot b}{E_x}, \quad c_0 = \frac{c_p \cdot q_p + c_h \cdot q_h}{q_p + q_h}$$
条件1: α≤0.027 且 Pe≥1 → x≥0: c₀·exp(-kx/u), x<0: 0
条件2: α≤0.027 且 Pe<1 → x<0: c₀·exp(ux/Ex), x≥0: c₀·exp(-kx/u)
条件3: 0.027<α≤380 → c₀=(cₚqₚ+cₕqₕ)/((qₚ+qₕ)√(1+4α))
x<0: c₀·exp(ux/(2Ex)·(1+√(1+4α))), x≥0: c₀·exp(ux/(2Ex)·(1-√(1+4α)))
条件4: α>380 → c₀=(cₚqₚ+cₕqₕ)/(2A√(kEx))
x<0: c₀·exp(x√(k/Ex)), x≥0: c₀·exp(-x√(k/Ex))
$$C(x,t) = \frac{m}{a\sqrt{4\pi E_x t}} \cdot e^{-kt} \cdot e^{-\frac{(x-ut)^2}{4E_x t}} + C_h$$
$$n = \lfloor t_0 / \Delta t \rfloor$$
$$C(x,t_j) = \sum_{i=1}^{n} \frac{\Delta t}{a\sqrt{4\pi E_x}} \cdot \frac{W_i}{\sqrt{t_j - t_{1/2}}} \cdot e^{-k(t_j - t_{1/2})} \cdot e^{-\frac{(x - u(t_j - t_{1/2}))^2}{4E_x(t_j - t_{1/2})}}$$
其中 t_{1/2} = (i - 0.5) · Δt