diff --git a/tutorial/numerical.tex b/tutorial/numerical.tex index 915df53..cfd6d20 100644 --- a/tutorial/numerical.tex +++ b/tutorial/numerical.tex @@ -460,6 +460,24 @@ \section{The 1D Diffusion Equation} \section{Convection-diffusion} +Given the three-dimensional convection diffusion equation + +\begin{equation}\label{eq:IBVP3d} + \begin{cases} + \diffp{u}{t} + \nabla(v u) = \nabla \cdot (D \nabla u), + & \left(x,y,z,t\right)\in + \left(a,b \right)\times\left(c,d \right)\times \left(e,f \right)\times\left(0, \infty \right). \\ + u\left(x,0\right)=f(x), + & x\in + \left[a,b\right]. \\ + u\left(a,t\right)= \alpha(t), & t\in + \left(0,\infty\right), \\ + u\left(b,t\right)= \beta(t), + & t\in + \left(0,\infty\right), + \end{cases} +\end{equation} + \begin{listing}[ht!] \tiny