I am asking for stiffness, because the CDR equation is often given as an example for a stiff equations. And there are multiple papers discussing different solvers because of the difficulties in handling it.

$\frac{c^{n+1}-c^n}{\tau} = \Theta (d \nabla^2 c^{n+1} - q \nabla c^{n+1}) + (1- \Theta)(d \nabla^2 c^{n} - q \nabla c^{n})$ q is the velocity and d the diffusion coefficient. I applied an upwind scheme for $\nabla^2 c^{n+1}$ and $\nabla^2 c^{n}$ (forward difference for negative q and vice versa). $\nabla^2$ is approximated with the 4 point stencil.