Is the CFL-Number of any importance when solving the Convection Diffusion Equation in 2D using the Theta Scheme and Finite Differences? 
How does the diffusion coefficent factor into the CFL-Condition? Is it only improtant for the explicit case? I know the implict case is suppossed to be stable for all time steps and step sizes, but I get ugly oscillations.
The velocity of the fluid and the diffusion coefficient is low in my case( in the range of $10^{-15}$). Open boundary on two sides, Dirichlet boundary $u=0$ on the other two.