[KTA]

I need to solve the 1D energy equation with the finite volume method:



I'm computing the gradients with central differences. For the temperatures on the borders I'm experimenting with upwind, central and quick schemes.

I've read that central difference schemes get instable if the Peclet number becomes higher than 2. But this was in the context of momentum equations. Is this also valid for the energy equation? And is the Peclet number than calculated as:
Pe = m*cp*dx/ (A*k)

When do quick schemes get instable?

Can someone advice me another scheme to reduce numerical diffusion without complicating the model? I'd like to stick with linear PDE's in T.