Question

For which of these problems is the Crank-Nicolson scheme unconditionally stable?

(a) Compressible flows

(b) Advection problems

(c) Diffusion problems

(d) Convection-Diffusion problems

This question was posed to me in a job interview.

My doubt stems from Transient Flows in section Transient Flows of Computational Fluid Dynamics

Answer 1

Correct choice is (c) Diffusion problems

To explain I would say: When the Crank-Nicolson scheme is applied to the diffusion problems, there is no restriction to the time-step from stability side. It is unconditionally stable for this case. This is why the scheme is often used for diffusion problems.