Question

Which of these time-steps are used to approximate the value at time-step t-\(\frac{\Delta t}{2}\) using the Crank-Nicolson scheme for finite volume approach?

(a) t and t+Δ t

(b) t and t-Δ t

(c) t and t-\(\frac{\Delta t}{2}\)

(d) t and t+\(\frac{\Delta t}{2}\)

The question was asked during a job interview.

My doubt is from Transient Flows in portion Transient Flows of Computational Fluid Dynamics

Answer 1

Right option is (b) t and t-Δ t

The best I can explain: The Crank-Nicolson scheme uses the cell centres of both the cells which share the face which is considered. The face considered here is t-\(\frac{\Delta t}{2}\) . It is shared by the faces t and t-Δ t. So, the scheme uses both of these values for the approximation.