Question

What is the equivalent of (ρC ΦC)^t+Δt/2 using the Crank-Nicolson scheme for finite volume approach?

(a) \(\frac{1}{2}\)(ρC ΦC)^t+\(\frac{1}{2}\)(ρC ΦC)^t+Δ t

(b) (ρC ΦC)^t+(ρC ΦC)^t+Δt

(c) (ρC ΦC)^t-(ρC ΦC)^t+Δt

(d) \(\frac{1}{2}\)(ρC ΦC)^t–\(\frac{1}{2}\)(ρC ΦC)^t+Δt

This question was addressed to me by my school principal while I was bunking the class.

This intriguing question originated from Transient Flows in division Transient Flows of Computational Fluid Dynamics

Answer 1

Right choice is (a) \(\frac{1}{2}\)(ρC ΦC)^t+\(\frac{1}{2}\)(ρC ΦC)^t+Δ t

Explanation: The Crank-Nicolson scheme gives equal weight to both the cells which share the face. The formula is given by,

(ρC ΦC)^t+Δt/2=\(\frac{1}{2}\)(ρC ΦC)^t+\(\frac{1}{2}\)(ρC ΦC)^t+Δt.