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+ΔtThis 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

What is the equivalent of (ρC ΦC)^t+Δt/2 using the Crank-Nicolson s

1.	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+ΔtThis 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» 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.

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