Question

If the first-order implicit Euler scheme is used, the value at t+Δt/2 is replaced by the value at _________

(a) t

(b) t-\(\frac{\Delta t}{2}\)

(c) t+Δt

(d) t-Δt

The question was posed to me by my college professor while I was bunking the class.

This interesting question is from Transient Flows topic in chapter Transient Flows of Computational Fluid Dynamics

Answer 1

The correct choice is (c) t+Δt

To explain: In the first-order implicit Euler scheme, the values at the cell faces are approximated by the values at cell centres of the backward direction. Therefore, the value at t+\(\frac{\Delta t}{2}\) is replaced by the value at t.