Question

According to the first-order explicit Euler scheme, the value at time-step t-\(\frac{\Delta t}{2}\) is approximated to be equal to the value at __________

(a) t+\(\frac{\Delta t}{2}\)

(b) t

(c) t-Δt

(d) t+Δt

This question was addressed to me in semester exam.

I need to ask this question from Transient Flows in portion Transient Flows of Computational Fluid Dynamics

Answer 1

Correct choice is (b) t

The best explanation: The value at t-\(\frac{\Delta t}{2}\) is at the interface of two cells. One has the cell centre t and the other has the cell centre t-Δ t. The first-order explicit Euler scheme is downstream biased. Therefore, the value at t is taken to approximate the value at t-\(\frac{\Delta t}{2}\).