Question

Which of these time-steps are needed to approximate the value at time-step \(\frac{\Delta t}{2}\) using the second-order upwind Euler scheme for finite volume approach?

(a) t-\(\frac{\Delta t}{2}\) and t-2Δ t

(b) t and t-Δ t

(c) t-Δ t and t-2Δ t

(d) t and t-2Δ t

This question was addressed to me in an online quiz.

The above asked question is from Transient Flows in chapter Transient Flows of Computational Fluid Dynamics

Answer 1

Right answer is (c) t-Δ t and t-2Δ t

Best explanation: The second-order upwind Euler scheme uses two upwind nodes to approximate the values. The immediate upwind and the far upwind of t-\(\frac{\Delta t}{2}\) are t-Δ t and t-2Δ t. The vales at these two nodes are used for the approximation.