Question

When the first-order implicit Euler scheme is unconditionally stable, the solution is ________

(a) stationary for large time-steps

(b) oscillatory for large time-steps

(c) stationary for small time-steps

(d) oscillatory for small time-steps

The question was posed to me during an interview.

Query is from Transient Flows in chapter Transient Flows of Computational Fluid Dynamics

Answer 1

Correct choice is (a) stationary for large time-steps

The explanation is: A numerical diffusion term scales with the time-step in a similar fashion to the upwind scheme for the advection term. Therefore, when this scheme is unconditionally stable, the solution using this scheme is stationary for large steps.