Question

The hybrid differencing scheme is ____________

(a) never bounded

(b) bounded unconditionally

(c) bounded in the low Peclet number

(d) bounded in the high Peclet number

The question was asked in a national level competition.

The origin of the question is Convection-Diffusion Problems in portion Convection-Diffusion Problems of Computational Fluid Dynamics

Answer 1

The correct answer is:

(c) bounded in the low Peclet number

Explanation:

The hybrid differencing scheme is a numerical method used to discretize the convection-diffusion equation. It is a combination of the upwind and central differencing schemes, providing a balance between accuracy and stability.

• When the Peclet number (Pe) is low, the problem is more dominated by diffusion than convection, so the hybrid scheme behaves similarly to central differencing, which is stable and bounded in this region.
• When the Peclet number is high, convection dominates, and the hybrid scheme may start showing instability (unbounded behavior), especially as convection becomes more pronounced.

Thus, the hybrid differencing scheme is generally bounded in the low Peclet number region, where the effects of diffusion are more significant.