Question

The central difference scheme gives unphysical results when the problem is _____________

(a) depends on the boundary conditions

(b) equally dominated by diffusion and convection

(c) diffusive dominant

(d) convective dominant

This question was addressed to me in exam.

This is a very interesting question from Convection-Diffusion Problems in portion Convection-Diffusion Problems of Computational Fluid Dynamics

Answer 1

The correct answer is:

(d) convective dominant

Explanation:

The central difference scheme is typically used for spatial discretization in numerical methods, but it can produce unphysical results when applied to problems where convection dominates over diffusion. This is because the central difference scheme, which is symmetric in nature, is not well-suited for handling convection-dominated problems.

In convection-dominated problems, the flow has strong directional motion (advection), and numerical methods need to accurately capture the direction of the flow. The central difference scheme, due to its symmetry, does not correctly capture the advection direction and may lead to unphysical oscillations or numerical instability. These oscillations can result in unrealistic behavior, such as negative concentrations or velocities.

On the other hand, when diffusion dominates, the central difference scheme generally provides accurate results, as diffusion tends to smooth out the solution, reducing the impact of numerical oscillations.

Correct Answer: (d) convective dominant