Question

When the transient term in the Rhie-Chow interpolation is not accounted for separately, the result will ___________

(a) be oscillatory

(b) be stable

(c) have overshoots

(d) have undershoots

The question was asked in an internship interview.

My enquiry is from Incompressible Flows in section Incompressible Flows & Compressible Flows of Computational Fluid Dynamics

Answer 1

When the transient term in the Rhie-Chow interpolation is not accounted for separately, the result will likely be oscillatory.

Here’s the reasoning:

• Rhie-Chow interpolation is primarily used to correct for pressure-velocity coupling in collocated grids, and it involves a correction term that helps prevent decoupling issues. However, if the transient term (which accounts for time-dependent changes in velocity) is neglected or not handled properly, it can lead to numerical instabilities.
• The failure to properly account for the transient term, especially in transient simulations (time-dependent flows), can result in oscillatory behavior in the velocity field. This can manifest as unphysical oscillations that cause instability in the solution, especially when the pressure-velocity coupling is not fully resolved.

Here’s a breakdown of the options:

• (a) Be oscillatory: Correct. If the transient term is neglected, the simulation can exhibit oscillatory behavior, leading to instability.
• (b) Be stable: If the transient term is ignored, stability is more likely to be compromised, not ensured.
• (c) Have overshoots: While overshoots can happen in numerical methods, they are generally a result of instability, which can be linked to oscillations.
• (d) Have undershoots: Similar to overshoots, undershoots are also indicative of instability or poor resolution of the solution, but they aren't directly the most likely outcome in this specific case.

Correct Answer: (a) Be oscillatory