Question

The collocated arrangement with Rhie-Chow interpolation will result in an equation which is dependent on the ___________

(a) staggered grid

(b) linear interpolation

(c) average

(d) under-relaxation factor

The question was asked in final exam.

The above asked question is from Incompressible Flows in portion Incompressible Flows & Compressible Flows of Computational Fluid Dynamics

Answer 1

The collocated arrangement with Rhie-Chow interpolation is commonly used in computational fluid dynamics (CFD) to solve the Navier-Stokes equations, especially in cases involving incompressible flows. The method addresses issues arising from the collocated grid (where velocity and pressure are located at the same grid points) and helps in maintaining accuracy and stability in the solution.

In this context, Rhie-Chow interpolation introduces a correction to the velocity field to ensure that the pressure-velocity coupling is consistent and that the mass conservation (continuity equation) is properly enforced.

The equation resulting from the collocated arrangement with Rhie-Chow interpolation depends on the average of the velocity components at neighboring cells. This helps in improving the accuracy of the pressure-velocity coupling.

Here's a breakdown of the options:

• (a) Staggered grid: While staggered grids are commonly used to avoid pressure-velocity decoupling, the question specifically deals with the collocated grid, so this is not the correct answer.
• (b) Linear interpolation: Linear interpolation is not specifically used in this method, which relies on a more advanced approach to adjust the velocity field.
• (c) Average: Correct. Rhie-Chow interpolation typically uses an average of the neighboring velocities to correct the velocity at the collocated grid points, ensuring proper coupling with pressure.
• (d) Under-relaxation factor: While under-relaxation factors are used in iterative solvers to improve convergence, they are not specifically related to the collocated arrangement with Rhie-Chow interpolation.

Correct Answer: (c) Average