Question

The value of the flow variable at face centre (Φf) in terms of the flow variable at the owner cell’s centre (ΦC) and the neighbouring cell’s centre (Φf) as given by the face-based stencil is ________

(Note: g is the weighted average)

(a) Φf=gC ΦC+gC Φf

(b) Φf=gC ΦC+gf Φf

(c) Φf=gC ΦC+(1-gC)Φf

(d) Φf=gC ΦC+(1+gC)Φf

I have been asked this question by my college professor while I was bunking the class.

My enquiry is from Diffusion Problem topic in portion Diffusion Problem of Computational Fluid Dynamics

Answer 1

The correct answer is:

(c) Φf = gC ΦC + (1 - gC) Φf

Explanation:

In the context of computational fluid dynamics (CFD), particularly for diffusion problems, the value of the flow variable at the face center (Φf\Phi_fΦf​) is calculated using a weighted average of the values at the centers of the owner cell (ΦC\Phi_CΦC​) and the neighboring cell.

• gCg_CgC​ is the weighting factor, which is based on the properties of the flow (such as diffusivity) and the discretization method.
• The formula essentially blends the value of the flow variable from the owner cell ΦC\Phi_CΦC​ and the neighboring cell Φf\Phi_fΦf​, weighted by gCg_CgC​ and 1−gC1 - g_C1−gC​ respectively.

So, the correct equation reflects the weighted averaging process:

Φf=gCΦC+(1−gC)Φf\Phi_f = g_C \Phi_C + (1 - g_C) \Phi_fΦf​=gC​ΦC​+(1−gC​)Φf​