Question

Which of these theorems is used to transform the general diffusion term into boundary based integral in the FVM?

(a) Gauss divergence theorem

(b) Stokes’ theorem

(c) Kelvin-Stokes theorem

(d) Curl theorem

I had been asked this question in class test.

My question is based upon FVM for 1-D Steady State Diffusion in chapter Diffusion Problem of Computational Fluid Dynamics

Answer 1

Correct answer is (a) Gauss divergence theorem

To explain: The general diffusion term is div(Γ gradΦ). Integrating for the finite volume method, it becomes

∫CV div(Γ gradΦ)dV

Applying the Gauss divergence theorem,

∫A\(\vec{n}.\)(Γ gradΦ)dA

This is the boundary based integration as the boundaries will be areas.