∂(ρϕ)∂t+div(ρϕu)=div(Γgradϕ)+Sϕ{"version":"1.1","math":"\frac{\partial (\rho \phi)}{\partial t}+ \textbf{div} (\rho \phi \textbf{u}) = \textbf{div}(\Gamma \textbf{grad} \phi) + S_\phi "}

In the transport equation, the quantity Γ{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#x393;</mi></math>;"} can represent:

Is this equation fully discretized ?

FeϕE−FwϕP=De(ϕE−ϕP)−Dw(ϕP−ϕW){"version":"1.1","math":"F_e\phi_E-F_w\phi_P=D_e\left(\phi_E-\phi_P\right)-D_w\left(\phi_P-\phi_W\right)"}

In the case of steady source-free convection-diffusion problems, when the hybrid formulation is used for |Pe|<2:

In the transport equation, the quantity PHI represent: 

How to estimate diffusion gradient at the west side?

How to evaluate this integral:

∫ΔVddx(Γdϕdx)dV{"version":"1.1","math":"\int_{\Delta V}\frac{d}{dx}\left(\Gamma\frac{d\phi}{dx}\right) dV"}

Consider a fluid flow inside a pipe with a fixed pressure drop. We would like to find the fluid velocity across the pipe axis using the finite volume method. In the transport equation:

Which equation represents a steady source-free convection-diffusion problem?

How to estimate diffusion coefficient at the east side?

[ΓeAe(ϕE−ϕPδxPE)−ΓwAw(ϕP−ϕWδxWP)]+[ΓnAn(ϕN−ϕPδyPN)−ΓsAs(ϕP−ϕSδySP)]+[ΓtAt(ϕT−ϕPδzPT)−ΓbAb(ϕP−ϕBδzBP)]+(Su+SpϕP)=0{"version":"1.1","math":"\left[\Gamma_e A_e \left( \frac{\phi_E-\phi_P}{\delta x_{PE}}\right)-\Gamma_w A_w \left( \frac{\phi_P-\phi_W}{\delta x_{WP}}\right)\right]%\\ +\left[\Gamma_n A_n \left( \frac{\phi_N-\phi_P}{\delta y_{PN}}\right) -\Gamma_s A_s \left( \frac{\phi_P-\phi_S}{\delta y_{SP}}\right)\right]+\left[\Gamma_t A_t \left( \frac{\phi_T-\phi_P}{\delta z_{PT}}\right)-\Gamma_b A_b \left( \frac{\phi_P-\phi_B}{\delta z_{BP}}\right)\right]+\left(S_u+S_p\phi_P\right)=0"}

is this equation fully discretized ?