∂(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 this equation the quantity ϕ{"version":"1.1","math":"\phi "}represents :

What does this equation represents:

aP=aW+aE+aS+aN−SP{"version":"1.1","math":"a_P=a_W+a_E+a_S+a_N-S_P"}

The linear approximation of the source term ∫CVSϕdV{"version":"1.1","math":"\int_{CV}S_\phi dV"} is:

In this relation Pe=FD{"version":"1.1","math":"P_e=\frac{F}{D}"}

the Peclet number is given as the ratio of 

Assuming a convection-diffusion problem where the velocity is in the positive direction (to the right side). Using the upwind scheme:

∂(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 this equation the quantity ϕ{"version":"1.1","math":"\phi "}

∂(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"}

∂ρu∂t+div(ρuu)=−∂ρ∂x+div(μgradu)+SMx{"version":"1.1","math":" \frac{\partial \rho u}{\partial t}+ \textbf{div}(\rho u\textbf{u}) = -\frac{\partial \rho}{\partial x} + \textbf{div}(\mu \textbf{grad} u) + S_{Mx}"}

What does the quantity "S" represent?

The transport equation can be used to :

[ΓeAe(∂ϕ∂x)e−ΓwAw(∂ϕ∂x)w]+[ΓnAn(∂ϕ∂y)n−ΓsAs(∂ϕ∂y)s]+[ΓtAt(∂ϕ∂z)t−ΓbAb(∂ϕ∂z)b]=0{"version":"1.1","math":"\left[\Gamma_e A_e\left(\frac{\partial \phi}{\partial x}\right)_e-\Gamma_w A_w\left(\frac{\partial \phi}{\partial x}\right)_w \right ]+\left[\Gamma_n A_n\left(\frac{\partial \phi}{\partial y}\right)_n -\Gamma_s A_s\left(\frac{\partial \phi}{\partial y}\right)_s \right ] +\left[\Gamma_t A_t\left(\frac{\partial \phi}{\partial z}\right)_t-\Gamma_b A_b\left(\frac{\partial \phi}{\partial z}\right)_b \right ]=0"}

is this equation fully discretized ?