∂(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 div(Γgradϕ){"version":"1.1","math":" \textbf{div}(\Gamma \textbf{grad} \phi)"}represents :

Consider a source-free problem to solve using finite volume method:

Assuming a convection-diffusion problem where the velocity is in the negative direction (to the left side).

Using the upwind scheme:

The Laplace equation which is represented by the laplacian of any quantity PHI is:

The marching problems are

∂(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 ∂(ρϕ)∂t{"version":"1.1","math":"\frac{\partial (\rho \phi)}{\partial t}"}represents :

The full momentum equation is:

to solve numerically a fluid mechanics problem we can use:

How to estimate diffusion coefficient at the east side?

The continuity equation is: