∂ρ∂t+div(ρu)=0{"version":"1.1","math":"\frac{\partial \rho}{\partial t}+ \textbf{div}(\rho \textbf{u}) = 0"}

What does the equation represent?

Is this equation fully discretized ?

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

This equation represents

∫CVdiv(Γgradϕ)dV+∫CVSϕdV=∫An.(Γgradϕ)dA+∫CVSϕdV{"version":"1.1","math":"\int_{CV} \textbf{div}(\Gamma \textbf{grad} \phi)dV + \int_{CV} S_\phi dV=\int_{A} \textbf{n}.(\Gamma \textbf{grad} \phi)dA + \int_{CV}S_\phi dV"}

The boundedness property of a scheme states that :

∑|anb||ap′|{≥1 at all nodes>1 at one node least{"version":"1.1","math":" \frac{\sum |a_{nb}|}{|a'_p|}\left\{ \begin{aligned} &\geq 1~ \text{at all nodes}\\ &> 1 ~\text{at one node least}\\ \end{aligned} \right."}

Which scheme has been used to discretize the convective term in this equation:Fe2(ϕP+ϕE)−Fw2(ϕW+ϕP)=De(ϕE−ϕP)−Dw(ϕP−ϕW){"version":"1.1","math":"\frac{F_e}{2}(\phi_P+\phi_E)-\frac{F_w}{2}(\phi_W+\phi_P)=D_e\left(\phi_E-\phi_P\right)-D_w\left(\phi_P-\phi_W\right)"}

The energy equation is:

∂(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(ρϕu){"version":"1.1","math":"\textbf{div} (\rho \phi \textbf{u}) "}represents :

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

The equilibrium problems are

This equation represents

0=div(Γgradϕ)+Sϕ{"version":"1.1","math":"\textbf{div}(\Gamma \textbf{grad} \phi) + S_\phi"}