Transport Equation

A transport equation describes the evolution of some quantity, $\varphi$ over time and space, taking into account a given field $u$.

$\frac{\partial \varphi }{\partial t}=\nabla \cdot \mathbf{u}\varphi -\nabla \cdot \Gamma \nabla \varphi +S$

Where:

• ϕ can be any scalar
• $\frac{\partial \varphi }{\partial t}$ is the change of the scalar over time
• $u$ is the velocity vector ($u,v,w$)
• ∇ (nabla) represents the gradient of a scalar
• ∇⋅ represents the divergence of a scalar
• S is the source of a scalar

Equation source