Convection–diffusion equation
The convection-diffusion equation is a more general version of the scalar transport equation. It is a combination of the diffusion and convection (advection) equations. It describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection.
\[\dfrac{\partial c}{\partial t} = \mathbf{\nabla} \cdot (D \mathbf{\nabla} c - \mathbf{v} c) + R\]
\[\dfrac{\partial c}{\partial t} = \underbrace{\mathbf{\nabla} \cdot (D \mathbf{\nabla} c)}_{\text{diffusion}}-\overbrace{\underbrace{\mathbf{\nabla}\cdot (\mathbf{v} c)}_{\text{advection}}}^\text{convection} + \overbrace{\underbrace{R}_\text{destruction}}^\text{creation}\]
\(\mathbf{\nabla} \cdot (D \mathbf{\nabla} c)\) is the contribution of diffusion.
\(- \mathbf{\nabla}\cdot (\mathbf{v} c)\) is the contribution of convection or advection.
\(R\) describes the creation or destruction of the quantity.
where
\(c\) is the variable of interest.
\(D\) is the diffusivity.
\(\mathbf{v}\) is the velocity field, and
\(R\) is the sources or sinks of the quantity \(c\).
#Convection #Diffusion #Transport #Advection #Equation #ConvectionDiffusionEquation #DifferentialEquations #AdvectionEquation #DiffusionEquation #TransportEquation #ConvectionEquation
