# 2D Advection-Diffusion

The Advection-Diffusion equation refers to a very common mathematical model in physics, to simulate mass or energy transported by a fluid in movement. Its general formulation is:

with its associated initial and boundary conditions:

where *C* (* x, t*) is the unknown state variable which in this work corresponds to the solute concentration,

*the fluid velocity,*

**V***the diffusion/dispersion tensor,*

**D***Ω*a bounded, polygonal open set of ,

*∂Ω*,

^{1}*∂Ω*and

^{2}*∂Ω*are partitions of the boundary

^{3}*∂Ω*of

*Ω*corresponding to Dirichlet, Neumann and total flux boundary conditions and

*the unit outward normal to the boundary*

**η**_{∂Ω}*∂Ω*.

This section on the element for the 2D Advection-Diffusion simulation is divided as follows:

Chapitre: advection diffusion ( 1 / 6 )