This module can be used for manipulating lagrangian particles advected by the fluid. For now, only passive/mass-less particles are defined; but any developer can use them for implementing more complex particles' behaviour such as particles with mass, chemical reactions, concentration dynamic, etc.

Advection

Particles are (passively) transported by the flow. Their position \(\mathbf{x}\) follows the trajectories of the fluid such as:

\[ \frac{d \mathbf{x}}{d t}\left( t \right) = \mathbf{u}\left( \mathbf{x}, t \right) \]

In this framework, for any quantity \( \phi \) transported by the fluid, the associated advection equation is solved in a lagrangian way:

\[ \frac{D \phi}{D t} = \frac{\partial \phi}{\partial t} + \mathbf{u} \cdot \nabla \phi = 0 \]