This directory provides a set of routines to discretize a scalar advection equation defined, in a conservative way, on cells such as:

\[ \frac{\partial \phi}{\partial t} = - \nabla \cdot \left( u(\mathbf{x},t) \phi \right) \]

with a given velocity field \( u(\mathbf{x},t) \).

Time discretization

Various schemes are proposed for the computation of the integral of the previous equation between \( t^n \) and \( t^{n+1} \), basicaly Runge-Kutta schemes.

Note

• The canonical first order Euler is the only temporal scheme currently implemented for the explicit dimensional splitting Lax-Wendroff TVD Superbee spatial scheme. Note: RK2 is implemented but Euler should be used until further notice.

Spatial discretization

Various spatial schemes are proposed for the spatial discretization: from the simple first order scheme to more complex WENO schemes. All the methods are implemented in a generic way, thanks to the use of appropriate node level schemes. Also, a classical semi lagrangian method is furnished.