Upwind scheme

**Figure:** Element participation for the Upwind Scheme
$\begin{figure}\epsfig{file=figF5.eps,width=8cm}\end{figure}$

In this simple scheme the facial value is set to the element center value upwind of the face. For instance for the flow in Figure :

\overrightarrow{\phi}_e = \phi_P.

(564)

The upwind scheme introduces spurious viscosity leading to smeared flow characteristics (unless a very fine mesh is used).