2.4.7 Lax-Friedrichs scheme

Figure 13: Stencil and example for Lax-Friedrichs scheme.

Figure 13 shows the stencil diagram and an example for the Lax-Friedrichs scheme with flux at $i+\frac{1}{2}$

$$\textstyle f_{i+\frac{1}{2}}^n = \frac{1}{2} \left[ f \! \... ...lta t} \left[ \rho_{i+1}^n - \rho_{i}^n \right] \enspace .$$ (110)