2.4.7 Lax-Friedrichs scheme

Figure 14: Stencil and example for Lax-Friedrichs scheme.

Figure 14: Lax-Friedrichs scheme with flux

$$\textstyle f_{i+\frac{1}{2}}^n = \frac{1}{2} \left[ f \! \... ...lta t} \left[ \rho_{i+1}^n - \rho_{i}^n \right] \enspace .$$ (115)

The smearing is so strong that not even the number of the initial spikes is conserved. And there are some non-decaying small-scale wiggles left.

Note: odd-even decoupling.