3.2.4 Example: Gaussian and conservativity

Figure 28: Non-conservative scheme (left), conservative scheme (right).

Burgers' equation allows also the non-conservative discretization using upwind values

$$v_{i}^{n+1} = v_{i}^{n} - \frac{\Delta t}{\Delta x} v_{i}^{n} \left( v_{i}^{n} - v_{i-1}^{n} \right)$$ (186)

which results in the time-evolution in the left panel in Fig. 28.

The right panel shows the result with the conservative scheme (185).