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3.2.4 Example: Gaussian and conservativity

Figure 28: Non-conservative scheme (left), conservative scheme (right).
\includegraphics[width=8.0cm]{images/} \includegraphics[width=8.0cm]{images/}
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)
\end{displaymath} (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).