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2.4.5 Donor cell (FTBS) scheme

Figure 12: Stencil and example for donor cell scheme.
\includegraphics[width=8.0cm]{images/} \includegraphics[width=8.0cm]{images/}
Figure 12: donor cell scheme (FTBS, 1st order upwind method, derived in Sect. 2.3.16), with flux
f_{i+\frac{1}{2}}^n = f \! \left( \rho_{i}^n \right)
\enspace .
\end{displaymath} (113)
The result is wonderfully smooth but smeared out severely. Upwinding seems promising to achieve stability. However, the accuracy of the scheme has to be improved.