next up previous contents index

2.4.9 Beam-Warming scheme

Figure 16: Stencil and example for Beam-Warming scheme.
\includegraphics[width=8.0cm]{images/} \includegraphics[width=8.0cm]{images/}
Figure 16: Beam-Warming scheme is \bgroup\color{DEFcolor}$O \! \left( \Delta x^2 , \Delta t^2 \right)$\egroup with flux
f_{i+\frac{1}{2}}^n = \frac{1}{2} \left[ 3 f \!...
...lta x}
\left[ \rho_{i}^n -
\enspace .
\end{displaymath} (117)
The result is smooth with considerable overshoot (that does not much grow with time anymore). This second order scheme might be useful for more regular initial conditions.