2.4.9 Beam-Warming scheme

Figure 16: Stencil and example for Beam-Warming scheme.

Figure 16: Beam-Warming scheme is $O \! \left( \Delta x^2 , \Delta t^2 \right)$ with flux

$$\textstyle f_{i+\frac{1}{2}}^n = \frac{1}{2} \left[ 3 f \!... ...lta x} \left[ \rho_{i}^n - \rho_{i-1}^n \right] \enspace .$$ (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.