2.6.4 Examples: PLM: slopes with linear parameter dependence

Slopes of already encountered (linear) schemes:

Donor cell scheme (slope zero):

$\begin{displaymath} \delta \! \rho_i = 0 \end{displaymath}$

(149)

Lax-Wendroff scheme:

$\begin{displaymath} \delta \! \rho_i = \rho_{i+1} - \rho_{i} \end{displaymath}$

(150)

Beam-Warming scheme:

$\begin{displaymath} \delta \! \rho_i = \rho_{i} - \rho_{i-1} \end{displaymath}$

(151)

Fromm scheme:

$\begin{displaymath} \delta \! \rho_i = \frac{1}{2} \left( \rho_{i+1} - \rho_{i-1} \right) \end{displaymath}$

(152)

Non-linear extension: use non-linear combination of slopes (slope-limiter, flux-limiter, flux-averaging)