2.6.5 PLM: slope-limiter

A slope can be written as

$$\delta \! \rho_i = \Phi \! \left( \frac{\rho_{i} - \rho_{... ...ht) \delta \! \rho_i \! \left( \mbox{Lax-Wendroff} \right)$$ (153)

with the help of a (possibly non-linear) slope-limiter or flux-limiter

$$\Phi \! \left( \frac{\rho_{i} - \rho_{i-1}}{\rho_{i+1} - \r... ...rho_i}{\delta \! \rho_i \! \left( \mbox{Lax-Wendroff} \right)}$$ (154)

A related concept is flux-averaging.

Note: The slope-limiter for the Lax-Wendroff scheme is $1$.

Note: The slope-limiter for the donor cell scheme is $0$.