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4.4.2 Linearized Riemann solver

The linearized flux vector becomes

\ensuremath{\mathchoice{\mbox{\boldmath$\displaystyle F$}}
...{fluxes of characteristic waves}}
}_{\mbox{flux corrections}}
\end{displaymath} (208)

Note: \bgroup\color{DEFcolor}$\bar{\bar{\ensuremath{\mathsf{\Lambda}}}}_{i+\frac{1}{2}}$\egroup is a diagonal matrix with the characteristic velocities on the diagonal.

Note: The fluxes of the characteristic waves are the result of a localized linear advection problem. A higher-order correction term (with slope-limiter) could be applied.