3.12 Useful TVD schemes
For irregular 3D polyhedral meshes, only TVD schemes whose limiter function avoids excessive downwind interpolation, are suﬃciently robust to be practically useful.
Limited linear and minmod
The limited linear scheme — as the name suggests — maintains the linear scheme as much as possible to be TVD, before limiting to upwind to improve boundedness, according to
Like limited linear, the minmod scheme9 does not introduce any downwind interpolation. It is symmetric but is more diﬀusive by limiting more readily towards upwind, according to
van Leer and van Albada
There are two notable TVD schemes that: exhibit low diﬀusion; maintain symmetry through some downwind interpolation; and, have limiter functions which are continuous in gradient which avoids problems due to sudden changes in limiter values.
The van Leer scheme10 is the original limited advection scheme described by the limiter function
The van Albada scheme11 is described by the limiter function