The following are common forms of flux/slope limiter function, formula_12:  CHARM [not 2nd order TVD] (Zhou, 1995)  HCUS [not 2nd order TVD] (Waterson & Deconinck, 1995)  HQUICK [not 2nd order TVD] (Waterson & Deconinck, 1995)  Koren (Koren, 1993) – third-order accurate for sufficiently smooth data  minmod – symmetric (Roe, 1986)  monotonized central (MC) – symmetric (van Leer, 1977)  Osher (Chakravarthy and Osher, 1983)  ospre – symmetric (Waterson & Deconinck, 1995)  smart [not 2nd order TVD] (Gaskell & Lau, 1988)  superbee – symmetric (Roe, 1986)  Sweby – symmetric (Sweby, 1984)  UMIST (Lien & Leschziner, 1994)  van Albada 1 – symmetric (van Albada, et al., 1982)  van Albada 2 – alternative form [not 2nd order TVD] used on high spatial order schemes (Kermani, 2003)  van Leer – symmetric (van Leer, 1974)  All the above limiters indicated as being "symmetric", exhibit the following symmetry property,  This is a desirable property as it ensures that the limiting actions for forward and backward gradients operate in the same way. Unless indicated to the contrary, the above limiter functions are second order TVD. This means that they are designed such that they pass through a certain region of the solution, known as the TVD region, in order to guarantee stability of the scheme. Second-order, TVD limiters satisfy at least the following criteria:   The admissible limiter region for second-order TVD schemes is shown in the "Sweby Diagram" opposite (Sweby, 1984), and plots showing limiter functions overlaid onto the TVD region are shown below. In this image, plots for the Osher and Sweby limiters have been generated using formula_33. An additional limiter that has an interesting form is the van-Leer's one-parameter family of minmod limiters (van Leer, 1979; Harten and Osher, 1987; Kurganov and Tadmor, 2000).