Flux Limiter - Limiter Functions

Limiter Functions

The following are common forms of flux/slope limiter function, :

CHARM (Zhou, 1995)

HCUS (Waterson & Deconinck, 1995)

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HQUICK (Waterson & Deconinck, 1995)

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Koren (Koren, 1993) – third-order accurate for sufficiently smooth data

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minmod – symmetric (Roe, 1986)

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monotonized central (MC) – symmetric (van Leer, 1977)

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Osher (Chatkravathy and Osher, 1983)

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ospre – symmetric (Waterson & Deconinck, 1995)

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smart (Gaskell & Lau, 1988)

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superbee – symmetric (Roe, 1986)

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Sweby – symmetric (Sweby, 1984)

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UMIST (Lien & Leschziner, 1994)

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van Albada 1 – symmetric (van Albada, et al., 1982)

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van Albada 2 – alternative form used on high spatial order schemes (Kermani, 2003)

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van Leer – symmetric (van Leer, 1974)

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All the above limiters indicated as being symmetric, exhibit the following symmetry property,

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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 .