Slope limiter

Slope limiters are needed to combat non-linear convective instabilities when jumps or shocks are present in the solution or coefficients. Ocellaris uses a special velocity slope limiting procedure to stabilise the momentum equation, see 1 for details.


The method employed to perform the slope limiting

Scalar methods:

  • None

  • OnlyBound

  • HierarchicalTaylor

Velocity methods:

  • Componentwise

  • Solenoidal (not ported to FEniCS 2018.1)

Default value: None


Take the min and max of the initial scalar field and clamp all subsequent solutions to be within these global bounds. Default value: off.


A list of boundary names to skip, cells sharing a facet with these boundaries are not limited. Default value: [].


Plot some information about the limiter. How much “wigglyness” is detected etc. Mostly for debug pruposes. Default value: off.


Use the C++ implementation and not the Python implementation if both exist. Default value: on.

Options for the HierarchicalTaylor limiter


Use the Dirichlet boundary conditions for the field in the limiter, not only to set the “safe range” of values, but also to clamp the boundary values directly to the BC values in the limiter. Default value: on.


Trust the solution at the Dirichlet boundaries. The weak Dirichlet BCs may have kept the solution at the boundary from blowing up. Use the solution instead of the user specified Dirichlet value. Default value: on.


The solution is expected to be close to the Robin BC dval value, so trust this value and use it to extend the “safe range” of values for vertices at the Robin boundary. Default value: on.

Options for velocity field limiters


Only relevant for Componentwise limiter. Select which scalar limiter to use for the velocity components. Default value: None.


Limit the convecting velocity. Default value: off.



Tormod Landet, Kent-Andre Mardal, and Mikael Mortensen. Slope limiting the velocity field in a discontinuous Galerkin divergence-free two-phase flow solver. Computers and Fluids, 2019. doi:10.1016/j.compfluid.2019.104322.