# 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.

method

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

enforce_bounds

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

skip_boundaries

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

plot

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

use_cpp

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

## Options for the HierarchicalTaylor limiter¶

enforce_bcs

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.

use_weak_bcs

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.

trust_robin_dval

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¶

comp_method

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

limit_conv

Limit the convecting velocity. Default value: off.

Citations

1

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.