libNonUniformROUND: An OpenFOAM Library of the ROUND scheme on non-uniform meshes

The library provides the ROUND schemes on Non-uniform meshes (ROUND-N). The library can offer an improved structure-preserving property that gives essentially oscillation-free solutions and preserves the structures of the passive transported scalar.

Compilation

The libROUNDSchemes library does not require any third-party dependency. After sourcing the OpenFOAM version, simply execute:

./Allwmake

Usage

The library can work with any OpenFOAM solvers containing convection terms.

The library should be linked to the solver. Add the following to your system/controlDict file:

libs
(
    "libNonUniformROUND.so" 
);

Validation and Verification

1. Advection of complex profiles on non-uniform meshes.

As shown in the figure below, the ROUND scheme produces low-dissipative results and preserves the structure of the passive transported scalar.

Citation

Deng, X., Jiang, Z.H., and Yan, C., Efficient ROUND schemes on non-uniform grids applied to discontinuous Galerkin schemes with Godunov-type finite volume sub-cell limiting.