With proper limiting, DG and FEM schemes can conserve mass, preserve bounds, and dissipate energy for the Cahn-Hilliard-Navier-Stokes system with degenerate mobility, with SWIP-L the most robust in the tests.
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Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement
With proper limiting, DG and FEM schemes can conserve mass, preserve bounds, and dissipate energy for the Cahn-Hilliard-Navier-Stokes system with degenerate mobility, with SWIP-L the most robust in the tests.