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arXiv · 2405.14763

Structure preserving finite element schemes for the Navier-Stokes-Cahn-Hilliard system with degenerate mobility

Francisco Guillén-González·Giordano Tierra
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Abstract

In this work we present two new numerical schemes to approximate the Navier-Stokes-Cahn-Hilliard system with degenerate mobility using finite differences in time and finite elements in space. The proposed schemes are conservative, energy-stable and preserve the maximum principle approximately (the amount of the phase variable being outside of the interval [0,1] goes to zero in terms of a truncation parameter). Additionally, we present several numerical results to illustrate the accuracy and the well behavior of the proposed schemes, as well as a comparison with the behavior of the Navier-Stokes-Cahn-Hilliard model with constant mobility.

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Francisco Guillén-González, Giordano Tierra. 2024-05-23. Structure preserving finite element schemes for the Navier-Stokes-Cahn-Hilliard system with degenerate mobility. https://arxiv.org/abs/2405.14763

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