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arXiv · 2009.09353

On fully decoupled MSAV schemes for the Cahn-Hilliard-Navier-Stokes model of Two-Phase Incompressible Flows

Xiaoli Li·Jie Shen
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Abstract

We construct first- and second-order time discretization schemes for the Cahn-Hilliard-Navier-Stokes system based on the multiple scalar auxiliary variables approach (MSAV) approach for gradient systems and (rotational) pressure-correction for Navier-Stokes equations. These schemes are linear, fully decoupled, unconditionally energy stable, and only require solving a sequence of elliptic equations with constant coefficients at each time step. We carry out a rigorous error analysis for the first-order scheme, establishing optimal convergence rate for all relevant functions in different norms. We also provide numerical experiments to verify our theoretical results.

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Xiaoli Li, Jie Shen. 2020-09-20. On fully decoupled MSAV schemes for the Cahn-Hilliard-Navier-Stokes model of Two-Phase Incompressible Flows. https://arxiv.org/abs/2009.09353

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