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arXiv · 2210.05625

Convergence of a Decoupled Splitting Scheme for the Cahn-Hilliard-Navier-Stokes System

Chen Liu·Rami Masri·Beatrice Riviere
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Abstract

This paper is devoted to the analysis of an energy-stable discontinuous Galerkin algorithm for solving the Cahn-Hilliard-Navier-Stokes equations within a decoupled splitting framework. We show that the proposed scheme is uniquely solvable and mass conservative. The energy dissipation and the $L^\infty$ stability of the order parameter are obtained under a CFL condition. Optimal a priori error estimates in the broken gradient norm and in the $L^2$ norm are derived. The stability proofs and error analysis are based on induction arguments and do not require any regularization of the potential function.

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Chen Liu, Rami Masri, Beatrice Riviere. 2022-10-11. Convergence of a Decoupled Splitting Scheme for the Cahn-Hilliard-Navier-Stokes System. https://arxiv.org/abs/2210.05625

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