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

10/11/2022

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by   Chen Liu, et al.

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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^∞ 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.