Numerical Modeling and Convergence Analysis of the Coupled Cahn-Hilliard-Navier-Stokes System Using a Combined Scalar Auxiliary Variable and HDG Scheme

In this presentation, we introduce an overview and a novel numerical approach for solving the Cahn-Hilliard-Navier-Stokes system. Our method integrates the Scalar Auxiliary Variable (SAV) technique with a Hybridized-Discontinuous Galerkin (HDG) scheme. Initially, we focus on the development and analysis of a first-order numerical scheme and establish its convergence properties. Through extensive numerical simulations, we validate the effectiveness of the proposed scheme in accurately simulating the Cahn-Hilliard-Navier-Stokes system. Additionally, we provide an analytical convergence proof to support our findings. This work enhances our understanding of the system dynamics and offers a robust numerical framework for future simulations.