On a SAV-MAC scheme for the Cahn-Hilliard-Navier-Stokes Phase Field Model

2019/05/21 by Xiaoli Li, Jie Shen, Li, Xiaoli +1 · 3 citations
Computer Science · Earth and Planetary Sciences · Materials Science · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Solidification and crystal growth phenomena #nanoparticles nucleation surface interactions

paper · pdf · doi:10.48550/arxiv.1905.08504

openalex publication_date 2019/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a numerical scheme based on the scalar auxiliary variable (SAV) approach in time and the MAC discretization in space for the Cahn-Hilliard-Navier-Stokes phase field model, and carry out stability and error analysis. The scheme is linear, second-order, unconditionally energy stable and can be implemented very efficiently. We establish second-order error estimates both in time and space for phase field variable, chemical potential, velocity and pressure in different discrete norms. We also provide numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy of the our scheme.

Citations

• A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities
• A new class of efficient and robust energy stable schemes for gradient flows

Cited by

• Error analysis of scalar auxiliary variable finite element methods for the Landau–Lifshitz–Bloch equation
• Convergence analysis of a second-order SAV-ZEC scheme for the Cahn-Hilliard-Navier-Stokes system
• New highly efficient and accurate numerical scheme for the Cahn-Hilliard-Brinkman system

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