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On a SAV-MAC scheme for the Cahn–Hilliard–Navier–Stokes phase-field model and its error analysis for the corresponding Cahn–Hilliard–Stokes case

School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University Xiamen, Fujian 361005, P. R. China

E-mail Address: xiaolisdu@163.com

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and

Jie Shen

Department of Mathematics, Purdue University West Lafayette, IN 47907, USA

E-mail Address: shen7@purdue.edu

Corresponding author.

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https://doi.org/10.1142/S0218202520500438Cited by:41 (Source: Crossref)

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, prove its energy stability, and carry out error analysis for the corresponding Cahn–Hilliard–Stokes model only. 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 for the Cahn–Hilliard–Stokes phase-field model. We also provide numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy of our scheme.

Communicated by Q. Du

Keywords:

AMSC: 35G25, 65M06, 65M12, 65M15, 65Z05, 76D07

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