A linear mass and energy conserving numerical scheme for two-phase flows with thermocapillary effects

Lihua Shao (), Zhenlin Guo () and Yanxiao Sun
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Lihua Shao: Beijing Key Laboratory for Magneto-Photoelectrical Composite and Interface Science, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, P. R. China
Zhenlin Guo: Mechanics Division, Beijing Computational Science Research Center, Building 9, East Zone ZPark II, No. 10, East Xibeiwang Road, Haidian District, Beijing 100193, P. R. China
Yanxiao Sun: Mechanics Division, Beijing Computational Science Research Center, Building 9, East Zone ZPark II, No. 10, East Xibeiwang Road, Haidian District, Beijing 100193, P. R. China

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 03, 1-12

Abstract: In this paper, a thermodynamically consistent phase-field model is employed to simulate the thermocapillary migration of a droplet. The model equations consist of a general Navier–Stokes equation for the two-phase flows, a Cahn–Hilliard equation for the diffuse interface, and a heat equation, and meanwhile satisfy the balance laws of mass, energy and entropy. In particular, the total energy of the system includes kinetic energy, potential energy and internal energy, which leads to a highly coupled and nonlinear equation system. We therefore develop a linear mass and energy conserving, semi-decoupled numerical method for the numerical simulations. As the model contains a heat (energy) equation, a simple error term introduced by the temporal discretization of the momentum equation can be absorbed into the heat equation, such that the numerical solutions satisfy the conservation laws of mass and energy exactly at the temporal discrete level. Several numerical tests are carried out to validate our numerical method.

Keywords: Two-phase flows; thermocapillary effects; phase-field method; thermodynamic consistency (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0129183124500359

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