Efficient numerical methods for phase-field equations

Tang, Tao; Qiao, Zhonghua

doi:10.1360/ssm-2020-0042

Cited by 17 publications

(1 citation statement)

References 60 publications

(70 reference statements)

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“…Thus, diffuse interface method has attracts the most attention among powerful modeling and numerical tools. About the literature on diffuse interface method, we also refer to [40,41,42,3,4] for two-phase flows, to [51,50] for ferrohydrodynamics flows, to [18,23,51] for electrowetting problems, to [38,28,20] for porous medium peoblems, to [31,16,24] for tumour growth, and to [56,15,59] for overviews.…”

Section: Introductionmentioning

confidence: 99%

Sharp-interface limits of the diffuse interface model for two-phase inductionless magnetohydrodynamic fluids

Zhang

2021

Preprint

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In this paper, we propose and analyze a diffuse interface model for inductionless magnetohydrodynamic fluids. The model couples a convective Cahn-Hilliard equation for the evolution of the interface, the Navier-Stokes system for fluid flow and the possion equation for electrostatics. The model is derived from Onsager's variational principle and conservation laws systematically. We perform formally matched asymptotic expansions and develop several sharp interface models in the limit when the interfacial thickness tends to zero. It is shown that the sharp interface limit of the models are the standard incompressible inductionless magnetohydrodynamic equations coupled with several different interface conditions for different choice of the mobilities. Numerical results verify the convergence of the diffuse interface model with different mobilitiess.

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