A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method

Chun Liu; Jie Shen

doi:10.1016/S0167-2789(03)00030-7

A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method

Chun Liu, Jie Shen

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536 Scopus citations

Abstract

A phase field model for the mixture of two incompressible fluids is presented in this paper. The model is based on an energetic variational formulation. It consists of a Navier-Stokes system (linear momentum equation) coupled with a Cahn-Hilliard equation (phase field equation) through an extra stress term and the transport term. The extra stress represents the (phase induced) capillary effect for the mixture due to the surface tension. A Fourier-spectral method for the numerical approximation of this system is proposed and analyzed. Numerical results illustrating the robustness and versatility of the model are presented.

Original language	English (US)
Pages (from-to)	211-228
Number of pages	18
Journal	Physica D: Nonlinear Phenomena
Volume	179
Issue number	3-4
DOIs	https://doi.org/10.1016/S0167-2789(03)00030-7
State	Published - May 15 2003

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/S0167-2789(03)00030-7

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title = "A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method",

abstract = "A phase field model for the mixture of two incompressible fluids is presented in this paper. The model is based on an energetic variational formulation. It consists of a Navier-Stokes system (linear momentum equation) coupled with a Cahn-Hilliard equation (phase field equation) through an extra stress term and the transport term. The extra stress represents the (phase induced) capillary effect for the mixture due to the surface tension. A Fourier-spectral method for the numerical approximation of this system is proposed and analyzed. Numerical results illustrating the robustness and versatility of the model are presented.",

author = "Chun Liu and Jie Shen",

note = "Funding Information: The work of C. Liu is supported in part by National Science Foundation Grant DMS-9972040 and that of J. Shen is supported in part by National Science Foundation Grant DMS-0074283. ",

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T1 - A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method

AU - Liu, Chun

AU - Shen, Jie

N1 - Funding Information: The work of C. Liu is supported in part by National Science Foundation Grant DMS-9972040 and that of J. Shen is supported in part by National Science Foundation Grant DMS-0074283.

PY - 2003/5/15

Y1 - 2003/5/15

N2 - A phase field model for the mixture of two incompressible fluids is presented in this paper. The model is based on an energetic variational formulation. It consists of a Navier-Stokes system (linear momentum equation) coupled with a Cahn-Hilliard equation (phase field equation) through an extra stress term and the transport term. The extra stress represents the (phase induced) capillary effect for the mixture due to the surface tension. A Fourier-spectral method for the numerical approximation of this system is proposed and analyzed. Numerical results illustrating the robustness and versatility of the model are presented.

AB - A phase field model for the mixture of two incompressible fluids is presented in this paper. The model is based on an energetic variational formulation. It consists of a Navier-Stokes system (linear momentum equation) coupled with a Cahn-Hilliard equation (phase field equation) through an extra stress term and the transport term. The extra stress represents the (phase induced) capillary effect for the mixture due to the surface tension. A Fourier-spectral method for the numerical approximation of this system is proposed and analyzed. Numerical results illustrating the robustness and versatility of the model are presented.

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ER -

A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method

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