TY - JOUR
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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U2 - 10.1016/S0167-2789(03)00030-7
DO - 10.1016/S0167-2789(03)00030-7
M3 - Article
AN - SCOPUS:0037880420
SN - 0167-2789
VL - 179
SP - 211
EP - 228
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 3-4
ER -