Decoupled Energy Stable Schemes for a Phase-Field Model of Two-Phase Incompressible Flows with Variable Density

被引：0
作者：
Chun Liu
Jie Shen
Xiaofeng Yang
机构：
[1] Penn State University,Department of Mathematics
[2] Purdue University,Department of Mathematics
[3] University of South Carolina,Department of Mathematics
来源：
Journal of Scientific Computing | 2015年 / 62卷
关键词：
Phase-field; Two-phase flow; Navier–Stokes; Variable density; Stability; Energy stable schemes;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider in this paper numerical approximations of two-phase incompressible flows with different densities and viscosities. We present a variational derivation for a thermodynamically consistent phase-field model that admits an energy law. Two decoupled time discretization schemes for the coupled nonlinear phase-field model are constructed and shown to be energy stable. Numerical experiments are carried out to validate the model and the schemes for problems with large density and viscosity ratios.
引用
收藏
页码：601 / 622
页数：21
相关论文
共 67 条
[1]  
Abels H(2009)Existence of weak solutions for a diffuse interface model for viscous, incompressible fluids with general densities Commun. Math. Phys. 289 45-73
[2]  
Becker R(2008)Finite element approximations of the Ericksen–Leslie model for nematic liquid crystal flow SIAM J. Numer. Anal. 46 1704-1731
[3]  
Feng X(1958)Free energy of a nonuniform system. I. Interfacial free energy J. Chem. Phys. 28 258-267
[4]  
Prohl A(2012)Efficient spectral-Galerkin methods for systems of coupled second-order equations and their applications J. Comput. Phys. 231 5016-5028
[5]  
Cahn JW(2007)Calculation of two-phase Navier–Stokes flows using phase-field modeling J. Comput. Phys. 226 2078-2095
[6]  
Hilliard JE(2003)Gauge method for viscous incompressible flows Commun. Math. Sci. 1 317-332
[7]  
Chen F(2007)Analysis of finite element approximations of a phase field model for two-phase fluids Math. Comput. 76 539-571
[8]  
Shen J(2011)Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography J. Comput. Phys. 230 5587-5609
[9]  
Ding H(2006)An overview of projection methods for incompressible flows Comput. Methods Appl. Mech. Eng. 195 6011-6045
[10]  
Spelt PDM(2000)A projection FEM for variable density incompressible flows J. Comput. Phys. 165 167-188
1234567