Consistent and conservative scheme for incompressible two-phase flows using the conservative Allen-Cahn model

被引:45
作者
Huang, Ziyang [1 ]
Lin, Guang [1 ,2 ]
Ardekani, Arezoo M. [1 ]
机构
[1] Purdue Univ, Sch Mech Engn, W Lafayette, IN 47907 USA
[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA
基金
美国国家科学基金会;
关键词
The conservative Allen-Cahn model; Phase-Field; Consistent scheme; Conservative scheme; Two-phase flow; Large density ratio; LEVEL SET METHOD; INTERFACE CAPTURING SCHEME; ENERGY STABLE SCHEMES; FRONT-TRACKING METHOD; PHASE-FIELD MODELS; DIFFUSE-INTERFACE; SURFACE-TENSION; NUMERICAL SIMULATIONS; THINC METHOD; HIGH-ORDER;
D O I
10.1016/j.jcp.2020.109718
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
In the present work, we consider the conservative Allen-Cahn model and applied it to two-phase flows in a consistent and conservative manner. The consistent formulation is proposed, where the conservative Allen-Cahn equation is reformulated in a conservative form using an auxiliary variable. As a result, the consistency analysis is performed and the resulting two-phase model honors the consistency of reduction, the consistency of mass conservation and the consistency of mass and momentum transport, which are important to reproduce the physical momentum and kinetic energy transport, to achieve mass and momentum conservation, and to satisfy the energy law of the two-phase system. A consistent and conservative scheme is developed, and its properties are carefully analyzed and validated. In order to honor the maximum principle of the conservative Allen-Cahn model, we proposed a boundedness mapping algorithm, which preserves the properties of consistency and conservation of the scheme. The applications of the consistent formulation and the proposed scheme to realistic two-phase flows show that they are accurate, robust and effective for complicated two-phase problems. The applicability of the consistent formulation and consistency analysis to multiphase flows and to the improved Cahn-Hilliard model is discussed. (C) 2020 Elsevier Inc. All rights reserved.
引用
收藏
页数:34
相关论文
共 80 条
[31]   An adaptive variational procedure for the conservative and positivity preserving Allen-Cahn phase-field model [J].
Joshi, Vaibhav ;
Jaiman, Rajeev K. .
JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 366 :478-504
[32]   A positivity preserving and conservative variational scheme for phase-field modeling of two-phase flows [J].
Joshi, Vaibhav ;
Jaiman, Rajeev K. .
JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 360 :137-166
[33]   A new conservative vector-valued Allen-Cahn equation and its fast numerical method [J].
Kim, Junseok ;
Lee, Hyun Geun .
COMPUTER PHYSICS COMMUNICATIONS, 2017, 221 :102-108
[34]   A conservative Allen-Cahn equation with a space-time dependent Lagrange multiplier [J].
Kim, Junseok ;
Lee, Seunggyu ;
Choi, Yongho .
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 2014, 84 :11-17
[35]   Phase-Field Models for Multi-Component Fluid Flows [J].
Kim, Junseok .
COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2012, 12 (03) :613-661
[36]   On the computation of viscous terms for incompressible two-phase flows with Level Set/Ghost Fluid Method [J].
Lalanne, Benjamin ;
Villegas, Lucia Rueda ;
Tanguy, Sebastien ;
Risso, Frederic .
JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 301 :289-307
[37]  
Leal LG., 2007, Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes
[38]   Comparison study of the conservative Allen-Cahn and the Cahn-Hilliard equations [J].
Lee, Dongsun ;
Kim, Junseok .
MATHEMATICS AND COMPUTERS IN SIMULATION, 2016, 119 :35-56
[39]   High-order and mass conservative methods for the conservative Allen-Cahn equation [J].
Lee, Hyun Geun .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2016, 72 (03) :620-631
[40]   A phase-field fluid modeling and computation with interfacial profile correction term [J].
Li, Yibao ;
Choi, Jung-Il ;
Kim, Junseok .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2016, 30 (1-3) :84-100