A novel fully decoupled scheme with second‐order time accuracy and unconditional energy stability for the Navier‐Stokes equations coupled with mass‐conserved Allen‐Cahn phase‐field model of two‐phase incompressible flow

2020 ◽  
Author(s):  
Xiaofeng Yang
Keyword(s):  
Incompressible Flow ◽  
Phase Field ◽  
Field Model ◽  
Stokes Equations ◽  
Phase Field Model ◽  
Energy Stability ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Time Accuracy

ANALYSIS OF A PHASE-FIELD MODEL FOR TWO-PHASE COMPRESSIBLE FLUIDS

2010 ◽  
Vol 20 (07) ◽  
pp. 1129-1160 ◽  
Author(s):  
EDUARD FEIREISL ◽  
HANA PETZELTOVÁ ◽  
ELISABETTA ROCCA ◽  
GIULIO SCHIMPERNA
Keyword(s):  
Field Model ◽  
Stokes Equations ◽  
Phase Field Model ◽  
Immiscible Fluids ◽  
Compressible Fluids ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Cahn Equation ◽  
System Coupling

A model describing the evolution of a binary mixture of compressible, viscous, and macroscopically immiscible fluids is investigated. The existence of global-in-time weak solutions for the resulting system coupling the compressible Navier–Stokes equations governing the motion of the mixture with the Allen–Cahn equation for the order parameter is proved without any restriction on the size of initial data.

NUMERICAL SIMULATION OF ISOTHERMAL AND THERMAL TWO-PHASE FLOWS USING PHASE-FIELD MODELING

2007 ◽  
Vol 18 (04) ◽  
pp. 536-545 ◽  
Author(s):  
NAOKI TAKADA ◽  
AKIO TOMIYAMA
Keyword(s):  
Phase Field ◽  
Stokes Equations ◽  
Density Ratio ◽  
Navier Stokes ◽  
Phase Field Modeling ◽  
Two Phase Flows ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Field Modeling ◽  
High Density Ratio

For interface-tracking simulation of two-phase flows in various micro-fluidics devices, we examined the applicability of two versions of computational fluid dynamics method, NS-PFM, combining Navier-Stokes equations with phase-field modeling for interface based on the van der Waals-Cahn-Hilliard free-energy theory. Through the numerical simulations, the following major findings were obtained: (1) The first version of NS-PFM gives good predictions of interfacial shapes and motions in an incompressible, isothermal two-phase fluid with high density ratio on solid surface with heterogeneous wettability. (2) The second version successfully captures liquid-vapor motions with heat and mass transfer across interfaces in phase change of a non-ideal fluid around the critical point.

scholarly journals Hierarchy of consistent n-component Cahn–Hilliard systems

2014 ◽  
Vol 24 (14) ◽  
pp. 2885-2928 ◽  
Author(s):  
Franck Boyer ◽  
Sebastian Minjeaud
Keyword(s):  
Phase Field ◽  
Multiphase Flows ◽  
Field Model ◽  
Phase Field Model ◽  
Numerical Results ◽  
Phase Model ◽  
Navier Stokes ◽  
Two Phase ◽  
Two Phases ◽  
Well Posed

In this paper, we propose a new generalization of the well-known Cahn–Hilliard two-phase model for the modeling of n-phase mixtures. The model is derived using the consistency principle: we require that our n-phase model exactly coincides with the classical two-phase model when only two phases are present in the system. We give conditions for the model to be well-posed. We also present numerical results (including simulations obtained when coupling the Cahn–Hilliard system with the Navier–Stokes so as to obtain a phase-field model for multiphase flows) to illustrate the capability of such modeling.

An Artificial Compressibility Method for 3D Phase-Field Model and its Application to Two-Phase Flows

2017 ◽  
Vol 14 (05) ◽  
pp. 1750059 ◽  
Author(s):  
Abdullah Shah ◽  
Sadia Saeed ◽  
L. Yuan
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
System Of Equations ◽  
Time Step ◽  
Two Phase ◽  
Spatial Direction ◽  
Artificial Compressibility ◽  
Flow Problems ◽  
Time Accuracy

In this work, a numerical scheme based on artificial compressibility formulation of a phase-field model is developed for simulating two-phase incompressible flow problems. The coupled nonlinear systems composed of the incompressible Navier–Stokes equations and volume preserving Allen–Cahn-type phase-field equation are recast into conservative form with source terms, which are suited to implement high-resolution schemes originally developed for hyperbolic conservation laws. The Boussinesq approximation is used to account for the buoyancy effect in flow with small density difference. The fifth-order weighted essentially nonoscillatory (WENO) scheme is used for discretizing the convective terms while dual-time stepping (DTS) technique is used for obtaining time accuracy at each physical time step. Beam–Warming approximate factorization scheme is utilized to obtain block tridiagonal system of equations in each spatial direction. The alternating direction implicit (ADI) algorithm is used to solve the resulting system of equations. The performance of the method is demonstrated by its application to some 2D and 3D benchmark viscous two-phase flow problems.

scholarly journals A thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects

2015 ◽  
Vol 766 ◽  
pp. 226-271 ◽  
Author(s):  
Z. Guo ◽  
P. Lin
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Stokes Equations ◽  
Phase Field Model ◽  
Energy Balance Equation ◽  
Thermodynamic Consistency ◽  
Sharp Interface ◽  
Additional Stress ◽  
Two Phase ◽  
Interfacial Conditions

AbstractIn this paper, we develop a phase-field model for binary incompressible (quasi-incompressible) fluid with thermocapillary effects, which allows for the different properties (densities, viscosities and heat conductivities) of each component while maintaining thermodynamic consistency. The governing equations of the model including the Navier–Stokes equations with additional stress term, Cahn–Hilliard equations and energy balance equation are derived within a thermodynamic framework based on entropy generation, which guarantees thermodynamic consistency. A sharp-interface limit analysis is carried out to show that the interfacial conditions of the classical sharp-interface models can be recovered from our phase-field model. Moreover, some numerical examples including thermocapillary convections in a two-layer fluid system and thermocapillary migration of a drop are computed using a continuous finite element method. The results are compared with the corresponding analytical solutions and the existing numerical results as validations for our model.

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