Numerical study of the stability of double fingers with the phase-field model

2004 ◽  
Vol 70 (1) ◽  
Author(s):  
Seiji Tokunaga ◽  
Hidetsugu Sakaguchi
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Numerical Study ◽  
Phase Field Model ◽  
The Stability

Phase-field model: Boundary layer, velocity of propagation, and the stability spectrum

1992 ◽  
Vol 46 (24) ◽  
pp. 16045-16057 ◽  
Author(s):  
Raz Kupferman ◽  
Ofer Shochet ◽  
Eshel Ben-Jacob ◽  
Zeev Schuss
Keyword(s):  
Boundary Layer ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Stability Spectrum ◽  
Layer Velocity ◽  
Velocity Of Propagation ◽  
The Stability

scholarly journals A Numerical Study on Stratified Shear Layers With Relevance to Oil-Boom Failure

2014 ◽  
Author(s):  
David Kristiansen ◽  
Odd M. Faltinsen
Keyword(s):  
Numerical Model ◽  
Phase Field ◽  
Field Model ◽  
Numerical Study ◽  
Phase Field Model ◽  
Processing Unit ◽  
Stable Model ◽  
Interface Instability ◽  
Two Phase ◽  
Oil Boom

Interface dynamics of two-phase flow, with relevance for leakage of oil retained by mechanical oil barriers, is studied by means of a 2D lattice-Boltzmann method combined with a phase-field model for interface capturing. A Multi-Relaxation-Time (MRT) model of the collision process is used to obtain a numerically stable model at high Reynolds-number flow. In the phase-field model, the interface is given a finite but small thickness where the fluid properties vary continuosly across a thin interface layer. Surface tension is modelled as a volume force in the transition layer. The numerical model is implemented for simulations with the graphic processing unit (GPU) of a desktop PC. Verification tests of the model are presented. The model is then applied to simulate gravity currents (GC) obtained from a lock-exchange configuration, using fluid parameters relevant for those of oil and water. Interface instability phenomena are observed, and obtained numerical results are in good agreement with theory. This work demonstrates that the numerical model presented can be used as a numerical tool for studies of stratified shear flows with relevance to oil-boom failure.

Numerical study of a morphology diagram in the large undercooling limit using a phase-field model

1994 ◽  
Vol 50 (2) ◽  
pp. 1005-1008 ◽  
Author(s):  
Raz Kupferman ◽  
Ofer Shochet ◽  
Eshel Ben-Jacob
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Numerical Study ◽  
Phase Field Model ◽  
Large Undercooling

scholarly journals Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method

2017 ◽  
Vol 27 (11) ◽  
pp. 1993-2030 ◽  
Author(s):  
Xiaofeng Yang ◽  
Jia Zhao ◽  
Qi Wang ◽  
Jie Shen
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Approximation Schemes ◽  
Numerical Schemes ◽  
Time Step ◽  
Invariant Energy Quadratization ◽  
The Stability ◽  
2D And 3D ◽  
Well Posed

How to develop efficient numerical schemes while preserving energy stability at the discrete level is challenging for the three-component Cahn–Hilliard phase-field model. In this paper, we develop a set of first- and second-order temporal approximation schemes based on a novel “Invariant Energy Quadratization” approach, where all nonlinear terms are treated semi-explicitly. Consequently, the resulting numerical schemes lead to well-posed linear systems with a linear symmetric, positive definite at each time step. We prove that the developed schemes are unconditionally energy stable and present various 2D and 3D numerical simulations to demonstrate the stability and the accuracy of the schemes.

scholarly journals A Numerical Study on Stratified Shear Layers With Relevance to Oil-Boom Failure

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
David Kristiansen ◽  
Odd M. Faltinsen
Keyword(s):  
Numerical Model ◽  
Phase Field ◽  
Field Model ◽  
Numerical Study ◽  
Phase Field Model ◽  
Processing Unit ◽  
Stable Model ◽  
Interface Instability ◽  
Two Phase ◽  
Oil Boom

Interface dynamics of two-phase flow, with relevance for leakage of oil retained by mechanical oil barriers, is studied by means of a two-dimensional (2D) lattice-Boltzmann method (LBM) combined with a phase-field model for interface capturing. A multirelaxation-time (MRT) model of the collision process is used to obtain a numerically stable model at high Reynolds number flow. In the phase-field model, the interface is given a finite but small thickness, where the fluid properties vary continuously across a thin interface layer. Surface tension is modeled as a volume force in the transition layer. The numerical model is implemented for simulations with the graphic processing unit (GPU) of a desktop personal computer. Verification tests of the model are presented. The model is then applied to simulate gravity currents (GCs) obtained from a lock-exchange configuration, using fluid parameters relevant for those of oil and water. Interface instability phenomena are observed, and obtained numerical results are in good agreement with theory. This work demonstrates that the numerical model presented can be used as a numerical tool for studies of stratified shear flows with relevance to oil-boom failure.

Domain coarsening via heat diffusion: A numerical study with the phase field model

1996 ◽  
Vol 36 (6) ◽  
pp. 431-436 ◽  
Author(s):  
M Conti ◽  
F Marinozzi ◽  
U. Marini Bettolo Marconi
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Numerical Study ◽  
Phase Field Model ◽  
Heat Diffusion ◽  
Domain Coarsening

scholarly journals Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. II. Numerical study

1999 ◽  
Vol 60 (2) ◽  
pp. 1734-1740 ◽  
Author(s):  
R. Folch ◽  
J. Casademunt ◽  
A. Hernández-Machado ◽  
L. Ramírez-Piscina
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Numerical Study ◽  
Phase Field Model ◽  
Viscosity Contrast

scholarly journals A unified phase-field model of fracture in viscoelastic materials

2021 ◽  
Author(s):  
Franz Dammaß ◽  
Marreddy Ambati ◽  
Markus Kästner
Keyword(s):  
Free Energy ◽  
Phase Field ◽  
Field Model ◽  
Numerical Study ◽  
Phase Field Model ◽  
Energy Functional ◽  
Internal Variables ◽  
Model Parameters ◽  
Rate Dependency ◽  
Viscoelastic Materials

AbstractThe phase-field approach has proven to be a powerful tool for the prediction of crack phenomena. When it is applied to inelastic materials, it is crucial to adequately account for the coupling between dissipative mechanisms present in the bulk and fracture. In this contribution, we propose a unified phase-field model for fracture of viscoelastic materials. The formulation is characterized by the pseudo-energy functional which consists of free energy and dissipation due to fracture. The free energy includes a contribution which is related to viscous dissipation that plays an essential role in coupling the phase-field and the viscous internal variables. The governing equations for the phase-field and the viscous internal variables are deduced in a consistent thermodynamic manner from the pseudo-energy functional. The resulting model establishes a two-way coupling between crack phase-field and relaxation mechanisms, i.e. viscous internal variables explicitly enter the evolution of phase-field and vice versa. Depending on the specific choice of the model parameters, it has flexibility in capturing the possible coupled responses, and the approaches of recently published formulations are obtained as limiting cases. By means of a numerical study of monotonically increasing load, creep and relaxation phenomena, rate-dependency of failure in viscoelastic materials is analysed and modelling assumptions of the present formulation are discussed.

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