scholarly journals A decoupled, stable, and linear FEM for a phase-field model of variable density two-phase incompressible surface flow

2021 ◽  
Vol 387 ◽  
pp. 114167
Author(s):  
Yerbol Palzhanov ◽  
Alexander Zhiliakov ◽  
Annalisa Quaini ◽  
Maxim Olshanskii
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Variable Density ◽  
Surface Flow ◽  
Incompressible Surface ◽  
Two Phase

scholarly journals Fully-discrete finite element numerical scheme with decoupling structure and energy stability for the Cahn-Hilliard phase-field model of two-phase incompressible flow system with variable density and viscosity

2021 ◽  
Author(s):  
chuanjun chen ◽  
Xiaofeng Yang
Keyword(s):  
Finite Element ◽  
Phase Field ◽  
Numerical Scheme ◽  
Field Model ◽  
Flow System ◽  
Phase Field Model ◽  
Variable Density ◽  
Two Phase ◽  
Fully Discrete ◽  
Discrete Finite Element

We construct a fully-discrete finite element numerical scheme for the Cahn-Hilliard phase-field model of the two-phase incompressible flow system with variable density and viscosity. The scheme is linear, decoupled, and unconditionally energy stable. Its key idea is to combine the penalty method of the Navier-Stokes equations with the Strang operator splitting method, and introduce several nonlical variables and their ordinary differential equations to process coupled nonlinear terms. The scheme is highly efficient and it only needs to solve a series of completely independent linear elliptic equations at each time step, in which the Cahn-Hilliard equation and the pressure Poisson equation only have constant coefficients. We rigorously prove the unconditional energy stability and solvability of the scheme and carry out numerous accuracy/stability examples and various benchmark numerical simulations in 2D and 3D, including the Rayleigh-Taylor instability and rising/coalescence dynamics of bubbles to demonstrate the effectiveness of the scheme, numerically.

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.

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