Efficient numerical scheme for a dendritic solidification phase field model with melt convection

2019 ◽  
Vol 388 ◽  
pp. 41-62 ◽  
Author(s):  
Chuanjun Chen ◽  
Xiaofeng Yang
Keyword(s):  
Phase Field ◽  
Numerical Scheme ◽  
Field Model ◽  
Phase Field Model ◽  
Dendritic Solidification ◽  
Melt Convection

scholarly journals Mesoscopic modeling of spacing and grain selection in columnar dendritic solidification: Envelope versus phase-field model

2017 ◽  
Vol 122 ◽  
pp. 386-399 ◽  
Author(s):  
Alexandre Viardin ◽  
Miha Založnik ◽  
Youssef Souhar ◽  
Markus Apel ◽  
Hervé Combeau
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Dendritic Solidification ◽  
Versus Phase ◽  
Mesoscopic Modeling

Phase-Field Modeling of Dendritic Solidification in Undercooled Droplets Processed by Electromagnetic Levitation

2006 ◽  
Vol 508 ◽  
pp. 431-436 ◽  
Author(s):  
Peter K. Galenko ◽  
Dieter M. Herlach ◽  
G. Phanikumar ◽  
O. Funke
Keyword(s):  
Phase Field ◽  
Dendritic Growth ◽  
Field Model ◽  
Phase Field Model ◽  
Electromagnetic Levitation ◽  
Dendritic Solidification ◽  
Field Modeling ◽  
Theoretical Predictions ◽  
Forced Convective Flow ◽  
Undercooled Melts

The results on modeling dendritic solidification from undercooled melts processed by the electromagnetic levitation technique are discussed. In order to model the details of formation of dendritic patterns we use a phase-field model of dendritic growth in a pure undercooled system with convection of the liquid phase. The predictions of the phase-field model are discussed referring to our latest high accuracy measurements of dendrite growth velocities in nickel samples. Special emphasis is given to the growth of dendrites at small and moderate undercoolings. At small undercoolings, the theoretical predictions deviate systematically from experimental data for solidification of nickel dendrites. It is shown that small amounts of impurities and forced convective flow can lead to an enhancement of the velocity of dendritic solidification at small undercoolings.

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.

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