共查询到20条相似文献,搜索用时 31 毫秒
1.
A Phase-Field Model Coupled with Lattice Kinetics Solver for Modeling Crystal Growth in Furnaces
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Guang Lin Jie Bao Zhijie Xu Alexandre M. Tartakovsky & Charles H. Henager Jr. 《Communications In Computational Physics》2014,15(1):76-92
In this study, we present a new numerical model for crystal growth in a
vertical solidification system. This model takes into account the buoyancy induced
convective flow and its effect on the crystal growth process. The evolution of the crystal growth interface is simulated using the phase-field method. A semi-implicit lattice
kinetics solver based on the Boltzmann equation is employed to model the unsteady
incompressible flow. This model is used to investigate the effect of furnace operational
conditions on crystal growth interface profiles and growth velocities. For a simple
case of macroscopic radial growth, the phase-field model is validated against an analytical solution. The numerical simulations reveal that for a certain set of temperature
boundary conditions, the heat transport in the melt near the phase interface is diffusion
dominant and advection is suppressed. 相似文献
2.
Mathematical Modelling and Numerical Simulation of Dendrite Growth Using Phase-Field Method with a Magnetic Field Effect
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In this paper, we present a new model developed in order to analyze phenomena which arise in the solidification of binary mixtures using phase-field method,
which incorporates the convection effects and the action of magnetic field. The model
consists of flow, concentration, phase field and energy systems which are nonlinear
evolutive and coupled systems. It represents the non-isothermal anisotropic solidification process of a binary mixture together with the motion in a melt with the applied magnetic field. To illustrate our model, numerical simulations of the influence
of magnetic-field on the evolution of dendrites during the solidification of the binary
mixture of Nickel-Copper (Ni-Cu) are developed. The results demonstrate that the
dendritic growth under the action of magnetic-field can be simulated by using our
model. 相似文献
3.
Phase-Field-Based Axisymmetric Lattice Boltzmann Method for Two-Phase Electro-Hydrodynamic Flows
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In this work, a novel and simple phase-field-based lattice Boltzmann (LB)
method is proposed for the axisymmetric two-phase electro-hydrodynamic flows. The
present LB method is composed of three LB models, which are used to solve the axisymmetric Allen-Cahn equation for the phase field, the axisymmetric Poisson equation for the electric potential, and the axisymmetric Navier-Stokes equations for the
flow field. Compared with the previous LB models for the axisymmetric Poisson
equation, which can be viewed as the solvers to the convection-diffusion equation,
the present model is a genuine solver to the axisymmetric Poisson equation. To test
the capacity of the LB method, the deformation of a single leaky or perfect dielectric
drop under a uniform electric field is considered, and the effects of electric strength,
conductivity ratio, and permittivity ratio are investigated in detail. It is found that
the present numerical results are in good agreement with some available theoretical,
numerical and/or experimental data. 相似文献
4.
An r-Adaptive Finite Element Method for the Solution of the Two-Dimensional Phase-Field Equations
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G. Beckett J. A. Mackenzie & M. L. Robertson 《Communications In Computational Physics》2006,1(5):805-826
An adaptive moving mesh method is developed for the numerical solution
of two-dimensional phase change problems modelled by the phase-field equations. The
numerical algorithm is relatively simple and is shown to be more efficient than fixed grid
methods. The phase-field equations are discretized by a Galerkin finite element method.
An adaptivity criterion is used that ensures that the mesh spacing at the phase front
scales with the diffuse interface thickness. 相似文献
5.
Junseok Kim 《Communications In Computational Physics》2012,12(3):613-661
In this paper, we review the recent development of phase-field models and
their numerical methods for multi-component fluid flows with interfacial phenomena. The models consist of a Navier-Stokes system coupled with a multi-component
Cahn-Hilliard system through a phase-field dependent surface tension force, variable
density and viscosity, and the advection term. The classical infinitely thin boundary of
separation between two immiscible fluids is replaced by a transition region of a small
but finite width, across which the composition of the mixture changes continuously. A
constant level set of the phase-field is used to capture the interface between two immiscible fluids. Phase-field methods are capable of computing topological changes such
as splitting and merging, and thus have been applied successfully to multi-component
fluid flows involving large interface deformations. Practical applications are provided
to illustrate the usefulness of using a phase-field method. Computational results of
various experiments show the accuracy and effectiveness of phase-field models. 相似文献
6.
An Iterative Discontinuous Galerkin Method for Solving the Nonlinear Poisson Boltzmann Equation
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Peimeng Yin Yunqing Huang & Hailiang Liu 《Communications In Computational Physics》2014,16(2):491-515
An iterative discontinuous Galerkin (DG) method is proposed to solve the
nonlinear Poisson Boltzmann (PB) equation. We first identify a function space in which
the solution of the nonlinear PB equation is iteratively approximated through a series
of linear PB equations, while an appropriate initial guess and a suitable iterative parameter
are selected so that the solutions of linear PB equations are monotone within
the identified solution space. For the spatial discretization we apply the direct discontinuous
Galerkin method to those linear PB equations. More precisely, we use one
initial guess when the Debye parameter λ=O(1), and a special initial guess for λ≪1
to ensure convergence. The iterative parameter is carefully chosen to guarantee the existence,
uniqueness, and convergence of the iteration. In particular, iteration steps can
be reduced for a variable iterative parameter. Both one and two-dimensional numerical
results are carried out to demonstrate both accuracy and capacity of the iterative
DG method for both cases of λ=O(1) and λ≪1. The (m+1)th order of accuracy for
L2 and mth order of accuracy for H1for Pm elements are numerically obtained. 相似文献
7.
Mengjiao Jiao Yingda Cheng Yong Liu & Mengping Zhang 《Communications In Computational Physics》2020,28(3):927-966
In this paper, we develop central discontinuous Galerkin (CDG) finite element methods for solving the generalized Korteweg-de Vries (KdV) equations in one
dimension. Unlike traditional discontinuous Galerkin (DG) method, the CDG methods evolve two approximate solutions defined on overlapping cells and thus do not
need numerical fluxes on the cell interfaces. Several CDG schemes are constructed, including the dissipative and non-dissipative versions. L2error estimates are established
for the linear and nonlinear equation using several projections for different parameter
choices. Although we can not provide optimal a priori error estimate, numerical examples show that our scheme attains the optimal (k+1)-th order of accuracy when using
piecewise k-th degree polynomials for many cases. 相似文献
8.
Bo Li John Lowengrub reas Rä tz & Axel Voigt 《Communications In Computational Physics》2009,6(3):433-482
Geometrical evolution laws are widely used in continuum modeling of surface
and interface motion in materials science. In this article, we first give a brief review
of various kinds of geometrical evolution laws and their variational derivations,
with an emphasis on strong anisotropy. We then survey some of the finite element
based numerical methods for simulating the motion of interfaces focusing on the field
of thin film growth. We discuss the finite element method applied to front-tracking,
phase-field and level-set methods. We describe various applications of these geometrical
evolution laws to materials science problems, and in particular, the growth and
morphologies of thin crystalline films. 相似文献
9.
An Efficient Immersed Boundary-Lattice Boltzmann Method for the Simulation of Thermal Flow Problems
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Yang Hu Decai Li Shi Shu & Xiaodong Niu 《Communications In Computational Physics》2016,20(5):1210-1257
In this paper, a diffuse-interface immersed boundary method (IBM) is proposed
to treat three different thermal boundary conditions (Dirichlet, Neumann, Robin)
in thermal flow problems. The novel IBM is implemented combining with the lattice
Boltzmann method (LBM). The present algorithm enforces the three types of thermal
boundary conditions at the boundary points. Concretely speaking, the IBM for the
Dirichlet boundary condition is implemented using an iterative method, and its main
feature is to accurately satisfy the given temperature on the boundary. The Neumann
and Robin boundary conditions are implemented in IBM by distributing the jump of
the heat flux on the boundary to surrounding Eulerian points, and the jump is obtained
by applying the jump interface conditions in the normal and tangential directions. A
simple analysis of the computational accuracy of IBM is developed. The analysis indicates
that the Taylor-Green vortices problem which was used in many previous studies
is not an appropriate accuracy test example. The capacity of the present thermal immersed
boundary method is validated using four numerical experiments: (1) Natural
convection in a cavity with a circular cylinder in the center; (2) Flows over a heated
cylinder; (3) Natural convection in a concentric horizontal cylindrical annulus; (4) Sedimentation
of a single isothermal cold particle in a vertical channel. The numerical
results show good agreements with the data in the previous literatures. 相似文献
10.
An Interface-Capturing Regularization Method for Solving the Equations for Two-Fluid Mixtures
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Jian Du Robert D. Guy Aaron L. Fogelson Grady B. Wright & James P. Keener 《Communications In Computational Physics》2013,14(5):1322-1346
Many problems in biology involve gels which are mixtures composed of
a polymer network permeated by a fluid solvent (water). The two-fluid model is a
widely used approach to described gel mechanics, in which both network and solvent
coexist at each point of space and their relative abundance is described by their volume
fractions. Each phase is modeled as a continuum with its own velocity and constitutive law. In some biological applications, free boundaries separate regions of gel and
regions of pure solvent, resulting in a degenerate network momentum equation where
the network volume fraction vanishes. To overcome this difficulty, we develop a regularization method to solve the two-phase gel equations when the volume fraction of
one phase goes to zero in part of the computational domain. A small and constant
network volume fraction is temporarily added throughout the domain in setting up
the discrete linear equations and the same set of equation is solved everywhere. These
equations are very poorly conditioned for small values of the regularization parameter, but the multigrid-preconditioned GMRES method we use to solve them is efficient
and produces an accurate solution of these equations for the full range of relevant regularization parameter values. 相似文献
11.
We develop a continuum hydrodynamic model for two-phase immiscible
flows that involve electroosmotic effect in an electrolyte and moving contact line at
solid surfaces. The model is derived through a variational approach based on the Onsager principle of minimum energy dissipation. This approach was first presented in
the derivation of a continuum hydrodynamic model for moving contact line in neutral two-phase immiscible flows (Qian, Wang, and Sheng, J. Fluid Mech. 564, 333–360
(2006)). Physically, the electroosmotic effect can be formulated by the Onsager principle as well in the linear response regime. Therefore, the same variational approach
is applied here to the derivation of the continuum hydrodynamic model for charged
two-phase immiscible flows where one fluid component is an electrolyte exhibiting
electroosmotic effect on a charged surface. A phase field is employed to model the
diffuse interface between two immiscible fluid components, one being the electrolyte
and the other a nonconductive fluid, both allowed to slip at solid surfaces. Our model
consists of the incompressible Navier-Stokes equation for momentum transport, the
Nernst-Planck equation for ion transport, the Cahn-Hilliard phase-field equation for
interface motion, and the Poisson equation for electric potential, along with all the
necessary boundary conditions. In particular, all the dynamic boundary conditions at
solid surfaces, including the generalized Navier boundary condition for slip, are derived together with the equations of motion in the bulk region. Numerical examples
in two-dimensional space, which involve overlapped electric double layer fields, have
been presented to demonstrate the validity and applicability of the model, and a few
salient features of the two-phase immiscible electroosmotic flows at solid surface. The
wall slip in the vicinity of moving contact line and the Smoluchowski slip in the electric
double layer are both investigated. 相似文献
12.
Mesh Sensitivity for Numerical Solutions of Phase-Field Equations Using r-Adaptive Finite Element Methods
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There have been several recent papers on developing moving mesh methods
for solving phase-field equations. However, it is observed that some of these moving
mesh solutions are essentially different from the solutions on very fine fixed meshes.
One of the purposes of this paper is to understand the reason for the differences. We
carried out numerical sensitivity studies systematically in this paper and it can be concluded that for the phase-field equations, the numerical solutions are very sensitive to
the starting mesh and the monitor function. As a separate issue, an efficient alternating Crank-Nicolson time discretization scheme is developed for solving the nonlinear
system resulting from a finite element approximation to the phase-field equations. 相似文献
13.
Ming-Jyh Chern Dedy Zulhidayat Noor Ching-Biao Liao & Tzyy-Leng Horng 《Communications In Computational Physics》2015,18(4):1072-1094
A direct-forcing immersed boundary method (DFIB) with both virtual force
and heat source is developed here to solve Navier-Stokes and the associated energy
transport equations to study some thermal flow problems caused by a moving rigid
solid object within. The key point of this novel numerical method is that the solid object,
stationary or moving, is first treated as fluid governed by Navier-Stokes equations
for velocity and pressure, and by energy transport equation for temperature in every
time step. An additional virtual force term is then introduced on the right hand side
of momentum equations in the solid object region to make it act exactly as if it were
a solid rigid body immersed in the fluid. Likewise, an additional virtual heat source
term is applied to the right hand side of energy equation at the solid object region
to maintain the solid object at the prescribed temperature all the time. The current
method was validated by some benchmark forced and natural convection problems
such as a uniform flow past a heated circular cylinder, and a heated circular cylinder
inside a square enclosure. We further demonstrated this method by studying a mixed
convection problem involving a heated circular cylinder moving inside a square enclosure.
Our current method avoids the otherwise requested dynamic grid generation in
traditional method and shows great efficiency in the computation of thermal and flow
fields caused by fluid-structure interaction. 相似文献
14.
Explicit Computation of Robin Parameters in Optimized Schwarz Waveform Relaxation Methods for Schrödinger Equations Based on Pseudodifferential Operators
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Xavier Antoine & Emmanuel Lorin 《Communications In Computational Physics》2020,27(4):1032-1052
The Optimized Schwarz Waveform Relaxation algorithm, a domain decomposition method based on Robin transmission condition, is becoming a popular computational method for solving evolution partial differential equations in parallel. Along
with well-posedness, it offers a good balance between convergence rate, efficient computational complexity and simplicity of the implementation. The fundamental question is the selection of the Robin parameter to optimize the convergence of the algorithm. In this paper, we propose an approach to explicitly estimate the Robin parameter which is based on the approximation of the transmission operators at the subdomain interfaces, for the linear/nonlinear Schrödinger equation. Some illustrating
numerical experiments are proposed for the one- and two-dimensional problems. 相似文献
15.
An Interface-Capturing Method for Resolving Compressible Two-Fluid Flows with General Equation of State
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T. S. Lee J. G. Zheng & S. H. Winoto 《Communications In Computational Physics》2009,6(5):1137-1162
In this study, a stable and robust interface-capturing method is developed
to resolve inviscid, compressible two-fluid flows with general equation of state (EOS).
The governing equations consist of mass conservation equation for each fluid, momentum
and energy equations for mixture and an advection equation for volume fraction
of one fluid component. Assumption of pressure equilibrium across an interface is
used to close the model system. MUSCL-Hancock scheme is extended to construct
input states for Riemann problems, whose solutions are calculated using generalized
HLLC approximate Riemann solver. Adaptive mesh refinement (AMR) capability is
built into hydrodynamic code. The resulting method has some advantages. First, it is
very stable and robust, as the advection equation is handled properly. Second, general
equation of state can model more materials than simple EOSs such as ideal and
stiffened gas EOSs for example. In addition, AMR enables us to properly resolve flow
features at disparate scales. Finally, this method is quite simple, time-efficient and easy
to implement. 相似文献
16.
Alina Chertock & Yongle Liu 《Communications In Computational Physics》2020,27(2):480-502
We study the two-component Camassa-Holm (2CH) equations as a model
for the long time water wave propagation. Compared with the classical Saint-Venant
system, it has the advantage of preserving the waves amplitude and shape for a long
time. We present two different numerical methods—finite volume (FV) and hybrid
finite-volume-particle (FVP) ones. In the FV setup, we rewrite the 2CH equations in a
conservative form and numerically solve it by the central-upwind scheme, while in the
FVP method, we apply the central-upwind scheme to the density equation only while
solving the momentum and velocity equations by a deterministic particle method. Numerical examples are shown to verify the accuracy of both FV and FVP methods. The
obtained results demonstrate that the FVP method outperforms the FV method and
achieves a superior resolution thanks to a low-diffusive nature of a particle approximation. 相似文献
17.
Three-Dimensional Lattice Boltzmann Flux Solver and Its Applications to Incompressible Isothermal and Thermal Flows
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Yan Wang Chang Shu Chiang Juay Teo Jie Wu & Liming Yang 《Communications In Computational Physics》2015,18(3):593-620
A three-dimensional (3D) lattice Boltzmann flux solver (LBFS) is presented
in this paper for the simulation of both isothermal and thermal flows. The present
solver combines the advantages of conventional Navier-Stokes (N-S) solvers and lattice
Boltzmann equation (LBE) solvers. It applies the finite volume method (FVM) to
solve the N-S equations. Different from the conventional N-S solvers, its viscous and
inviscid fluxes at the cell interface are evaluated simultaneously by local reconstruction
of LBE solution. As compared to the conventional LBE solvers, which apply the
lattice Boltzmann method (LBM) globally in the whole computational domain, it only
applies LBM locally at each cell interface, and flow variables at cell centers are given
from the solution of N-S equations. Since LBM is only applied locally in the 3D LBFS,
the drawbacks of the conventional LBM, such as limitation to uniform mesh, tie-up
of mesh spacing and time step, tedious implementation of boundary conditions, are
completely removed. The accuracy, efficiency and stability of the proposed solver are
examined in detail by simulating plane Poiseuille flow, lid-driven cavity flow and natural
convection. Numerical results show that the LBFS has a second order of accuracy
in space. The efficiency of the LBFS is lower than LBM on the same grids. However,
the LBFS needs very less non-uniform grids to get grid-independence results and its
efficiency can be greatly improved and even much higher than LBM. In addition, the
LBFS is more stable and robust. 相似文献
18.
A Gas-Kinetic Unified Algorithm for Non-Equilibrium Polyatomic Gas Flows Covering Various Flow Regimes
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Wen-Qiang Hu Zhi-Hui Li Ao-Ping Peng & Xin-Yu Jiang 《Communications In Computational Physics》2021,30(1):144-189
In this paper, a gas-kinetic unified algorithm (GKUA) is developed to investigate the non-equilibrium polyatomic gas flows covering various regimes. Based
on the ellipsoidal statistical model with rotational energy excitation, the computable
modelling equation is presented by unifying expressions on the molecular collision relaxing parameter and the local equilibrium distribution function. By constructing the
corresponding conservative discrete velocity ordinate method for this model, the conservative properties during the collision procedure are preserved at the discrete level
by the numerical method, decreasing the computational storage and time. Explicit
and implicit lower-upper symmetric Gauss-Seidel schemes are constructed to solve
the discrete hyperbolic conservation equations directly. Applying the new GKUA,
some numerical examples are simulated, including the Sod Riemann problem, homogeneous flow rotational relaxation, normal shock structure, Fourier and Couette flows,
supersonic flows past a circular cylinder, and hypersonic flow around a plate placed
normally. The results obtained by the analytic, experimental, direct simulation Monte
Carlo method, and other measurements in references are compared with the GKUA
results, which are in good agreement, demonstrating the high accuracy of the present
algorithm. Especially, some polyatomic gas non-equilibrium phenomena are observed
and analysed by solving the Boltzmann-type velocity distribution function equation
covering various flow regimes. 相似文献
19.
Solving Allen-Cahn and Cahn-Hilliard Equations Using the Adaptive Physics Informed Neural Networks
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Colby L. Wight & Jia Zhao 《Communications In Computational Physics》2021,29(3):930-954
Phase field models, in particular, the Allen-Cahn type and Cahn-Hilliard
type equations, have been widely used to investigate interfacial dynamic problems.
Designing accurate, efficient, and stable numerical algorithms for solving the phase
field models has been an active field for decades. In this paper, we focus on using
the deep neural network to design an automatic numerical solver for the Allen-Cahn
and Cahn-Hilliard equations by proposing an improved physics informed neural network (PINN). Though the PINN has been embraced to investigate many differential
equation problems, we find a direct application of the PINN in solving phase-field
equations won't provide accurate solutions in many cases. Thus, we propose various
techniques that add to the approximation power of the PINN. As a major contribution of this paper, we propose to embrace the adaptive idea in both space and time
and introduce various sampling strategies, such that we are able to improve the efficiency and accuracy of the PINN on solving phase field equations. In addition, the
improved PINN has no restriction on the explicit form of the PDEs, making it applicable to a wider class of PDE problems, and shedding light on numerical approximations
of other PDEs in general. 相似文献
20.
This paper presents a fourth-order Cartesian grid based boundary integral
method (BIM) for heterogeneous interface problems in two and three dimensional
space, where the problem interfaces are irregular and can be explicitly given by parametric curves or implicitly defined by level set functions. The method reformulates the
governing equation with interface conditions into boundary integral equations (BIEs)
and reinterprets the involved integrals as solutions to some simple interface problems
in an extended regular region. Solution of the simple equivalent interface problems for
integral evaluation relies on a fourth-order finite difference method with an FFT-based
fast elliptic solver. The structure of the coefficient matrix is preserved even with the
existence of the interface. In the whole calculation process, analytical expressions of
Green’s functions are never determined, formulated or computed. This is the novelty
of the proposed kernel-free boundary integral (KFBI) method. Numerical experiments
in both two and three dimensions are shown to demonstrate the algorithm efficiency
and solution accuracy even for problems with a large diffusion coefficient ratio. 相似文献