The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
X Tong - One of the best experts on this subject based on the ideXlab platform.
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Phase-field simulations of Dendritic Crystal growth in a forced flow.
Physical review. E Statistical nonlinear and soft matter physics, 2001Co-Authors: X Tong, C Beckermann, A KarmaAbstract:Convective effects on free Dendritic Crystal growth into a supercooled melt in two dimensions are investigated using the phase-field method. The phase-field model incorporates both melt convection and thermal noise. A multigrid method is used to solve the conservation equations for flow. To fully resolve the diffuse interface region and the interactions of Dendritic growth with flow, both the phase-field and flow equations are solved on a highly refined grid where up to 2.1 million control volumes are employed. A multiple time-step algorithm is developed that uses a large time step for the flow-field calculations while reserving a fine time step for the phase-field evolution. The operating state (velocity and shape) of a dendrite tip in a uniform axial flow is found to be in quantitative agreement with the prediction of the Oseen-Ivantsov transport theory if a tip radius based on a parabolic fit is used. Furthermore, using this parabolic tip radius, the ratio of the selection parameters without and with flow is shown to be close to unity, which is in agreement with linearized solvability theory for the ranges of the parameters considered. Dendritic sidebranching in a forced flow is also quantitatively studied. Compared to a dendrite growing at the same supercooling in a diffusive environment, convection is found to increase the amplitude and frequency of the sidebranches. The phase-field results for the scaled sidebranch amplitude and wavelength variations with distance from the tip are compared to linear Wentzel-Kramers-Brillouin theory. It is also shown that the asymmetric sidebranch growth on the upstream and downstream sides of a dendrite arm growing at an angle with respect to the flow can be explained by the differences in the mean shapes of the two sides of the arm.
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Velocity and Shape Selection of Dendritic Crystals in a Forced Flow
Physical Review E, 2000Co-Authors: X Tong, Christoph Beckermann, Alain KarmaAbstract:The phase-field method is used to simulate the two-dimensional growth of a Dendritic Crystal in a forced flow. The selection of the velocity and shape of the dendrite tip is investigated as a function of flow rate, growth direction relative to the flow, as well as anisotropy strength, and the results for the upstream growing tips are compared to existing theoretical predictions.
Xiaofeng Yang - One of the best experts on this subject based on the ideXlab platform.
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Efficient linear, stabilized, second-order time marching schemes for an anisotropic phase field Dendritic Crystal growth model
Computer Methods in Applied Mechanics and Engineering, 2019Co-Authors: Xiaofeng YangAbstract:Abstract We consider numerical approximations for a phase field Dendritic Crystal growth model, which is a highly nonlinear system that couples the anisotropic Allen–Cahn type equation and the heat equation together. We propose two efficient, linear, second-order time marching schemes. The first one is based on the linear stabilization approach where all nonlinear terms are treated explicitly and one only needs to solve two linear and decoupled second-order equations. The second one combines the recently developed Invariant Energy Quadratization approach with the linear stabilization technique. Two linear stabilization terms, which are shown to be crucial to remove the oscillations caused by the anisotropic coefficients numerically, are added to enhance the stability while keeping the required accuracy. We further show the obtained linear system is well-posed and prove its unconditional energy stability rigorously. Various 2D and 3D numerical simulations are implemented to demonstrate the stability and accuracy of the schemes.
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A novel decoupled and stable scheme for an anisotropic phase-field Dendritic Crystal growth model
Applied Mathematics Letters, 2019Co-Authors: Jun Zhang, Chuanjun Chen, Xiaofeng YangAbstract:Abstract We consider numerical approximations for a phase-field Dendritic Crystal growth model, which is a highly nonlinear system that couples the anisotropic Allen–Cahn type equation and the heat equation. By combining the stabilized-Invariant Energy Quadratization method with a novel decoupling technique, the scheme requires solving only a sequence of linear elliptic equations at each time step, making it the first, to the best of the author’s knowledge, totally decoupled, linear, unconditionally energy stable scheme for the model. We further prove the unconditional energy stability rigorously and present various numerical simulations to demonstrate the stability and accuracy.
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numerical approximations for a phase field Dendritic Crystal growth model based on the invariant energy quadratization approach
International Journal for Numerical Methods in Engineering, 2017Co-Authors: Jia Zhao, Qi Wang, Xiaofeng YangAbstract:Summary We present two accurate and efficient numerical schemes for a phase field Dendritic Crystal growth model, which is derived from the variation of a free-energy functional, consisting of a temperature dependent bulk potential and a conformational entropy with a gradient-dependent anisotropic coefficient. We introduce a novel Invariant Energy Quadratization approach to transform the free-energy functional into a quadratic form by introducing new variables to substitute the nonlinear transformations. Based on the reformulated equivalent governing system, we develop a first and a second order semi-discretized scheme in time for the system, in which all nonlinear terms are treated semi-explicitly. The resulting semi-discretized equations consist of a linear elliptic equation system at each time step, where the coefficient matrix operator is positive definite and thus, the semi-discrete system can be solved efficiently. We further prove that the proposed schemes are unconditionally energy stable. Convergence test together with 2D and 3D numerical simulations for Dendritic Crystal growth are presented after the semi-discrete schemes are fully discretized in space using the finite difference method to demonstrate the stability and the accuracy of the proposed schemes. Copyright © 2016 John Wiley & Sons, Ltd.
Alain Karma - One of the best experts on this subject based on the ideXlab platform.
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Velocity and Shape Selection of Dendritic Crystals in a Forced Flow
Physical Review E, 2000Co-Authors: X Tong, Christoph Beckermann, Alain KarmaAbstract:The phase-field method is used to simulate the two-dimensional growth of a Dendritic Crystal in a forced flow. The selection of the velocity and shape of the dendrite tip is investigated as a function of flow rate, growth direction relative to the flow, as well as anisotropy strength, and the results for the upstream growing tips are compared to existing theoretical predictions.
A Karma - One of the best experts on this subject based on the ideXlab platform.
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Phase-field simulations of Dendritic Crystal growth in a forced flow.
Physical review. E Statistical nonlinear and soft matter physics, 2001Co-Authors: X Tong, C Beckermann, A KarmaAbstract:Convective effects on free Dendritic Crystal growth into a supercooled melt in two dimensions are investigated using the phase-field method. The phase-field model incorporates both melt convection and thermal noise. A multigrid method is used to solve the conservation equations for flow. To fully resolve the diffuse interface region and the interactions of Dendritic growth with flow, both the phase-field and flow equations are solved on a highly refined grid where up to 2.1 million control volumes are employed. A multiple time-step algorithm is developed that uses a large time step for the flow-field calculations while reserving a fine time step for the phase-field evolution. The operating state (velocity and shape) of a dendrite tip in a uniform axial flow is found to be in quantitative agreement with the prediction of the Oseen-Ivantsov transport theory if a tip radius based on a parabolic fit is used. Furthermore, using this parabolic tip radius, the ratio of the selection parameters without and with flow is shown to be close to unity, which is in agreement with linearized solvability theory for the ranges of the parameters considered. Dendritic sidebranching in a forced flow is also quantitatively studied. Compared to a dendrite growing at the same supercooling in a diffusive environment, convection is found to increase the amplitude and frequency of the sidebranches. The phase-field results for the scaled sidebranch amplitude and wavelength variations with distance from the tip are compared to linear Wentzel-Kramers-Brillouin theory. It is also shown that the asymmetric sidebranch growth on the upstream and downstream sides of a dendrite arm growing at an angle with respect to the flow can be explained by the differences in the mean shapes of the two sides of the arm.
Jurgenhinrich Fuhrhop - One of the best experts on this subject based on the ideXlab platform.
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Dendritic Crystal growth in n dodecylgluconamide monolayers at the air water interface
Langmuir, 1995Co-Authors: D Vollhardt, Thomas Gutberlet, G Emrich, Jurgenhinrich FuhrhopAbstract:Monolayers of pure enantiomers and the racemic mixture of the amphiphilic N-dodecylgluconamide were investigated at the air-water interface using Brewster angle microscopy and surface pressure measurements. A striking chiral discrimination is demonstrated comparing the pure enantiomeric forms and the racemic mixtures. The monolayer morphology obtained on compression was visualized and studied by Brewster angle microscopy. The enantiomeric N-dodecylgluconamides form regular ramified growth pattern of high stability in a shape characteristic for Dendritic Crystallization, while the racemic mixtures show isotropical solidification. The chiral discrimination effect is supported by differences in the surface pressure isotherms and the constant surface pressure relaxations of the pure enantiomeric forms and the racemic mixtures. The Dendritic Crystallization found experimentally is discussed in respect of the molecular organization at the air-water interface.