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Hilliard Equation (hilliard + equation)

Distribution by Scientific Domains
Mathematics and Statistics83%

Selected Abstracts

3-D viscous Cahn,Hilliard equation with memory

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2009
Monica Conti
Abstract We deal with the memory relaxation of the viscous Cahn,Hilliard equation in 3-D, covering the well-known hyperbolic version of the model. We study the long-term dynamic of the system in dependence of the scaling parameter of the memory kernel , and of the viscosity coefficient ,. In particular we construct a family of exponential attractors, which is robust as both , and , go to zero, provided that , is linearly controlled by ,. Copyright © 2008 John Wiley & Sons, Ltd. [source]

On non-Newtonian incompressible fluids with phase transitions

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2006
Namkwon Kim
Abstract A modified model for a binary fluid is analysed mathematically. The governing equations of the motion consists of a Cahn,Hilliard equation coupled with a system describing a class of non-Newtonian incompressible fluid with p -structure. The existence of weak solutions for the evolution problems is shown for the space dimension d=2 with p, 2 and for d=3 with p, 11/5. The existence of measure-valued solutions is obtained for d=3 in the case 2, p< 11/5. Similar existence results are obtained for the case of nondifferentiable free energy, corresponding to the density constraint |,| , 1. We also give regularity and uniqueness results for the solutions and characterize stable stationary solutions. Copyright © 2006 John Wiley & Sons, Ltd. [source]

A numerical scheme for the solution of viscous Cahn,Hilliard equation

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2008
Shaher Momani
Abstract In this paper, we present a numerical scheme for the solution of viscous Cahn,Hilliard equation. The scheme is based on Adomian's decomposition approach and the solutions are calculated in the form of a convergent series with easily computable components. Some numerical examples are presented. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 [source]

Numerical simulation of drop deformation and breakup in shear flow

HEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 5 2007
Lin Chang-Zhi
Abstract Three-dimensional numerical simulation of the deformation and breakup of an isolated liquid drop suspended in immiscible viscous fluid under shear flow was performed with diffuse interface method. The governing equations of the model were described by Navier, Stokes, Cahn, Hilliard equations. The surface tension was treated as a modified stress. In this paper, a uniform staggered Cartesian grid was used. The transient Navier, Stokes equations were solved by an approximation projection method based on pressure increment formulation, while the Cahn, Hilliard equations were solved by a nonlinear full approximation multigrid method. The numerical results of the drop deformation and breakup were in good agreement with the experimental measurements. Therefore, the present model could be perfectly applied to study the mechanism of drop deformation and breakup. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(5): 286, 294, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20160 [source]