Phase-Field Modeling of Droplet Movement Using the Discontinuous Finite Element Method

2007 ◽  
Author(s):  
H. Chen ◽  
Y. Shu ◽  
B. Q. Li ◽  
P. Mohanty ◽  
S. Sengupta
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Numerical Results ◽  
Navier Stokes ◽  
Discontinuous Finite Element ◽  
Droplet Movement ◽  
Cahn Hilliard Equation ◽  
Discontinuous Finite Element Method ◽  
Element Method

In this paper, a discontinuous finite element method is presented for the fourth-order nonlinear Cahn-Hilliard equation that models multiphase flows together with the Navier-Stokes equations. A flux scheme suitable for the method is proposed and analyzed together with numerical results. The model is applied to simulate the droplet movement and numerical results are presented.

The Discontinuous Finite Element Method for Polycrystalline Grain Growth With Convection

2005 ◽  
Author(s):  
X. Ai ◽  
Y. Shu ◽  
Ben Q. Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Grain Growth ◽  
Stokes Equations ◽  
Numerical Study ◽  
Phase Field Model ◽  
Navier Stokes ◽  
Convection Flow ◽  
Discontinuous Finite Element ◽  
Element Method

In this paper, a numerical study of the convection effect on polycrystalline grain growth is performed. The coupled two-dimensional polycrystalline phase field model, energy equation and Navier-Stokes equations are solved, which is based on the discontinuous Galerkin finite element method. The numerical algorithm is validated, and the effect of the external convection flow is examined for growth of grains with different orientation.

A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle

2017 ◽  
Vol 32 (4) ◽  
Author(s):  
Alexander Danilov ◽  
Alexander Lozovskiy ◽  
Maxim Olshanskii ◽  
Yuri Vassilevski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Left Ventricle ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Computed Tomography Images ◽  
Time Dependent Domain ◽  
Element Method

AbstractThe paper introduces a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method is based on a quasi-Lagrangian formulation of the problem and handling the geometry in a time-explicit way. We prove that numerical solution satisfies a discrete analogue of the fundamental energy estimate. This stability estimate does not require a CFL time-step restriction. The method is further applied to simulation of a flow in a model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

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