A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier–Stokes Equations

1997 ◽  
Vol 131 (2) ◽  
pp. 267-279 ◽  
Author(s):  
F. Bassi ◽  
S. Rebay
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Stokes Equations ◽  
High Order ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Discontinuous Finite Element ◽  
Discontinuous Finite Element Method ◽  
Element Method

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.

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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