scholarly journals A fractional-step finite-element method for the Navier–Stokes equations applied to magma-chamber withdrawal

1999 ◽  
Vol 25 (3) ◽  
pp. 263-275 ◽  
Author(s):  
Arnau Folch ◽  
Mariano Vázquez ◽  
Ramon Codina ◽  
Joan Martı́
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Magma Chamber ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Fractional Step ◽  
Navier Stokes Equations ◽  
Element Method

A stabilized fractional-step finite element method for the time-dependent Navier–Stokes equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yueqiang Shang ◽  
Qing Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Convergence Rate ◽  
Stokes Equations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Fractional Step ◽  
Navier Stokes Equations ◽  
Subgrid Model ◽  
Element Method

Abstract We present a fractional-step finite element method based on a subgrid model for simulating the time-dependent incompressible Navier–Stokes equations. The method aims to the simulation of high Reynolds number flows and consists of two steps in which the nonlinearity and incompressibility are split into different steps. The first step of this method can be seen as a linearized Burger’s problem where a subgrid model based on an elliptic projection of the velocity into a lower-order finite element space is employed to stabilize the system, and the second step is a Stokes problem. Under mild regularity assumptions on the continuous solution, we obtain the stability of the numerical method, and derive error bound of the approximate velocity, which shows that first-order convergence rate in time and optimal convergence rate in space can be gotten by the method. Numerical experiments verify the theoretical predictions and demonstrate the promise of the proposed method, which show superiority of the proposed method to the compared method in the literature.

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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