Finite Element Method for Stokes Equations under Leak Boundary Condition of Friction Type

2013 ◽  
Vol 51 (4) ◽  
pp. 2448-2469 ◽  
Author(s):  
Takahito Kashiwabara
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Stokes Equations ◽  
Element Method

scholarly journals Finite element method for a stationary Stokes hemivariational inequality with slip boundary condition

2019 ◽  
Vol 40 (4) ◽  
pp. 2696-2716
Author(s):  
Changjie Fang ◽  
Kenneth Czuprynski ◽  
Weimin Han ◽  
Xiaoliang Cheng ◽  
Xiaoxia Dai
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Directional Derivative ◽  
Slip Boundary Condition ◽  
Hemivariational Inequality ◽  
Slip Boundary ◽  
Element Method

Abstract This paper is devoted to the study of a hemivariational inequality problem for the stationary Stokes equations with a nonlinear slip boundary condition. The hemivariational inequality is formulated with the use of the generalized directional derivative and generalized gradient in the sense of Clarke. We provide an existence and uniqueness result for the hemivariational inequality. Then we apply the finite element method to solve the hemivariational inequality. The incompressibility constraint is treated through a mixed formulation. Error estimates are derived for numerical solutions. Numerical simulation results are reported to illustrate the theoretically predicted convergence orders.

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.

scholarly journals Modeling Free Surface Flows Using Stabilized Finite Element Method

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Deepak Garg ◽  
Antonella Longo ◽  
Paolo Papale
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Computer Code ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Element Method

This work aims to develop a numerical wave tank for viscous and inviscid flows. The Navier-Stokes equations are solved by time-discontinuous stabilized space-time finite element method. The numerical scheme tracks the free surface location using fluid velocity. A segregated algorithm is proposed to iteratively couple the fluid flow and mesh deformation problems. The numerical scheme and the developed computer code are validated over three free surface problems: solitary wave propagation, the collision between two counter moving waves, and wave damping in a viscous fluid. The benchmark tests demonstrate that the numerical approach is effective and an attractive tool for simulating viscous and inviscid free surface flows.

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