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A quasi-Lagrangian finite element method for the Navier–Stokes equations in a time-dependent domain.
- Source :
-
Computer Methods in Applied Mechanics & Engineering . May2018, Vol. 333, p55-73. 19p. - Publication Year :
- 2018
-
Abstract
- The paper develops a finite element method for the Navier–Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and convergence analysis of the fully discrete (finite-difference in time and finite-element in space) method. The analysis does not assume any CFL time-step restriction, it rather needs mild conditions of the form Δ t ≤ C , where C depends only on problem data, and h 2 m u + 2 ≤ c Δ t , m u is polynomial degree of velocity finite element space. Both conditions result from a numerical treatment of practically important non-homogeneous boundary conditions. The theoretically predicted convergence rate is confirmed by a set of numerical experiments. Further we apply the method to simulate a flow in a simplified 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00457825
- Volume :
- 333
- Database :
- Academic Search Index
- Journal :
- Computer Methods in Applied Mechanics & Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 128390552
- Full Text :
- https://doi.org/10.1016/j.cma.2018.01.024