Abstract
The 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.
Funding source: Russian Science Foundation
Award Identifier / Grant number: 14-31-00024
Funding statement: This work has been supported by the Russian Science Foundation (RSF) grant 14-31-00024
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© 2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Preface
- Efficient synthesis of optimal multiband filter
- A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle
- A Newton-type method for non-linear eigenproblems
- The structure and stabilization by boundary conditions of an annular flow of Kolmogorov type
- Monotone discretizations for diffusion equations on triangular and tetrahedral meshes
- A posteriori estimates for a coupled piezoelectric model
- The triviality condition for kernels of quadratic mappings and its application in optimization methods
Articles in the same Issue
- Frontmatter
- Preface
- Efficient synthesis of optimal multiband filter
- A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle
- A Newton-type method for non-linear eigenproblems
- The structure and stabilization by boundary conditions of an annular flow of Kolmogorov type
- Monotone discretizations for diffusion equations on triangular and tetrahedral meshes
- A posteriori estimates for a coupled piezoelectric model
- The triviality condition for kernels of quadratic mappings and its application in optimization methods