Variational implementation of immersed finite element methods
Luca Heltai,Francesco Costanzo +1 more
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In this paper, the authors generalize the FEIBM to the case where an incompressible Newtonian fluid interacts with a general hyperelastic solid, allowing the mass density to be different in the solid and the fluid, and the solid to be either viscoelastic of differential type or purely elastic.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2012-07-01 and is currently open access. It has received 51 citations till now. The article focuses on the topics: Immersed boundary method & Mixed finite element method.read more
Citations
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Fluid–structure interaction, immersed boundary-finite element method simulations of bio-prosthetic heart valves
TL;DR: The capabilities of the FSI solver are demonstrated by simulating the first fully three-dimensional fluid–structure interaction of tissue valves implanted in the aortic position during systole under physiologic flow conditions, and it is observed that the flow’s threefold symmetry breaks during the early systoles, questioning the three fold symmetry assumption of previous simulations.
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Hybrid finite difference/finite element immersed boundary method.
Boyce E. Griffith,Xiaoyu Luo +1 more
TL;DR: In this article, a coupling scheme for the immersed boundary method is introduced to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid.
Journal ArticleDOI
Nonsingular isogeometric boundary element method for Stokes flows in 3D
TL;DR: A nonsingular formulation of IGA-BEM is proposed for 3D Stokes flows, whose convergence is carefully tested numerically and standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices.
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A fictitious domain approach with Lagrange multiplier for fluid-structure interactions
Daniele Boffi,Lucia Gastaldi +1 more
TL;DR: A recently introduced formulation for fluid-structure interaction problems which makes use of a distributed Lagrange multiplier in the spirit of the fictitious domain method is studied and optimal convergence estimates are proved.
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The Finite Element Immersed Boundary Method with Distributed Lagrange Multiplier
TL;DR: In this article, a new formulation for the finite element immersed boundary method which makes use of a distributed Lagrange multiplier is introduced. But it is not shown that the model is stable with respect to the time step size.
References
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Book
Mixed and Hybrid Finite Element Methods
Franco Brezzi,Michel Fortin +1 more
TL;DR: Variational Formulations and Finite Element Methods for Elliptic Problems, Incompressible Materials and Flow Problems, and Other Applications.
Book
Computational Geometry: Algorithms and Applications
TL;DR: In this article, an introduction to computational geometry focusing on algorithms is presented, which is related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems.
Journal ArticleDOI
The immersed boundary method
TL;DR: This paper is concerned with the mathematical structure of the immersed boundary (IB) method, which is intended for the computer simulation of fluid–structure interaction, especially in biological fluid dynamics.