Title

Goal-oriented mesh adaptivity for fluid-structure interaction with application to heart-valve settings

Journal title

Archive of Mechanical Engineering

Yearbook

2012

Volume

vol. 59

Issue

No 1

Authors

Wick, Thomas

Keywords

heart-valve dynamics ; elastic waves ; arbitrary Lagrangian Eulerian method ; ALE ; finite element method ; fluid-structure interaction ; FSI ; goal-oriented mesh adaption

Divisions of PAS

Nauki Techniczne

Coverage

73-99

Publisher

Polish Academy of Sciences, Committee on Machine Building

Date

2012

Type

Artykuły / Articles

Identifier

DOI: 10.2478/v10180-012-0005-2 ; ISSN 0004-0738, e-ISSN 2300-1895

Source

Archive of Mechanical Engineering; 2012; vol. 59; No 1; 73-99

References

Quarteroni A.: What mathematics can do for the simulation of blood circulation. MOX Report, 2006. ; Figueroa C. (2006), A coupled momentum method for modeling blood ow in three-dimensional deformable arteries, Comput. Methods Appl. Mech. Engrg, 195, 5685, doi.org/10.1016/j.cma.2005.11.011 ; Nobile F. (2008), An Effective Fluid-Structure Interaction Formulation for Vascular Dynamics by Generalized Robin Conditions, SIAM J. Sci. Comput, 30, 2, 731, doi.org/10.1137/060678439 ; Janela J. (2010), Absorbing boundary conditions for a 3D non-Newtonian fluid-structure interaction model for blood flow in arteries, Int. J. Engrg. Sci. ; Formaggia L. (2009), Cardiovascular Mathematics: Modeling and simulation of the circulatory system. ; Formaggia L. (2010), Flow rate boundary problems for an incompressible fluid in deformable domains: formulations and solution methods, Comput. Meth. Appl. Mech. Engrg, 199, 677, doi.org/10.1016/j.cma.2009.10.017 ; Wick T.: An energy absorbing layer for the structure outflow boundary for fluid-structure interactions applied to valve dynamics, in review, 2011. ; Wick T.: Adaptive finite element simulation of fluid-structure interaction with application to heart valve dynamics, PhD thesis, 2011. ; Jianhai Z. (2006), ALE finite element analysis of the opening and closing process of the artificial mechanical valve, Applied Math. Mech, 17, 5, 403, doi.org/10.1007/BF00131088 ; P. Le Tallec (2001), Fluid structure interaction with large structural displacements, Comput. Meth. Appl. Mech. Engrg, 190, 3039, doi.org/10.1016/S0045-7825(00)00381-9 ; Peskin C. (2002), Acta Numerica, 1. ; N. Diniz Dos Santos (2008), A partitioned fluid-structure algorithm for elastic thin valves with contact, Comp. Meth. Appl. Mech. Engng, 197, 19-20, 1750, doi.org/10.1016/j.cma.2007.03.019 ; Vierendeels J. (2008), A partitioned strongly coupled fluid-structure interaction method to model heart valve dynamics, J. Comp. Appl. Math. ; Baaijens F. (2001), A fictitious domain/mortar element method for fluid-structure interaction, Int. J. Num. Methods Fluids, 35, 743, doi.org/10.1002/1097-0363(20010415)35:7<743::AID-FLD109>3.0.CO;2-A ; Causin P. (2005), Added-mass effect in the design of partitioned algorithms for fluid-structure problems, Comput. Methods Appl. Mech. Engrg, 194, 4506, doi.org/10.1016/j.cma.2004.12.005 ; (2001), Acta Numerica. ; Dunne T. (2006), An Eulerian approach to fluid-structure interaction and goal-oriented mesh adaption, Int. J. Numer. Methods in Fluids, 51, 1017, doi.org/10.1002/fld.1205 ; Galdi G. (2010), Numerical Fluid Structure Interaction. ; Richter T. (2012), Goal oriented error estimation for fluid-structure interaction problems, Computer Methods in Applied Mechanics and Engineering, 223-224, 38, doi.org/10.1016/j.cma.2012.02.014 ; K. van der Zee (2008), Goal-oriented error estimation for Stokes flow interacting with a flexible channel, Int. J. Numer. Meth. Fluids, 56, 1551, doi.org/10.1002/fld.1652 ; Bathe K.-J. (2006), Goal-oriented error estimation in the analysis of fluid flows with structural interactions, Comp. Methods Appl. Mech. Engrg, 195, 5673, doi.org/10.1016/j.cma.2005.10.020 ; Fung Y. (1984), Biodynamics: Circulation. ; Holzapfel G. (2000), Nonlinear Solid Mechanics: A continuum approach for engineering. ; Holzapfel G. (2006), Mechanics of Biological Tissue, doi.org/10.1007/3-540-31184-X ; Humphrey J. (2002), Cardiovascular Solid Mechanics: Cells, Tissues, and Organs. ; Wloka J. (1987), Partielle Differentialgleichungen. ; Berenger J.-P. (1994), A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys, 114, 185. ; Formaggia L., Moura A., Nobile F.: On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations. Technical Report at MOX, 2006, Vol. 94. ; Vignon-Clementel I. (2006), Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries, Comput. Meth. Appl. Mech. Engrg, 195, 3776, doi.org/10.1016/j.cma.2005.04.014 ; Stein K. (2003), Mesh moving techniques for fluid-structure interactions with large displacements, J. Appl. Math, 70, 58. ; Tezduyar T. (1992), Computation of Unsteady Incompressible Flows With the Finite Element MethodsSpace- Time Formulations, Iterative Strategies and Massively Parallel Implementations, ASME: New Methods in Transient Analysis, 143, 7. ; Wick T. (2011), Fluid-Structure Interactions using Different Mesh Motion Techniques, Comput. Struct, 89, 1456, doi.org/10.1016/j.compstruc.2011.02.019 ; Brooks A. (1982), Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg, 32, 1-3, 199, doi.org/10.1016/0045-7825(82)90071-8 ; Wall Wolfgang A.: Fluid-Struktur-Interaktion mit stabilisierten Finiten Elementen, PhD Thesis, University of Stuttgart, 1999. ; Braack M. (2007), Stabilized finite element methods for the generalized Oseen equations, Comput. Methods Appl. Mech. Engrg, 196, 4-6, 853, doi.org/10.1016/j.cma.2006.07.011 ; Besier M. (2009), Adaptive Finite Element methods for computing nonstationary incompressible Flows. ; Besier M. (2011), On the dependence of the pressure on the time step in incompressible flow simulations on varying spatial meshes, Int. J. Num. Methods in Fluids. ; Becker R. (1996), A feed-back approach to error control in finite element methods: basic analysis and examples, East-West J. Numer. Math, 4, 237. ; Wick T. (2011), Adaptive Finite Elements for Fluid-Structure Interactions on a Prolongated Domain: Applied to Valve Simulations, null. ; Zienkiewicz O. (1992), The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique, Int. J. of Numer. Methods Engrg, 33, 1331, doi.org/10.1002/nme.1620330702 ; Zienkiewicz O. (1992), The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity, Int. J. of Numer. Methods Engrg, 33, 1365, doi.org/10.1002/nme.1620330703 ; Bangerth W. (2003), Lectures in Mathematics, ETH Zuerich. ; Bangerth W., Hartmann R., Kanschat G.: Differential Equations Analysis Library. Technical Reference, 2010. <a target="_blank" href='http://www.dealii.org'>http://www.dealii.org</a> ; Wick T.: Solving Monolithic Fluid-Structure Interaction Problems in Arbitrary Lagrangian Eulerian Coordinates with the deal. II Library. IWR-Preprint, 2011, in review for publication in Archive of Numerical Software. ; Heywood J. (1996), Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations, Int. J. Num. Meth. Fluids, 22, 325, doi.org/10.1002/(SICI)1097-0363(19960315)22:5<325::AID-FLD307>3.0.CO;2-Y