A non-conforming monolithic finite element method for problems of coupled mechanics

In this study, a Lagrange multiplier technique is developed to solve problems of coupled mechanics and is applied to the case of a Newtonian fluid coupled to a quasi-static hyperelastic solid. Based on theoretical developments in [57], an additional Lagrange multiplier is used to weakly impose displ...

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Vydáno v:Journal of computational physics Ročník 229; číslo 20; s. 7571 - 7593
Hlavní autoři: Nordsletten, D., Kay, D., Smith, N.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Kidlington Elsevier Inc 01.10.2010
Elsevier
Témata:
Arbitrary Lagrangian Eulerian
Computational techniques
Continuity
Convergence
Exact sciences and technology
Finite elasticity mechanics
Finite element method
Interpolation
Lagrange multipliers
Mathematical analysis
Mathematical methods in physics
Mathematical models
Mortar/domain decomposition
Navier–Stokes
Newtonian fluids
Non-matching grids
Optimization
Physics
Finite element method
Navier–Stokes
Mortar/domain decomposition
Arbitrary Lagrangian Eulerian
Finite elasticity mechanics
Non-matching grids
Fluid mechanics
Lagrangian
Digital simulation
Elasticity
Calculation methods
Interpolation
Lagrange multiplier
Kinematics
Convergence rate
Navier-Stokes
Models
Calculation
Newtonian fluid
ISSN:0021-9991, 1090-2716
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Popis
Shrnutí:In this study, a Lagrange multiplier technique is developed to solve problems of coupled mechanics and is applied to the case of a Newtonian fluid coupled to a quasi-static hyperelastic solid. Based on theoretical developments in [57], an additional Lagrange multiplier is used to weakly impose displacement/velocity continuity as well as equal, but opposite, force. Through this approach, both mesh conformity and kinematic variable interpolation may be selected independently within each mechanical body, allowing for the selection of grid size and interpolation most appropriate for the underlying physics. In addition, the transfer of mechanical energy in the coupled system is proven to be conserved. The fidelity of the technique for coupled fluid–solid mechanics is demonstrated through a series of numerical experiments which examine the construction of the Lagrange multiplier space, stability of the scheme, and show optimal convergence rates. The benefits of non-conformity in multi-physics problems is also highlighted. Finally, the method is applied to a simplified elliptical model of the cardiac left ventricle.
Bibliografie:ObjectType-Article-2
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content type line 23
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2010.05.043