Viscous flow with large free surface motion
Computer Methods in Applied Mechanics and Engineering
A three-dimensional computational method for blood flow in the heart. II. contractile fibers
Journal of Computational Physics
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Combined immmersed-boundary finite-difference methods for three-dimensional complex flow simulations
Journal of Computational Physics
Mixed Finite Element Methods on Nonmatching Multiblock Grids
SIAM Journal on Numerical Analysis
Efficient preconditioning of the linearized Navier—Stokes equations for incompressible flow
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
A Preconditioner for the Steady-State Navier--Stokes Equations
SIAM Journal on Scientific Computing
A three-dimensional computer model of the human heart for studying cardiac fluid dynamics
ACM SIGGRAPH Computer Graphics
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Journal of Computational Physics
Journal of Computational Physics
Sharp interface Cartesian grid method III: Solidification of pure materials and binary solutions
Journal of Computational Physics
Benchmark problems for incompressible fluid flows with structural interactions
Computers and Structures
Application of Lagrange multipliers for coupled problems in fluid and structural interactions
Computers and Structures
Numerical simulation of fluid-structure interaction by SPH
Computers and Structures
Triangulation of p-Order Parametric Surfaces
Journal of Scientific Computing
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
SIAM Journal on Scientific Computing
The mortar finite element method for contact problems
Mathematical and Computer Modelling: An International Journal
FIMH'11 Proceedings of the 6th international conference on Functional imaging and modeling of the heart
Flow analysis in cardiac chambers combining phase contrast, 3D tagged and cine MRI
FIMH'13 Proceedings of the 7th international conference on Functional Imaging and Modeling of the Heart
Hi-index | 31.45 |
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.