An immersed boundary energy-based method for incompressible viscoelasticity

Journal of Computational Physics

Volumn 231, Issue 14, 2012, Pages 4613-4642

  Devendran, Dharshi ^a   Peskin, Charles S ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

Energy based method; Fluid structure interaction; Immersed boundary method; Incompressible viscoelasticity

Indexed keywords

BIOLOGICAL MATERIALS; COMPUTATIONAL FLUID DYNAMICS; EQUATIONS OF MOTION; FIBER REINFORCED MATERIALS; LAGRANGE MULTIPLIERS; STRESS TENSOR; TURBULENT FLOW; VISCOELASTICITY;

DEFORMATION MAP; ENERGY-BASED METHODS; EULERIAN; FLUID-STRUCTURE INTERACTION; FORCE DENSITY; IMMERSED BOUNDARY; IMMERSED BOUNDARY METHODS; INCOMPRESSIBLE VISCOELASTICITY; LAGRANGIAN; SECOND ORDERS;

FLUID STRUCTURE INTERACTION;

EID: 84861235476     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2012.02.020     Document Type: Article

References (16)

1. D.M. McQueen, C.S. Peskin, Heart simulation by an immersed boundary method with formal second-order accuracy and reduced numerical viscosity, in: Proceedings of the ICTAM, 2000.
2. Belytschko T., Liu W.K., Moran B. Nonlinear Finite Elements for Continua and Structures 2000, John Wiley and Sons, Ltd., New York. first ed.
3. Peskin C.S. The immersed boundary method. Acta Numer. 2002, 11:479-517.
4. Griffith B.E. On the volume conservation of the immersed boundary method. Commun. Comput. Phys. 2012, 12:401-432.
5. C.S. Peskin, The immersed boundary method. III. Energy functions for the representation of immersed elastic boundaries and materials, handwritten lecture notes available from , 2007. http://math.nyu.edu/faculty/peskin/iblecturenotes/index.html.
6. Doghri I. Mechanics of Deformable Solids: Linear, Nonlinear, Analytical, and Computational Aspects 2000, Springer-Verlag, Berlin. first ed.
7. Merodio J., Ogden R.W. Mechanical response of fiber-reinforced incompressible non-linearly elastic solids. Int. J. Nonlinear Mech. 2005, 40:213-227.
8. Rosar M.E., Peskin C.S. Fluid flow in collapsible elastic tubes: a three-dimensional numerical model. New York J. Math. 2001, 7:281-302.
9. Lai M-C, Peskin C.S. An immersed boundary method with formal second order accuracy and reduced numerical viscosity. J. Comput. Phys. 2000, 160:705-719.
10. McQueen D.M., Peskin C.S. Heart simulation by an immersed boundary method with formal second-order accuracy and reduced numerical viscosity. Mechanics for a New Millennium, Proceedings of the International Conference on Theoretical and Applied Mechanics (ICTAM)2000 2001, Kluwer Academic Publishers. H. Aref, J.W. Phillips (Eds.).
11. Boffi D., Gastaldi L., Heltai L., Peskin C.S. On the hyper-elastic formulation of the immersed boundary method. Comput. Methods Appl. Mech. Engrg. 2008, 197:2210-2231.
12. Parthasarathy V.N., Graichen C.M., Hathaway A.F. A comparison of tetrahedron quality measures. Finite Elem. Anal. Design 1993, 15:255-261.
13. Kim Y., Peskin C.S. Numerical study of incompressible fluid dynamics with nonuniform density by the immersed boundary method. Phys. Fluids 2008, 20.
14. Zhu L., Peskin C.S. Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method. J. Comput. Phys. 2002, 179:452-468.
15. Mori Y., Peskin C.S. Implicit second order immersed boundary methods with boundary mass. Comput. Methods Appl. Mech. Engrg. 2008, 197:2049-2067.
16. Wang X., Liu W.K. Extended immersed boundary method using FEM and RKPM. Comput. Methods Appl. Mech. Engrg. 2004, 193:1305-1321.