Efficient solutions to robust, semi-implicit discretizations of the immersed boundary method

Journal of Computational Physics

Volumn 228, Issue 19, 2009, Pages 7137-7158

  Ceniceros, Hector D ^a   Fisher, Jordan E ^a   Roma, Alexandre M ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Heart valve; Multigrid; Navier Stokes equations; Semi implicit method; Stokes flow

Indexed keywords

COMPUTATIONAL METHODS; COST EFFECTIVENESS; INTERPOLATION; ITERATIVE METHODS; LINEAR SYSTEMS; MATRIX ALGEBRA; PRODUCT DESIGN; TURBULENT FLOW;

DISCRETIZATIONS; HEART VALVES; IMMERSED BOUNDARY METHODS; INTERFACE CONFIGURATION; INTERFACIAL FORCES; MULTIGRIDS; NAVIER-STOKES EQUATION; SEMI-IMPLICIT; SEMI-IMPLICIT METHODS; STOKES FLOWS;

NAVIER STOKES EQUATIONS;

EID: 68549099499     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.05.031     Document Type: Article

References (12)

1. Peskin C.S. Numerical analysis of blood flow in the heart. J. Comput. Phys 25 (1977) 220-252
2. Stockie J.M., and Wetton B.T.R. Stability analysis for the immersed fiber problem. SIAM J. Appl. Math. 55 6 (1995) 1577-1591
3. Stockie J.M., and Wetton B.R. Analysis of stiffness in the immersed boundary method and implications for time-stepping schemes. J. Comput. Phys. 154 (1999) 41-64
4. Tu C., and Peskin C.S. Stability and instability in the computations of flows with moving immersed boundaries: a comparison of three methods. SIAM J. Sci. Stat. Comput. 13 6 (1992) 1361-1376
5. A.A. Mayo, C.S. Peskin, An implicit numerical method for fluid dynamics problems with immersed elastic boundaries, in: A.Y. Cheer, C.P.V. Dam (Eds.), Fluid Dynamics in Biology: Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Biofluiddynamics, American Mathematical Society, 1993, pp. 261-277.
6. Hou T.Y., and Shi Z. Removing the stiffness of elastic force from the immersed boundary method for 2D Stokes equations. J. Comput. Phys. 227 (2008) 9138-9169
7. Hou T.Y., and Shi Z. An efficient semi-implicit immersed boundary method for the Navier-Stokes equations. J. Comput. Phys. 227 (2008) 8968-8991
8. Newren E.P., Fogelson A.L., Guy R.D., and Kirby R.M. Unconditionally stable discretizations of the immersed boundary equations. J. Comput. Phys. 222 (2007) 702-719
9. Mori Y., and Peskin C.S. Implicit second-order immersed boundary methods with boundary mass. Comput. Meth. Appl. Mech. Eng. 197 (2008) 2049-2067
10. Tryggvason G., Bunner B., Esmaeeli A., Juric D., Al-Rawahi N., Tauber W., Han J., Nas S., and Jan Y.-J. A front-tracking method for computations of multiphase flow. J. Comput. Phys. 169 (2001) 708-759
11. McQueen C., and Peskin D.M. A three-dimensional computer model of the human heart for studying cardiac fluid dynamics. ACM SIGGRAPH Comput. Graph. 34 1 (2000) 56-60
12. Mori Y. Convergence proof of the velocity field for a Stokes flow immersed boundary method. Commun. Pure Appl. Math. 61 (2008) 1213-1263