Approximate imposition of boundary conditions in immersed boundary methods

International Journal for Numerical Methods in Engineering

Volumn 80, Issue 11, 2009, Pages 1379-1405

  Codina, Ramon ^a   Baiges, Joan ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Approximate boundary conditions; Finite element methods; Immersed boundaries; Nitsche's method

Indexed keywords

APPROXIMATE BOUNDARY CONDITION; APPROXIMATE BOUNDARY CONDITIONS; APPROXIMATION TECHNIQUES; COMPUTATIONAL DOMAINS; DEGREES OF FREEDOM; DIRICHLET BOUNDARY CONDITION; FINITE ELEMENT MESHES; IMMERSED BOUNDARY; IMMERSED BOUNDARY METHODS; VARIATIONAL APPROACHES;

BOUNDARY CONDITIONS; COMPUTATIONAL FLUID DYNAMICS; FINITE ELEMENT METHOD; TURBULENT FLOW;

BOUNDARY ELEMENT METHOD;

EID: 70450186433     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2662     Document Type: Article

References (35)

1. Houzeaux G, Codina R. A Chimera method based on a Dirichlet/Neumann (Robin) coupling for the Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 2003; 192:3343-3377.
2. Codina R, Houzeaux J, Coppola-Owen H, Baiges J. The fixed-mesh ALE approach for the numerical approximation of flows in moving domains. Journal of Computational Physics 2009; 8:1591-1611.
3. Tezduyar TE. Finite element methods for flow problems with moving boundaries and interfaces. Archives of Computational Methods in Engineering 2001; 8(2):83-130.
4. Mittal R, Iaccarino G. Immersed boundary methods. Annual Review of Fluid Mechanics 2005; 37:239-261.
5. Löhner R, Cebral JR, Camelli FF, Baum JD, Mestreau EL. Adaptive embedded/immersed unstructured grid techniques. Archives of Computational Methods in Engineering 2007; 14:279-301.
6. Peskin CS. Flow patterns around heart valves: a numerical method. Journal of Computational Physics 1972; 10:252-271.
7. Lai M-C, Peskin CS. An immersed boundary method with formal second-order accuracy and reduced numerical viscosity. Journal of Computational Physics 2000; 160:705-719.
8. LeVeque RJ, Li Z. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM Journal on Numerical Analysis 1994; 31(4):1019-1044.
9. LeVeque RJ, Li Z. Immersed interface method for incompressible Navier-Stokes equations. SIAM Journal on Scientific and Statistical Computing 1997; 18(3):709-735.
10. Xu S, Wang ZJ. An immersed interface method for simulating the interaction of a fluid with moving boundaries. Journal of Computational Physics 2006; 216:454-493.
11. Babuska I. Error bounds for finite element method. Numerische Mathematik 1971; 16:322-333.
12. Dolbow J, Mourad HM, Harari I. A bubble-stabilized finite element method for Dirichlet constraints on embedded interfaces. International Journal for Numerical Methods in Engineering 2007; 69:772-793.
13. Barbosa HJC, Hughes TJR. The finite element method with Lagrangian multipliers on the boundary: circumventing the Babuška-Brezzi condition. Computer Methods in Applied Mechanics and Engineering 1991; 85:109-128.
14. Ji H, Dolbow JE. On strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method. International Journal for Numerical Methods in Engineering 2004; 61:2508-2535.
15. Glowinski R, Pan TW, Périaux J. A fictitious domain method for Dirichlet problems and applications. Computer Methods in Applied Mechanics and Engineering 1994; 111:203-303.
16. Glowinski R, Pan TW, Hesla TI, Joseph DD, Périaux J. A distributed Lagrange multiplier/fictitious domain method for flows around moving rigid bodies: application to particulate flow. International Journal for Numerical Methods in Fluids 1999; 30:1043-1066.
17. Glowinski R. Finite element methods for incompressible viscous flows. Numerical Methods for Fluids (Part 3), Handbook of Numerical Analysis, vol. 9. Elsevier: Amsterdam, 2003.
18. Gilmanov A, Sotiropoulos F. A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies. Journal of Computational Physics 2005; 207:457-492.
19. Ferziger JH, Tseng YH. A ghost-cell immersed boundary method for flow in complex geometry. Journal of Computational Physics 2003; 192:593-623.
20. Mohd-Yusof J. Combined immersed boundaries/B-splines methods for simulations of flows in complex geometries. CTR Annual Research Briefs, Stanford University, NASA Ames, 1997.
21. Lew AJ, Buscaglia GC. A discontinuous-Galerkin-based immersed boundary method. submitted for publication.
22. Brenner SC, Scott LR. The Mathematical Theory of Finite Element Methods. Springer: Berlin, 1994.
23. Ern A, Guermond J-L. Theory and Practice of Finite Elements. Springer: Berlin, 2004.
24. Juntunen M, Stenberg R. Nitsche's method for general boundary conditions. Research Reports A530, Helsinki University of Technology, Institute of Mathematics, 2007.
25. Arnold DN. An interior penalty finite element method with discontinuous elements. SIAM Journal on Numerical Analysis 1982; 19:742-760.
26. Hansbo P, Larson MG. Discontinuous Galerkin methods for incompressible and nearly incompressible elasticity by Nitsche's method. Computer Methods in Applied Mechanics and Engineering 2002; 191:1895-1908.
27. Becker R, Hansbo P, Stenberg R. A finite element method for domain decomposition with non-matching grids. Mathematical Modelling and Numerical Analysis 2003; 37:209-225.
28. Hansbo A, Hansbo P. An unfitted finite element method, based on Nitsche's method, for elliptic interface problems. Computer Methods in Applied Mechanics and Engineering 2002; 191:5537-5552.
29. Burman E, Fernández MA, Hansbo P. Continuous interior penalty finite element method for Oseen's equations. SIAM Journal on Numerical Analysis 2006; 44:1248-1274.
30. Coppola-Owen H, Codina R. A finite element model for free surface flows on fixed meshes. International Journal for Numerical Methods in Fluids 2007; 54:1151-1171.
31. Durbin P, Majumdar S, Iaccarino G. RANS solvers with adaptive structured boundary non-conforming grids. Annual Research Briefs, NASA Ames Research Center/Stanford University Center for Turbulence Research, Stanford, CA, 2001; 353-366.
32. Codina R. Comparison of some finite element methods for solving the diffusion-convection-reaction equation. Computer Methods in Applied Mechanics and Engineering 1998; 156:185-210.
33. Codina R, Zienkiewicz OC. CBS versus GLS stabilization of the incompressible Navier-Stokes equations and the role of the time step as stabilization parameter. Communications in Numerical Methods in Engineering 2002; 18:99-112.
34. Codina R. A stabilized finite element method for generalized stationary incompressible flows. Computer Methods in Applied Mechanics and Engineering 2001; 190:2681-2706.
35. Codina R. A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation. Computer Methods in Applied Mechanics and Engineering 1993; 110:325-342.