A well-conditioned augmented system for solving Navier-Stokes equations in irregular domains

Journal of Computational Physics

Volumn 228, Issue 7, 2009, Pages 2616-2628

  Ito, Kazufumi ^a   Lai, Ming Chih ^b   Li, Zhilin ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

Augmented system; Embedding technique; Immersed interface method; Irregular domain; Level set representation; Navier Stokes equations; Projection method

Indexed keywords

BENCHMARKING; LINEAR SYSTEMS; NUMBER THEORY; NUMERICAL METHODS; VISCOUS FLOW;

AUGMENTED SYSTEMS; AUGMENTED VARIABLES; CARTESIAN GRID; EMBEDDING TECHNIQUE; IMMERSED INTERFACE METHOD; INCOMPRESSIBLE (NAVIER )STOKES EQUATION; IRREGULAR DOMAINS; LEVEL SET REPRESENTATION; NAVIER-STOKES EQUATION; PROJECTION METHOD;

NAVIER STOKES EQUATIONS;

EID: 60149091268     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.12.028     Document Type: Article

References (23)

1. Bell J.B., Colella P., and Glaz H.M. A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys. 85 (1989) 257-283
2. Brown D.L., Cortez R., and Minion M.L. Accurate projection methods for the incompressible Navier-Stokes equations. J. Comput. Phys. 168 (2001) 464
3. Calhoun D. A Cartesian grid method for solving the streamfunction-vorticity equation in irregular regions. J. Comput. Phys. 176 (2002) 231-275
4. Weinan E., and Liu J. Projection method: I. Convergence and numerical boundary-layers. SIAM J. Numer. Anal. 32 (1995) 1017-1057
5. Guendelman E., Selle A., Losasso F., and Fedkiw R. Coupling water and smoke to thin deformable and rigid shells. SIGGRAPH, ACM TOG 24 (2005) 973-981
6. Hunter J., Li Z., and Zhao H. Autophobic spreading of drops. J. Comput. Phys. 183 (2002) 335-366
7. Van Kan J. A second-order accurate pressure-correction scheme for viscous incompressible flow. SIAM J. Sci. Comput. 7 (1986) 870-891
8. Kim J., and Moin P. Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys. 59 (1985) 308-323
9. Lai M.-C., and Peskin C.S. An immersed boundary method with formal second-order accuracy and reduced numerical viscosity. J. Comput. Phys. 160 (2000) 705-719
10. Le D.V., Khoo B.C., and Peraire J. An immersed interface method for viscous incompressible flows involving rigid and flexible boundaries. J. Comput. Phys. 220 (2006) 109-138
11. Li Z. A fast iterative algorithm for elliptic interface problems. SIAM J. Numer. Anal. 35 (1998) 230-254
12. Li Z., and Ito K. The immersed interface method - numerical solutions of PDEs involving interfaces and irregular domains. SIAM Front. Ser. Appl. Math. (2006) FR33
13. Li Z., Ito K., and Lai M.-C. An augmented approach for Stokes equations with a discontinuous viscosity and singular forces. Comput. Fluids 36 (2007) 622-635
14. Li Z., and Lai M.-C. The immersed interface method for the Navier-Stokes equations with singular forces. J. Comput. Phys. 171 (2001) 822-842
15. Li Z., Zhao H., and Gao H. A numerical study of electro-migration voiding by evolving level set functions on a fixed cartesian grid. J. Comput. Phys. 152 (1999) 281-304
16. Linnick M.N., and Fasel H.F. A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains. J. Comput. Phys. 204 (2005) 157-192
17. Losasso F., Irving G., Guendelman E., and Fedkiw R. Melting and burning solids into liquids and gases. IEEE TVCG 12 (2006) 343-352
18. Marella S., Krishnan S., Liu H., and Udaykumar H.S. Sharp interface Cartesian grid method I: an easily implemented technique for 3D moving boundary computations. J. Comput. Phys. 210 (2005) 1-31
19. Mittal R., and Iaccarino G. Immersed boundary methods. Ann. Rev. Fluid Mech. 37 (2005) 239-261
20. Russell D., and Wang Z.J. A Cartesian grid method for modeling multiple moving irregular objects in 2D incompressible viscous flow. J. Comput. Phys. 191 (2003) 177-205
21. Su S.-W., Lai M.-C., and Lin C.-A. An immersed boundary technique for simulating complex flows with rigid boundary. Comput. Fluids 36 (2007) 313-324
22. Xu S., and Wang Z.J. An immersed interface method for simulating the interaction of a fluid with moving boundaries. J. Comput. Phys. 216 (2006) 454-493
23. Ye T., Mittal R., Udaykumar H.S., and Shyy W. An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries. J. Comput. Phys. 156 (1999) 209-240