An immersed boundary method based on discrete stream function formulation for two- and three-dimensional incompressible flows

Journal of Computational Physics

Volumn 230, Issue 9, 2011, Pages 3479-3499

  Wang, Shizhao ^a   Zhang, Xing ^a  

^a INSTITUTE OF MECHANICS   (China)

Author keywords

Discrete stream function formulation; Immersed boundary method; Incompressible flow; Navier Stokes equations; Parallel computing

Indexed keywords

ASPECT RATIO; COMPUTATIONAL FLUID DYNAMICS; DOMAIN DECOMPOSITION METHODS; FLOW SIMULATION; INCOMPRESSIBLE FLOW; LINEAR SYSTEMS; OSCILLATING FLOW; REYNOLDS NUMBER; TURBULENT FLOW; VORTEX FLOW;

DISCRETE STREAM FUNCTION FORMULATION; FLOW SOLVER; IMMERSED BOUNDARY METHODS; NAVIER-STOKES EQUATION; NON-SLIP BOUNDARIES; PARALLEL COM- PUTING; SLIP BOUNDARY CONDITIONS; STREAMFUNCTION FORMULATION; THREE DIMENSIONAL INCOMPRESSIBLE FLOW; TWO-DIMENSIONAL;

NAVIER STOKES EQUATIONS;

EID: 79952455522     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.01.045     Document Type: Article

References (54)

1. Peskin C.S. The immersed boundary method. Acta Numer. 2002, 11:479-517.
2. Mittal R., Iaccarino G. Immersed boundary methods. Annu. Rev. Fluid Mech. 2005, 37:239-261.
3. Peskin C.S. Flow patterns around heart valves: a numerical method. J. Comput. Phys. 1972, 10:252-271.
4. Zhu L.D., Peskin C.S. Simulation of a flexible flapping filament in a flowing soap film by the immersed boundary method. J. Comput. Phys. 2002, 179:452-468.
5. 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.
6. Goldstein D., Handler R., Sirovich L. Modeling a no-slip flow boundary with an external force field. J. Comput. Phys. 1993, 105:354-366.
7. Saiki E.M., Biringen S. Spatial simulation of a cylinder in uniform flow: application of a virtual boundary method. J. Comput. Phys. 1996, 123:450-465.
8. J. Mohd-Yusof, Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries, CTR Annual Research Briefs, NASA Ames/Stanford University, 1997, pp. 317-327.
9. Fadlun E.A., Verzicco R., Orlandi P., Mohd-Yusof J. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 2000, 161:35-60.
10. Iaccarino G., Verzicco R. Immersed boundary technique for turbulent flow simulations. Appl. Mech. Rev. 2003, 56:331-347.
11. Kim J., Kim D., Choi H. An immersed-boundary finite-volume method for simulations of flow in complex geometries. J. Comput. Phys. 2001, 171:132-150.
12. Tseng Y.H., Ferziger J.H. A ghost-cell immersed boundary method for flow in complex geometry. J. Comput. Phys. 2000, 192:593-623.
13. Balaras E. Modeling complex boundaries using an external force field on fixed Cartesian grids in Large-eddy simulations. Comput. Fluids 2004, 33:375-404.
14. Yang J., Balaras E. An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries. J. Comput. Phys. 2006, 215:12-40.
15. Kim D., Choi H. Immersed boundary method for flow around an arbitrarily moving body. J. Comput. Phys. 2006, 212:662-680.
16. Zhang N., Zheng Z.C. An improved direct-forcing immersed-boundary method for finite difference applications. J. Comput. Phys. 2007, 221:250-268.
17. Ikeno T., Kajishima T. Finite-difference immersed boundary method consistent with wall conditions for incompressible turbulent flow simulations. J. Comput. Phys. 2007, 226:1485-1508.
18. Uhlmann M. An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 2005, 209:448-476.
19. Su S.W., Lai M.C., Lin C.A. An immersed boundary technique for simulating complex flows with rigid boundary. Comput. Fluids 2007, 36:313-324.
20. Taira K., Colonius T. The immersed boundary method: a projection approach. J. Comput. Phys. 2007, 225:2118-2137.
21. Yang X.L., Zhang X., Li Z.L., He G.W. A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations. J. Comput. Phys. 2009, 228:7821-7836.
22. Wang X.D., Liu W.K. Extended immersed boundary method using FEM and RKPM. Comput. Meth. Appl. M. 2004, 193:1305-1321.
23. Feng Z.G., Michaelides E.E. The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems. J. Comput. Phys. 2004, 195:602-628.
24. Hieber S.E., Koumoutsakos P. An immersed boundary method for smoothed particle hydrodynamics of self-propelled swimmers. J. Comput. Phys. 2008, 227:8636-8654.
25. de Tullio M.D., De Palma P., Iaccarino G., Pascazio G., Napolitano M. An immersed boundary method for compressible flows using local grid refinement. J. Comput. Phys. 2007, 225:2098-2117.
26. You D., Mittal R., Wang M., Moin P. Computational methodology for large-eddy simulation of tip-clearance flows. AIAA J. 2004, 42:271-279.
27. Borazjani I., Ge L., Sotiropoulos F. Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies. J. Comput. Phys. 2008, 227:7587-7620.
28. Denaro F.M., Sarghini F. 2-D transmittal flows simulation by means of the immersed boundary method on unstructured grids. Int. J. Numer. Meth. Fluids 2002, 38:1133-1157.
29. Young D.L., Jan Y.J., Chiu C.L. A novel immersed boundary procedure for flow and heat simulations with moving boundary. Comput. Fluids 2009, 38:1145-1159.
30. Laizet S., Lamballais E. High-order compact schemes for incompressible flows: a simple and efficient method with quasi-spectral accuracy. J. Comput. Phys. 2009, 228:5989-6015.
31. Ferreira de Sousa Paulo J.S.A., Pereira Jose C.F., Allen J.J. Two-dimensional compact finite difference immersed boundary method. Int. J. Numer. Meth. Fluids 2009, 10.1002/fld.2199.
32. Calhoun D. A Cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions. J. Comput. Phys. 2002, 176:231-275.
33. Russell D., Wang Z.J. A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow. J. Comput. Phys. 2003, 191:177-205.
34. LeVeque R.J., Li Z. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 1994, 31:1019-1044.
35. Wang Z.L., Fan J.R., Cen K.F. Immersed boundary method for the simulation of 2D viscous flow based on vorticity-velocity formulations. J. Comput. Phys. 2009, 228:1504-1520.
36. Colonius T., Taira K. A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions. Comput. Meth. Appl. M. 2008, 197:2131-2146.
37. Perot B. Conservation properties of unstructured staggered mesh schemes. J. Comput. Phys. 2000, 159:58-89.
38. Wang C., Giraldo F., Perot B. Analysis of an exact fractional step method. J. Comput. Phys. 2002, 180:183-199.
39. Zhang X., Schmidt D., Perot B. Accuracy and conservation properties of a three-dimensional unstructured staggered mesh scheme for fluid dynamics. J. Comput. Phys. 2002, 175:764-791.
40. Perot B., Nallapati R. A moving unstructured staggered mesh method for the simulation of incompressible free-surface flows. J. Comput. Phys. 2003, 184:192-214.
41. Le D.V., Khoo B.C., Peraire J. An immersed interface method for viscous incompressible flows involving rigid and flexible boundaries. J. Comput. Phys. 2006, 220:109-138.
42. W.P. Breugem, A combined soft-sphere collision/immersed boundary method for resolved simulations of particulate flows, in: Proceedings of the ASME 2010 Third Joint US-European Fluids Engineering Summer Meeting, Montreal, Quebec, Canada, 1-5 August 2010 (FEDSM-ICNMM2010-30634).
43. Kang S., Iaccarino G., Ham F., Moin P. Prediction of wall-pressure fluctuation in turbulent flows with an immersed boundary method. J. Comput. Phys. 2009, 228:6753-6772.
44. Karypis G., Kumar V. A fast and high quality scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 1999, 20:259-392.
45. Coutanceau M., Bouard R. Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 1. Steady flow. J. Fluid Mech. 1977, 79:231-256.
46. Dennis S.C.R., Chang G. Numerical solutions for steady flow past a circular cylinder at Reynolds number up to 100. J. Fluid Mech. 1970, 42:471-489.
47. Linnick M.N., Fasel H.F. A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains. J. Comput. Phys. 2005, 204:157-192.
48. Liu C., Zheng X., Sung C. Preconditioned multigrid methods for unsteady incompressible flows. J. Comput. Phys. 1998, 139:35-57.
49. Park J., Kwon K., Choi H. Numerical solutions of flow past a circular cylinder at Reynolds numbers up to 160. KSME Int. J. 1998, 12:1200-1205.
50. Dutsch H., Durst F., Becker S., Lienhart H. Low-Reynolds-number flow around an oscillating circular cylinder at low Keulegan-Carpenter numbers. J. Fluid Mech. 1998, 360:249-271.
51. Griffin O.M. The unsteady wake of an oscillating cylinder at low Reynolds number. J. Appl. Mech. 1971, 38:729-738.
52. Jeong J., Hussain F. On the identification of a vortex. J. Fluid Mech. 1995, 285:69-94.
53. Johnson T.A., Patel V.C. Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 1999, 378:19-70.
54. Taira K., Colonius T. Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers. J. Fluid Mech. 2009, 623:187-207.