Simulation of steady and unsteady incompressible flow using gradient smoothing method (GSM)

Computers and Structures

Volumn 90-91, Issue 1, 2012, Pages 131-144

  Xu, George X ^a,c   Li, Eric ^a   Tan, Vincent ^a   Liu, G R ^a,b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b UNIVERSITY OF CINCINNATI   (United States)

^c INSTITUTE OF HIGH PERFORMANCE COMPUTING   (Singapore)

Author keywords

GSD; GSM; Incompressible; Meshfree method; Numerical method; Stencil

Indexed keywords

ARTIFICIAL COMPRESSIBILITY; BACK STEP; BENCHMARKING PROBLEMS; DUAL TIME STEPPING; FLUID FLOW PROBLEMS; GOVERNING EQUATIONS; GRADIENT SMOOTHING; GRADIENT SMOOTHING METHODS; GSD; INCOMPRESSIBLE; INCOMPRESSIBLE FLUID FLOW; INCOMPRESSIBLE NAVIER STOKES EQUATIONS; ITERATIVE SOLUTIONS; LID-DRIVEN CAVITIES; LITERATURE DATA; MESH-FREE METHOD; POSITIVE COEFFICIENTS; RUNGE-KUTTA; SPATIAL DERIVATIVES; STEADY-STATE FLOWS; STENCIL; STRONG FORM; TESTING CASE;

CIRCULAR CYLINDERS; COMPRESSIBLE FLOW; COMPUTATIONAL MECHANICS; GLOBAL SYSTEM FOR MOBILE COMMUNICATIONS; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; RUNGE KUTTA METHODS;

INCOMPRESSIBLE FLOW;

EID: 81855198933     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2011.10.001     Document Type: Article

References (43)

1. J.C. Tannehill, D.A. Anderson, and R.H. Pletcher Computational fluid mechanics and heat transfer 2nd ed. 1997 Taylor & Francis Washington
2. R. Peyret, and H. Viviand Pseudo-unsteady methods for inviscid or viscous flow computations C. Casi, Recent advances in the aerospace sciences 1985 Plenum New York 312 343
3. D. Choi, and C.L. Merkle The application of preconditioning in viscous flows J Comput Phys 105 1993 203 223
4. E. Turkel Preconditioned methods for solving the incompressible and low speed compressible equations J Comput Phys 72 1987 277 298
5. F.H. Harlow, and J.E. Welch Numerical calculation of time-dependent viscous incompressible flow of fluids with free surface Phys Fluids 8 1965 2182 2189
6. S.V. Patankar, and D.B. Spalding A calculation procedure for heat mass and momentum transfer in three-dimensional parabolic flows Int J Heat Mass Transfer 15 1972 1787 1806
7. S.V. Patankar Numerical heat transfer and fluid flow 1980 McGraw-Hill New York
8. A.J. Chorin A numerical method for solving incompressible viscous flow problems J Comput Phys 2 1967 203 223
9. J.L. Steger, and P. Kulter Implicit finite-difference procedures for the computation of vortex wakes AIAA J 15 4 1977 581 590
10. S.E. Rogers, and D. Kwak An upwind differencing scheme for the steady-state incompressible Navier-Stokes Equations Appl Numer Math 8 1991 3 64
11. Turkel E. Review of preconditioning methods for fluid dynamics. ICASE Report 92-47. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Langley, Virginia; 1992.
12. D. Kwak, J.L.C. Chang, S.P. Shanks, and S.K. Chakravarthy A three-dimensional incompressible Navier-Stokes solver using primitive variables AIAA J 24 1986 390 396 (Pubitemid 16565531)
13. G.R. Liu, and G.X. Xu A gradient smoothing method (GSM) for fluid dynamics problems Int J Numer Method Fluids 58 2008 1101 1133
14. K.A. Hoffmann, and S.T. Chiang Computational fluid dynamics for engineers Vols. I and II 1993 Engineering Education System™ Austin, TX
15. J.S. Chen, S. Yoon, and C.T. Wu Non-linear version of stabilized conforming nodal integration for Galekin grid-free methods Int J Numer Methods Eng 53 2002 2587 2615 (Pubitemid 34254094)
16. 2) form for a unified formulation of compatible and incompatible methods: Part I theory Int J Numer Methods Eng 81 2010 1093 1126
17. 2) form for a unified formulation of compatible and incompatible methods: Part II applications to solid mechanics problems Int J Numer Methods Eng 81 2010 1127 1156
18. G.R. Liu, G.Y. Zhang, K.Y. Dai, Y.Y. Wang, Z.H. Zhong, and G.Y. Li A linearly conforming point interpolation method (LC-PIM) for 2D solid mechanics problems Int J Comput Method 2 4 2005 645 665
19. G.Y. Zhang, G.R. Liu, Y.Y. Wang, H.T. Huang, Z.H. Zhong, and G.Y. Li A linearly conforming point interpolation method (LC-PIM) for three-dimensional elasticity problems Int J Numer Methods Eng 72 2007 524 1543
20. G.R. Liu, B.T.B. Kee, and C. Lu A stabilized least-squares radial point collocation method (LS-RPCM) for adaptive analysis Comput Meth Appl Mech Eng 195 2006 4843 4861 (Pubitemid 43842603)
21. G.R. Liu, Y. Li, K.Y. Dai, M.T. Luan, and W. Xue A linearly conforming radial point interpolation method for solid mechanics Int J Comput Method 3 2006 401 428 (Pubitemid 47082588)
22. L. Lucy A numerical approach to testing the fission hypothesis Astron J 82 1977 1013 1024
23. G.R. Liu, and M.B. Liu Smoothing particle hydrodynamics - a meshfree particle method 2003 World Scientific Singapore
24. A.C. Eringen, and D.G.B. Edelen On nonlocal elasticity Int J Eng Sci 10 1972 233 248
25. J. Blazek Computational fluid dynamics: principles and application 1st ed. 2001 Elsevier Press Oxford
26. P.L. Roe Approximate Riemann solvers parameter vectors and difference schemes J Comput Phys 43 1981 357 382
27. Barth TJ, Jespersen DC. The design and application of upwind schemes on unstructured grids. AIAA paper 89-0366; 1989.
28. Whitfield DL, Taylor LK. Numerical solution of the two-dimensional time-dependent incompressible Euler equations. NASA-CR-195775; 1994.
29. Shin S. Reynolds-averaged Navier-Stokes computation of tip clearance flow in a compressor cascade using an unstructured grid. Virginia Polytechnic Institute and State University, PhD thesis; 2001.
30. Arnone A, Liou MS, Provinelli LA. Multigrid time-accurate integration of Navier-Stokes equations. AIAA Paper 93-3361CP; 1993.
31. Melson ND, Sanetrik MD, Atkins HL. Time-accurate Navier-Stokes calculations with multigrid acceleration. In: 6th copper mountain conf. on multigrid methods; 1993. pp. 423-39.
32. D. Kwak, J.L. C Chang, S.P. Shanks, and S.K. Chakravarthy A three-dimensional incompressible Navier-Stokes solver using primitive variables AIAA J 24 1986 390 396 (Pubitemid 16565531)
33. S. Teneda Experimental investigation of the wakes behind cylinders and plates at low Reynolds numbers J Phys Soc Jpn 11 3 1956 302 307
34. Y.Q. Huang, J. Deng, and A.L. Ren Research on lift and drag in unsteady viscous flow around circular cylinders J Zhejiang Univ Sci A 37 5 2003 596 601
35. B.F. Armaly, F. Durst, J.C.F. Pereira, and B. Schonung Experimental and theoretical investigation of backward-facing step flow J Fluid Mech 127 1982 473 496
36. B.N. Jiang A least-squares finite element method for incompressible Navier-Stokes problems Int J Numer Methods fluids 14 1992 843 859
37. Song CX, Liu GR, Li H, Xu GX. A Meshfree smoothed least-squares (SLS) method for simulating steady incompressible viscous flows. Int Numer Methods Fluids; submitted for publication.
38. U. Ghia, K.N. Ghia, and C.T. Shin High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method J Comput Phys 3 1982 217 231
39. C.H. K Williamson Defining a universal and continuous Strouhal Reynolds number relationship for the laminar vortex shedding of a circular cylinder Phys Fluids 31 1988 2742 2744
40. Relf EF. Discussion of results of measurements of the resistance of wires, with some additional tests on the resistance of wires of small diameter, Technical Report 102. The advisory committee for aeronautics; 1915.
41. Belov A, Jameson A, Martinelli L. A new implicit algorithm with multigrid for unsteady incompressible flow calculations. AIAA Paper 95-0049; 1995.
42. Lin PT. Two-dimensional implicit time dependent calculation for incompressible flows on adaptive unstructured meshes. Princeton University, PhD thesis; 2001.
43. Ahn HT. A new incompressible Navier-Stokes method with general hybrid meshes and its application to flow/structure interactions. University of Texas at Austin, PhD thesis; 2005.