Comparison of simple- and piso-type algorithms for transient flows

International Journal for Numerical Methods in Fluids

Volumn 26, Issue 4, 1998, Pages 459-483

  Barton, I E ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

PISO algorithm; SIMPLE algorithm; Unsteady incompressible flow

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; CYLINDERS (CONTAINERS); LAMINAR FLOW; UNSTEADY FLOW;

PRESSURE IMPLICIT WITH SPLITTING OF OPERATORS (PISO) ALGORITHMS; SEMI IMPLICIT METHOD FOR PRESSURE LINKED (SIMPLE) ALGORITHMS; UNSTEADY INCOMPRESSIBLE FLOW;

COMPUTATIONAL FLUID DYNAMICS;

ALGORITHM; COMPRESSIBLE FLOW; PRESSURE;

ALGORITHMS; FLUID FLOW; INCOMPRESSIBLE; UNSTEADY FLOW;

EID: 0032005658     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0363(19980228)26:4<459::AID-FLD645>3.0.CO;2-U     Document Type: Review

References (77)

1. F. H. Harlow and J. E. Welch, 'Numerical calculations of time-dependent viscous incompressible flow of fluid with free surface', Phys. Fluids, 8, 2182-2189 (1965).
2. 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, 1787-1806 (1972).
3. L. S. Caretto, A. D. Gosman, S. V. Patankar and D. B. Spalding, 'Two calculation procedures for steady, three-dimensional flows with recirculation', Proc. 3rd Int. Conf. on Numerical Methods in Fluid Dynamics, Paris, 1972.
4. G. D. Raithby and G. E. Schneider, 'Numerical solution of problems in incompressible fluid flow: treatment of the velocity-pressure coupling', Numer. Heat Transfer, 2, 417-440 (1979).
5. S. V. Patankar, Numerical Heat Transfer and fluid Flow, Hemisphere, Washington, DC, 1980.
6. J. P. Van Doormaal and G. D. Raithby, 'Enhancements of the SIMPLE method for predicting incompressible fluid flows', Numer. Heat Transfer, 7, 147-163 (1984).
7. R. I. Issa, 'Solution of the implicitly discretized fluid flow equations by operator-splitting', J. Comput. Phys., 62, 40-65 (1985).
8. R. I. Issa, B. Ahmadi-Befrui, K. R. Beshay and A. D. Gosman, 'Solution of the implicitly discretized reacting flow equations by operator-splitting', J. Comput. Phys., 93, 388-410 (1991).
9. A Wanik and U. Schnell, 'Some remarks on the PISO and SIMPLE algorithms for steady turbulent flow problems', Comput. Fluids, 17, 555-570 (1989).
10. S. W. Kim and T. J. Benson, 'Comparison of the SMAC, PISO and iterative time-advancing schemes for unsteady flows', Comput. Fluids, 21, 435-454 (1992).
11. L. Cheng and S. Armfield, 'A simplified marker and cell method for unsteady flows on non-staggered grids', Int. j. numer. meth. fluids, 21, 15-34 (1995).
12. P. F. Galpin, J. P. Van Doormaal and G. D. Raithby. 'Solution of the incompressible mass and momentum equations by application of a coupled equation line solver', Int. j. numer. meth. fluids, 5, 615-625 (1985).
13. L. Guoyan, 'A numerical method of solving two-phase fluid flow', in Cheung, Lee and Leung (eds), Computational Mechanics, Balkema, Rotterdam, 1991, pp. 1589-1594.
14. S. L. Lee and R. Y. Tzong, 'Artificial pressure for pressure-linked equation', Int. J. Heat Mass Transfer, 35, 2705-2716 (1992).
15. J. P. Van Doormaal and G. D. Raithby, 'An evaluation of the segregated approach for predicting incompressible fluid flows', ASME Paper 85-HT-9, 1985.
16. C. A. J. Fletcher, Computational Techniques for Fluid Dynamics, Vol. II. Springer, New York, 1988.
17. B. Lakshminarayana, 'An assessment of computational fluid dynamic techniques in the analysis and design of turbomachinery - the 1990 Freeman scholar lecture'. Trans. ASME, J. Fluids Engng., 113, 315-352 (1991).
18. J. Simoneau and A. Pollard, 'Finite volume methods for laminar and turbulent flows using a penalty function approach', Int. j. numer. meth. fluids, 18, 733-746 (1994).
19. J. J. McGuirk and J. M. L. M. Palma, 'The efficiency of alternative pressure-correction formulations for incompressible turbulent flow problems', Comput. Fluids, 22, 77-87 (1993).
20. H. Ströll, F. Durst, M. Peric, J. C. F. Pereira and G. Scheuerer, 'Study of laminar, unsteady piston-cylinder flows', Trans. ASME, J. Fluids Engng., 115, 687-693 (1993).
21. I. E. Barton, 'A numerical investigation of incompressible dilute particulate flows', Ph.D. Thesis, Aerospace Division, School of Engineering, University of Manchester, 1995.
22. W. Shyy, 'A study of finite difference approximations to steady-state, convection-dominated flow problems', J. Comput. Phys., 57, 415-438 (1985).
23. I. E. Barton, 'Laminar flow past an enclosed and open backward-facing step', Phys. Fluids A. 6, 4054-4056 (1994).
24. I. E. Barton, 'A numerical study of flow over a confined backward-facing step', Int. j. numer. meth. fluids, 21, 653-665 (1995).
25. I. E. Barton, 'The computation of the entrance effect for laminar flow over a backward-facing step', Int. j. numer. meth. fluids, in press.
26. S. V. Patankar, 'A calculation procedure for two-dimensional elliptic situations', Numer. Heat Transfer, 4, 409-425 (1981).
27. D. M. Wang, A. P. Watkins and R. S. Cant, 'Three-dimensional diesel engine combustion simulation with a modified EPISO procedure', Numer. Heat Transfer A, 24, 249-272 (1993).
28. G. D. Thiart, 'Finite difference scheme for the numerical solution of fluid flow and heat transfer problems on non-staggered grids', Numer. Heat Transfer B, 17, 43-62 (1990).
29. C. Y. Perng and R. L. Street. 'Three-dimensional unsteady flow simulations: alternative strategies for a volume averaged calculation', Int. j. numer. meth. fluids, 9, 341-362 (1989).
30. W. Shyy and C. S. Sun, 'Development of a pressure-correction/staggered-grid based multigrid solver for incompressible recirculating flows', Comput. Fluids, 22, 51-76 (1993).
31. C. R. Maliska and G. D. Raithby, 'A method for computing three-dimensional flows using non-orthogonal boundary-fitted co-ordinates', Int. j. numer. meth. fluids, 4, 519-537 (1984).
32. P. Tamamidis and D. N. Assanis, 'Prediction of three-dimensional steady incompressible flows using body-fitted co-ordinates', Trans. ASME, J. Fluids Engng., 115, 457-462 (1993).
33. M. M. Grigor'ev, 'A boundary element formulation using the SIMPLE method', Int. j. numer. meth. fluids, 16, 549-579 (1993).
34. B. R. Latimer and A. Pollard, 'Comparison of pressure-velocity coupling solution algorithms', Numer. Heat Transfer, 8, 635-652 (1985).
35. S. V. Patankar, 'Recent developments in computational heat transfer', Trans. ASME, J. Heat Transfer, 110, 1037-1045 (1988).
36. D. M. Wang and A. P. Watkins, 'Numerical modelling of diesel spray wall impaction phenomena', Int. J. Heat Fluid Flow, 14, 301-312 (1993).
37. W. K. Chow and N. K. Fong, 'Application of field modelling technique to simulate interaction of sprinkler and fire-induced smoke layer', Combust. Sci. Technol., 89, 101-151 (1993).
38. P. Luchini and A. D'Alascio, 'Multigrid pressure correction techniques for the computation of quasi-incompressible internal flows', Int. j. numer. meth. fluids, 18, 489-507 (1994).
39. J. K. Dukowicz. 'A particle-fluid numerical model for liquid sprays', J. Comput. Phys., 35, 229-253 (1980).
40. D. A. Anderson, J. C. Tannehill and R. H. Pletcher, Computational Fluid Mechanics and Heat Transfer, Hemisphere, Washington, DC, 1984.
41. C. Hirsch, Numerical Computation of Internal and External Flows, Vol. 1, Fundamentals of Numerical Discretization, Wiley, Chichester, 1988.
42. H. C. Lowe, Fluid Mechanics, Macmillan, London, 1979.
43. R. W. Davis, E. F. Moore and L. P. Purtell, 'A numerical-experimental study of confined flow around rectangular cylinders', Phys. Fluids, 27, 46-59 (1984).
44. T. Yoshida, I. Nakamura and T. Watanabe, 'Effect of boundary conditions and finite difference schemes on the numerical analysis of a flow past a square cylinder', Trans. JSME, 59B, 374-381 (1993).
45. I. Nakamura, T. Watanabe and T. Yoshida, 'On the numerical outflow boundary condition of the viscous flow around a square cylinder', Mem. School Engng., Nagoya Univ., 45, 105-117 (1993).
46. P. M. Gresho and S. T. Chan, 'On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part 2: Implementation', Int. j. numer. meth. fluids, 11, 621-659 (1990).
47. B. Ramaswamy, 'Theory and implementation of a semi-implicit finite element method for viscous incompressible flow', Comput. Fluids, 22, 725-747 (1993).
48. R. W. Davis and E. F. Moore, 'A numerical study of vortex shedding from rectangles', J. Fluid Mech., 116, 475-506 (1982).
49. A. Okajima, 'Strouhal numbers of rectangular cylinders', J. Fluid Mech., 123, 379-398 (1982).
50. A. Okajima, 'Numerical simulation of flow around rectangular cylinders', J. Wind Engng. Ind. Aerodyn., 33, 171-180 (1990).
51. G. C. Buscaglia and E. A. Dari, 'Implementation of the Lagrange-Galerkin method for the incompressible Navier-Stokes equations', Int. j. numer. meth. fluids, 15, 23-36 (1992).
52. M. P. Arnal, D. J. Goering and J. A. C. Humphrey, 'Vortex shedding from a bluff body adjacent to a plane sliding wall', Trans. ASME, J. Fluids Engng., 113, 384-398 (1991).
53. J. E. Fromm and F. H. Harlow, 'Numerical solution of the problem of vortex street development', Phys. Fluids, 6, 975-982 (1963).
54. K. M. Kelkar and S. V. Patankar, 'Numerical prediction of vortex shedding behind a square cylinder', Int. j. numer. meth. fluids, 14, 327-341 (1992).
55. D. B. Spalding, 'A novel finite difference formulation for differential expressions involving both first and second derivatives', Int. j. numer. meth. engng., 4, 551-559 (1972).
56. M. K. Patel and N. C. Markatos, 'An evaluation of eight discretization schemes for two-dimensional convection-diffusion equations', Int. j. numer. meth. fluids, 6, 129-154 (1986).
57. M. K. Patel, N. C. Markatos and M. Cross. 'A critical evaluation of seven discretization schemes for convection-diffusion equations', Int. j. numer. meth. fluids, 5, 225-244 (1985).
58. H. Laschefski, D. Braes, H. Hank and N. K. Mitre, 'Numerical investigations of radial jet reattachment flows', Int. j. numer. meth. fluids, 18, 629-646 (1994).
59. B. J. Vickery, 'Fluctuating lift and drag on a long cylinder of square cross-section in a smooth and in a turbulent stream', J. Fluid Mech., 25, 481-494 (1966).
60. B. P. Leonard, 'A stable and accurate convective modelling procedure based on quadratic upstream interpolation', Comput. Meth. Appl. Mech. Engng., 19, 59-98 (1979).
61. B. F. Armaly, F. Durst, J. C. F. Pereira and B. Schönung, 'Experimental and theoretical investigation of backward-facing step flow', J. Fluid Mech., 127, 473-496 (1983).
62. P. M. Gresho, 'Letter to the editor', Numer. Heat Transfer A, 20, 123 (1991).
63. P. M. Gresho, D. K. Gartling, J. R. Torczynski, K. A. Cliffe, K. H. Winters, T. J. Garrat, A. Spence and J. W. Goodrich, 'Is the steady viscous incompressible two-dimensional flow over a backward-facing step at Re = 800 stable?', Int. j. numer. meth. fluids, 17, 501-541 (1993).
64. J. Kim and P. Moin, 'Application of a fractional step method to incompressible Navier-Stokes equations', J. Comput. Phys., 59, 308-323 (1985).
65. S. C. Caruso, J. H. Ferziger and J. Oliger, 'Adaptive grid techniques for elliptic fluid flow problems', AIAA Paper 86-0498, 1986.
66. P. Orlandi, 'Vorticity-velocity formulation for high Re flows', Comput. Fluids, 15, 137-149 (1987).
67. A. K. Runchal, 'CONDIF: a modified central-differencing scheme for convective flows', Int. j. numer. meth. engng., 24, 1593-1608 (1987).
68. F. Durst and J. C. F. Periera, 'Time-dependent laminar backward-facing step flow in a two-dimensional duct', Trans. ASME, J. Fluids Engng., 110, 289-296 (1988).
69. G. Guj and F. Stella, 'Numerical solutions of high-Re recirculating flows in vorticity-velocity form', Int. j. numer. meth. fluids, 8, 405-416 (1988).
70. J. L. Sohn, 'Evaluation of FIDAP on some classical laminar and turbulent benchmarks', Int. j. numer. meth. fluids, 8, 1469-1490 (1988).
71. S. Thangam and D. D. Knight, 'Effect of stepheight on the separated flow past a backward-facing step', Phys. Fluids A, 1, 604-606 (1989).
72. S. Thangam and D. D. Knight, 'A computational scheme in generalized co-ordinates for viscous incompressible flows', Comput. Fluids, 18, 317-327 (1990).
73. J. T. Lin, B. F. Armaly and T. S. Chen, 'Mixed convection heat transfer in inclined backward-facing step flows', Int. J. Heat Mass Transfer, 34, 1568-1571 (1991).
74. T. Kondoh, Y. Nagano and T. Tsuji, 'Computational study of laminar heat transfer downstream of a backward-facing step', Int. J. Heat Mass Transfer, 36, 577-591 (1993).
75. A. Pollard, personal communication, 1986.
76. D. K. Gartling, 'A test problem for outflow boundary conditions - flow over a backward-facing step', Int. j. numer. meth. fluids, 11, 953-967 (1990).
77. R. L. Sani and P. M. Gresho, 'Résumé and remarks on the open boundary condition minisymposium', Int. j. numer. meth. fluids, 18, 983-1008 (1994).