A numerical comparison of outflow boundary conditions for spectral element simulations of incompressible flows

Communications in Computational Physics

Volumn 2, Issue 3, 2007, Pages 477-500

  Xu, Chuanju ^a   Lin, Yumin ^a  

^a XIAMEN UNIVERSITY   (China)

Author keywords

Incompressible flows; Outflow boundary conditions; Spectral element methods

Indexed keywords

EID: 35348847479     PISSN: 18152406     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (42)

1. A. Bottaro, Note on open boundary conditions for elliptic flows, Numer. Heat Tr. B - Fund., 18 (1990), 243-256.
2. W. Z. Bao and H. D. Han, Local artificial boundary conditions for the incompressible viscous flow in a slip channel, J. Comput. Math., 15(4) (1997),335-344.
3. C. Bernardi and Y. Maday, Approximations Spectrales de Problèmes aux Limites Elliptiques, Springer-Verlag, Paris, 1992.
4. C. Canuto, M. Y. Hussaini, A. Quarteroni and Z. A. Zang, Spectral Methods in Fluid Dynamics, Springer, New York, Berlin, Heidelberg, London, Paris, Tokyo, 1987.
5. J. Cahouet and J. P, Chabard, Some fast 3d finite elements solvers for the generalized Stokes problem, Int. J. Numer. Meth. Fluids, 8(1988), 869-895.
6. W. Couzy and M. O. Deville, A fast Schur complement method for the spectral element discretization of the incompressible Navier-Stokes equations, J. Comput. Phys., 116 (1995), 135-142.
7. G. Evans and S. Paolucci, The thermoconvective instability of a plane Poiseuille flow heated from below: a proposed benchmark solution for open boundary flows, Int. J. Numer. Meth. Fluids, 11 (1990), 1001-1013.
8. P. Fischer, An overlapping Schwarz method for spectral element solution of the incompressible Navier-Stokes equations, J. Comput. Phys., 133(1997), 84-101.
9. M. Y. Forestier, R. Pasquetti and R. Peyret, Calculation of 3D wakes in stratified fluids, in the CD of the ECCOMAS 2000 Congress, Barcelona.
10. M. Y. Forestier, R. Pasquetti, R. Peyret and C. Sabbah, Spatial development of wakes using a spectral multi-domain method, Appl. Numer. Math., 3 (2000), 207-216.
11. D. F. Griffiths, The 'no boundary condition' outflow boundary condition, Int. J. Numer. Meth. Fluids, 24 (1997), 393-411.
12. N. K. Ghaddar, G. E. Karniadakis and A. T. Patera, A conservative isoparametric spectral element method for forced convection; Application to fully developed flow in periodic geometries, Numer. Heat Transfer, 9 (1986), 277-300.
13. J. L. Guermond, P. Minev and J. Shen, Error analysis of pressure-correction schemes for the time-dependent Stokes equations with open boundary conditions, SIAM J. Numer. Anal., 43 (2005), 239-258.
14. J. L. Guermond and J. Shen, On the error estimates for the rotational pressure-correction projection methods, Math. Comput., 73 (2004), 1719-1737.
15. F. H. Huang and C. J. Xu, On the error estimates for the rotational pressure-correction projection spectral methods for the unsteady Stokes equations, J. Comput. Math., 23(3) (2005), 285-304.
16. B. C. V. Johansson, Boundary conditions for open boundaries for the boundaries for the incompressible Navier-Stokes equations, J. Comput. Phys., 105 (1993), 233-251.
17. M. H. Kobayashi, J. C. F. Pereira and J. M. M. Sousa, Comparison of several open boundary numerical treatments for laminar recirculating flows, Int. J. Numer. Meth. Fluids, 16 (1993), 403-419.
18. D= 3900, Phys. Fluids, 12(2) (2000), 403-417.
19. Y. M. Lin and C. J. Xu, A fractional step method for the unsteady viscous/inviscid coupled equations, in: Y. Lu, W. Sun and T. Tang (Eds.), Advances in Scientific Computing and Applications, Science Press, Beijing/New York, 2004, pp. 286-294.
20. J. M. Luijkx, J. K. Platten and J. C. Legros, On the existence of thermoconvective rolls, transverse to a superimposed mean Poiseuille flow, Int. J. Heat Mass Tran., 24 (1981), 803-817.
21. Y. Maday, D. Meiron, A. T. Patera and E. M. Ronquist, Analysis of iterative methods for the steady and unsteady Stokes problem: Application to spectral element discretization, SIAM J. Sci. Comput., 14(2) (1993), 310-337.
22. Y. Maday and A. T. Patera, Spectral element methods for the Navier-Stokes equations, in: A. K. Noor (Ed.), State-of-the-Art Surveys in Computational Machanics, ASME, New York, 1988, pp. 71-143.
23. Y. Maday, A. T. Patera and E. M. Ronquist, An operator integration-factor splitting method for time-dependent problems: Application to incompressible fluid flow, J. Sci. Comput., 5 (1990), 263-292.
24. S. Mittal, Computation of three-dimensional flows past circular cylinder of low aspect ratio, Phys. Fluids, 13(1) (2001), 177-191.
25. J. Nordstrom, Accurate solutions of the Navier-Stokes equations despite unknown outflow boundary data, J. Comput. Phys., 120 (1995), 184-205.
26. X. Nicolas, P. Traore, A. Mojtabi and J. P. Caltagirone, Augmented Lagrangian method and open boundary conditions in 2D simulation of Poiseuille-Bénard channel flow, Int. J. Numer. Meth. Fluids, 25 (1997), 265-283.
27. I. Orlanski, A simple boundary condition for unbounded hyperbolic flows, J. Comput. Phys., 21 (1976), 251-269.
28. M. T. Ouazzani, J. P. Caltagirone, G. Meyer and A. Mojtabi, Etude numérique et expérimentale de la convection mixte entre deux plans horizontaux à températures différentes, Int. J. Heat Mass Tran., 32 (1989), 261-269.
29. S. A. Orszag, M. Israeli and M. O. Deville, Boundary condition for incompressible flows, J. Sci. Comput., 1 (1986), 75-111.
30. M. T. Ouazzani, J. K. Platten and A. Mojtabi, Etude expérimentale de la convection mixte entre deux plans horizontaux à températures différentes-2, Int. J. Heat Mass Tran., 33 (1990), 1417-1427.
31. R. Pasquetti and C. J. Xu, High-order algorithms for large-eddy simulation of incompressible flows, J. Sci. Comput., 17(1-3) (2002), 297-309.
32. A. T. Patera, A Spectral element method for fluid dynamics; laminar flow in a channel expansion, J. Comput. Phys., 54 (1984), 468-488.
33. J. B. Perot, An analysis of the fractional step method, J. Comput. Phys., 108 (1993), 51-58.
34. T. C. Papanastasiou, M. Malamataris and K. Ellwood, A new outflow boundary condition, Int. J. Numer. Meth. Fluids, 14 (1992), 587-608.
35. E. Schroder and K. Buhler, Three-dimensional convection in rectangular domains with horizontal throughflow, Int. J. Heat Mass Tran., 38 (1995), 1249-1259.
36. R. L. Sani and P. M. Gresho, Résumé and remarks on the open boundary condition minisymposium, Int. J. Numer. Meth. Fluids, 18 (1994), 983-1008.
37. Y. Sun, Z. J. Wang and Y. Liu, High-order multidomain spectral difference method for the Navier-Stokes equations on unstructured hexahedral grids, Commun. Comput. Phys., 2 (2007), 310-333.
38. C. H. K. Williamson, Vortex dynamics in the cylinder wake, Annu. Rev. Fluid Mech., 28 (1996), 477-539.
39. C. J. Xu and Y. M. Lin, Open boundary conditions for the spectral simulation of Poiseuille-Bénard flow, Acta Mech. Sinica, 32(1) (2000), 1-10, (in Chinese).
40. C. J. Xu and Y. M. Lin, Analysis of iterative methods for the viscous/ inviscid coupled problem via a spectral element approximation, Int. J. Numer. Meth. Fluids, 32 (2000), 619-646.
41. C. J. Xu and R. Pasquetti, On the efficiency of semi-implicit and semi-Lagrangian spectral methods for the calculation of incompressible flows, Int. J. Numer. Meth. Fluids, 35 (2001), 319-340.
42. M. M. Zdravkovich, Flow Around Circular Cylinders, Oxford University Press, New York, 1997.