A non-hybrid method for the PDF equations of turbulent flows on unstructured grids

Journal of Computational Physics

Volumn 227, Issue 11, 2008, Pages 5896-5935

  Bakosi, J ^a   Franzese, P ^a   Boybeyi, Z ^a  

^a GEORGE MASON UNIVERSITY   (United States)

Author keywords

Finite element method; Langevin equation; Monte Carlo method; Particle tracking; Particle in cell method; Probability density function method; Scalar dispersion; Turbulent flow; Unstructured grids

Indexed keywords

ADAPTIVE ALGORITHMS; CHANNEL FLOW; DIFFERENTIAL EQUATIONS; DISPERSIONS; FINITE ELEMENT METHOD; PROBABILITY DENSITY FUNCTION; REYNOLDS NUMBER; STOCHASTIC SYSTEMS; TURBULENT FLOW; WALL FLOW;

FUNCTION EQUATIONS; JOINT PROBABILITY DENSITY FUNCTION; LANGEVIN EQUATION; MONTECARLO METHODS; PARTICLE IN CELL METHOD; PARTICLE TRACKING; PASSIVE SCALARS; PROBABILITY DENSITY FUNCTION METHOD; SCALAR DISPERSION; UNSTRUCTURED GRID;

MONTE CARLO METHODS;

EID: 42649104057     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.02.024     Document Type: Article

References (87)

1. T.S. Lundgren Model equation for nonhomogeneous turbulence Phys. Fluids 12 3 1969 485 497
2. S.B. Pope PDF methods for turbulent reactive flows Prog. Energy Combust. 11 1985 119 192
3. C. Dopazo Recent developments in pdf methods P.A. Libby Turbulent Reactive Flows 1994 Academic New York
4. W.P. Jones B.E. Launder The prediction of laminarization with a two-equation model of turbulence Int. J. Heat Mass Tran. 15 2 1972 301 314
5. J.C. Rotta Statistiche theorie nichthomogener turbulenz Z. Phys. 129 1951 547
6. B.E. Launder G.J. Reece W. Rodi Progress in the development of a Reynolds-stress turbulent closure J. Fluid Mech. 68 1975 537
7. K. Hanjalić B.E. Launder A Reynolds stress model of turbulence and its application to thin shear flows J. Fluid Mech. 52 1972 609 638
8. C.G. Speziale S. Sarkar T.B. Gatski Modelling the pressure-strain correlation of turbulence: an invariant dynamical systems approach J. Fluid Mech. 227 1991 245 272
9. S.B. Pope Computations of turbulent combustion: progress and challenges Proc. Combust. Inst. 23 1990 591 612
10. Q. Tang J. Xu S.B. Pope Probability density function calculations of local extinction and NO production in piloted-jet turbulent methane/air flames P. Combust. Inst. 28 2000 133 192
11. J. Xu S.B. Pope PDF calculations of turbulent nonpremixed flames with local extinction Combust. Flame 123 2000 281 307
12. S. James, M.S. Anand, S.B. Pope, The Lagrangian pdf transport method for simulations of gas turbine combustor flows, AIAA Paper (2002-4017).
13. S. Subramaniam D.C. Haworth A probability density function method for turbulent mixing and combustion on three-dimensional unstructured deforming meshes Int. J. Engine Res. 1 2 2000 171 190
14. S. Heinz Connections between Lagrangian stochastic models and the closure theory of turbulence for stratified flows Int. J. Heat Fluid Flow 19 1998 193 200
15. M. Cassiani P. Franzese U. Giostra A PDF micromixing model of dispersion for atmospheric flow. Part II: application to convective boundary layer Atmos. Environ. 39 8 2005 1471 1479
16. R. Löhner Applied CFD Techniques: An Introduction Based on Finite Element Methods 2001 John Wiley UK
17. D.P. Bacon N.N. Ahmad Z. Boybeyi T.J. Dunn M.S. Hall P.C.S. Lee R.A. Sarma M.D. Turner K.T. Waight S.H. Young J.W. Zack A dynamically adapting weather and dispersion model: the operational multiscale environment model with grid adaptivity (OMEGA) Mon. Weather Rev. 128 2000 2044 2076
18. R. Löhner, Advances in unstructured grid generation, in: ECCOMAS 2000, 2000.
19. A. Shostko, R. Löhner, Parallel 3-D H-refinement, AIAA-95-1662-CP, 1995.
20. M. Muradoglu P. Jenny S.B. Pope D.A. Caughey A consistent hybrid finite-volume/particle method for the PDF equations of turbulent reactive flows J. Comput. Phys. 154 1999 342 371
21. P. Jenny S.B. Pope M. Muradoglu D.A. Caughey A hybrid algorithm for the joint PDF equation of turbulent reactive flows J. Comput. Phys. 166 2001 218 252
22. P. Givi, Model free simulations of turbulent reactive flows, Prog. Energy Combust. 15 (1989).
23. C.K. Madnia P. Givi Direct numerical simulation and large eddy simulation of reacting homogeneous turbulence B. Galperin S.A. Orszag Large Eddy Simulations of Complex Engineering and Geophysical Flows 1993 Cambridge University Press 315 346
24. P.J. Colucci F.A. Jaberi P. Givi S.B. Pope Filtered density function for large eddy simulation of turbulent reacting flows Phys. Fluids 10 2 1998 499 515
25. L.Y.M. Gicquel P. Givi F.A. Jaberi S.B. Pope Velocity filtered density function for large eddy simulation of turbulent flows Phys. Fluids 14 3 2002 1196 1213
26. M.R.H. Sheikhi T.G. Drozda P. Givi S.B. Pope Velocity-scalar filtered density function for large eddy simulation of turbulent flows Phys. Fluids 15 8 2003 2321 2337
27. M. Muradoglu S.B. Pope D.A. Caughey The hybrid method for the PDF equations of turbulent reactive flows: consistency conditions and correction algorithms J. Comput. Phys. 172 2001 841 878
28. Y.Z. Zhang D.C. Haworth A general mass consistency algorithm for hybrid particle/finite-volume PDF methods J. Comput. Phys. 194 2004 156 193
29. B. Rembold P. Jenny A multiblock joint pdf finite-volume hybrid algorithm for the computation of turbulent flows in complex geometries J. Comput. Phys. 220 2006 59 87
30. D.C. Haworth S.B. Pope A generalized Langevin model for turbulent flows Phys. Fluids 29 2 1986 387 405
31. S.B. Pope On the relationship between stochastic Lagrangian models of turbulence and second-moment closures Phys. Fluids 6 2 1994 973 985
32. E.R. van Driest On the turbulent flow near a wall J. Aeronaut. Sci. 23 11 1956 1007 1011
33. Y.G. Lai R.M.C. So On near wall turbulent flow modelling J. Fluid Mech. 221 1990 641 673
34. T.J. Craft B.E. Launder Reynolds stress closure designed for complex geometries Int. J. Heat Fluid Flow 17 1996 245 254
35. Low Reynolds number k-ε modelling with the aid of direct numerical simulation data
36. B.E. Launder D.B. Spalding The numerical computation of turbulent flows Comput. Meth. Appl. M. 3 1974 269 289
37. Predictions of two-dimensional boundary layers with the aid of the k-ε model of turbulence
38. W. Rodi, Turbulence Models and Their Application in Hydraulics – A State-of-the-art Review, International Association for Hydraulics Research, Delft, The Netherlands, 1980.
39. D.B. Spalding, GENMIX – A General Computer Program for Two-Dimensional Parabolic Phenomena, International Association for Hydraulics Research, 1977.
40. P.A. Durbin A Reynolds stress model for near-wall turbulence J. Fluid Mech. 249 1993 465 498
41. T.D. Dreeben S.B. Pope Probability density function/Monte Carlo simulation of near-wall turbulent flows J. Fluid Mech. 357 1998 141 166
42. T.D. Dreeben S.B. Pope Wall-function treatment in pdf methods for turbulent flows Phys. Fluids 9 9 1997 2692 2703
43. Z. Warhaft Passive scalars in turbulent flows Annu. Rev. Fluid Mech. 32 2000 203 240
44. U. Karnik S. Tavoularis Measurements of heat diffusion from a continuous line source in a uniformly sheared turbulent flow J. Fluid Mech. 202 1989 233 261
45. S.B. Pope Turbulent Flows 2000 Cambridge University Press Cambridge
46. N.G. van Kampen Stochastic Processes in Physics and Chemistry second ed. 2004 North Holland, Elsevier B.V. Amsterdam, The Netherlands
47. P. Langevin Sur la théorie du mouvement Brownien Comptes Rendus Acad. Sci., Paris 146 1908 530 533
48. S.B. Pope Ten questions concerning the large-eddy simulation of turbulent flows New J. Phys. 6 35 2004 1 24
49. T.D. Dreeben S.B. Pope Probability density function and Reynolds-stress modeling of near-wall turbulent flows Phys. Fluids 9 1 1997 154 163
50. C.W. Gardiner Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences third ed. 2004 Springer-Verlag Berlin Heidelberg, New York
51. V. Whizman D. Laurence M. Kanniche P.A. Durbin A. Demuren Modeling near-wall effects in second-moment closures by elliptic relaxation Int. J. Heat Fluid Flow 17 1996 255 266
52. P.R. van Slooten Jayesh S.B. Pope Advances in PDF modeling for inhomogeneous turbulent flows Phys. Fluids 10 1 1998 246 265
53. S.B. Pope The vanishing effect of molecular diffusivity on turbulent dispersion: implications for turbulent mixing and the scalar flux J. Fluid Mech. 359 1998 299 312
54. J. Villermaux J.C. Devillon Représentation de la coalescence et de la redispersion des domaines de ségrégation dans un fluide par un modèle d’interaction phénoménologique Proceedings of the Second International Symposium on Chemical Reaction Engineering 1972 Elsevier New York 1 13
55. C. Dopazo E.E. O’Brien An approach to the autoignition of a turbulent mixture Acta Astronaut. 1 1974 1239 1266
56. R.O. Fox On velocity-conditioned scalar mixing in homogeneous turbulence Phys. Fluids 8 10 1996 2678 2691
57. J. Bakosi P. Franzese Z. Boybeyi Probability density function modeling of scalar mixing from concentrated sources in turbulent channel flow Phys. Fluids 19 11 2007 115106
58. P.E. Kloeden E. Platen Numerical Solution of Stochastic Differential Equations 1999 Springer Berlin
59. R. Courant K. Friedrichs H. Lewy Über die partiellen differenzengleichungen der mathematischen physik Mathe. Ann. 100 1 1928 32 74
60. R.O. Fox Computational Models for Turbulent Reacting Flows 2003 Cambridge University Press
61. S.M. Correa, S.B. Pope, Comparison of a Monte Carlo PDF/finite-volume mean flow model with bluff-body raman data, in: Twenty-fourth Symposium (International) on Combustion, Pittsburgh, PA: The Combustion Institute, 1992, pp. 279–285.
62. B.J. Delarue S.B. Pope Application of PDF methods to compressible turbulent flows Phys. Fluids 9 9 1997 2704 2715
63. A.J. Chorin Numerical solution of the Navier–Stokes equations Math. Comput. 22 1968 745 762
64. Y. Saad Iterative Methods for Sparse Linear Systems second ed. 2003 Society for Industrial and Applied Mathematics Philadelphia
65. Y.N. Grigoryev V.A. Vshivkov M.P. Fedoruk Numerical “Particle-in-cell” Methods: Theory and Applications 2002 Utrecht Boston
66. R. Löhner Robust, vectorized search algorithms for interpolation on unstructured grids J. Comput. Phys. 118 1995 380 387
67. S.B. Pope Particle method for turbulent flows: integration of stochastic model equations J. Comput. Phys. 117 1995 332 349
68. M. Cassiani A. Radicchi J.D. Albertson U. Giostra An efficient algorithm for scalar PDF modelling in incompressible turbulent flow; numerical analysis with evaluation of IEM and IECM micro-mixing models J. Comput. Phys. 223 2007 519 550
69. J. Xu, S.B. Pope, Analysis of numerical errors in solving particle Langevin equations, Technical Report FDA 97–07, Cornell University, 1997.
70. L. Arnold Stochastic Differential Equations: Theory and Applications 1974 Krieger Publishing Company
71. I. Karatzas S.E. Shreve Brownian Motion and Stochastic Calculus second ed. 1991 Springer
72. M. Mascagni Some methods of parallel pseudorandom number generation R. Schreiber M. Heath A. Ranade Proceedings of the IMA Workshop on Algorithms for Parallel Processing 1997 Springer-Verlag
73. K. Entacher A. Uhl S. Wegenkittl Linear congruential generators for parallel Monte-Carlo: the Leap-Frog case Monte Carlo Methods Appl. 4 1 1998 1 16
74. F. Camelli, R. Löhner, E.L. Mestreau, Timings of an unstructured-grid CFD code on common hardware platforms and compilers, AIAA-07-1107, 2007.
75. Direct numerical simulation of turbulent channel flow up to Reτ=590
76. K. Iwamoto Y. Suzuki N. Kasagi Reynolds number effect on wall turbulence: toward effective feedback control Int. J. Heat Fluid Flow 23 2002 678 689
77. Surface heat-flux fluctuations in a turbulent channel flow up to Reτ=1020 with Pr=0.025 and 0.71
78. M. Wacławczyk J. Pozorski J.-P. Minier Probability density function computation of turbulent flows with a new near-wall model Phys. Fluids 16 5 2004 1410 1422
79. G.I. Taylor Diffusion by continuous movements P. Lond. Math. Soc. 20 1921 196 211
80. R.A. Lavertu L. Mydlarski Scalar mixing from a concentrated source in turbulent channel flow J. Fluid Mech. 528 2005 135 172
81. B.L. Sawford Conditional scalar mixing statistics in homogeneous isotropic turbulence New J. Phys. 6 55 2004 1 30
82. W.C. Reynolds The potential and limitations of direct and large eddy simulations J.L. Lumley Whither Turbulence? Turbulence at the Crossroads 1990 Springer-Verlag Berlin 313 343
83. R.N. Meroney M. Pavageau S. Rafailidis M. Schatzmann Study of line source characteristics for 2-d physical modelling of pollutant dispersion in street canyons J. Wind Eng. Ind. Aerod. 62 1 1996 37 56
84. C.-H. Liu M.C. Barth Large-eddy simulation of flow and scalar transport in a modeled street canyon J. Appl. Meteorol. 41 6 2002 660 673
85. C. Geuzaine, J. Remacle, Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities, (2006).
86. M. Pavageau, Concentration fluctuations in urban street canyons – groundwork for future studies, Technical Report, Meteorological Institute of the University of Hamburg, 1996.
87. M. Pavageau M. Schatzmann Wind tunnel measurements of concentration fluctuations in an urban street canyon Atmos. Environ. 33 1999 3961 3971