Mathematical modeling for complex fluids and flows

Mathematical Modeling for Complex Fluids and Flows

Volumn 9783642252952, Issue , 2012, Pages 1-264

  Deville, Michel O ^a   Gatski, Thomas B ^b,c  

^a EPFL   (Switzerland)

^b UNIVERSITÉ DE POITIERS   (France)

^c OLD DOMINION UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOLTZMANN EQUATION; CONTINUUM MECHANICS; FOOD PROCESSING; NON NEWTONIAN LIQUIDS; POLYNOMIALS; TURBULENT FLOW; VISCOELASTICITY;

EMERGING TECHNOLOGIES; ENGINEERING PHYSICS; ENGINEERING PRACTITIONERS; FUNDAMENTAL CONCEPTS; LAMINAR AND TURBULENT FLOW; NON-NEWTONIAN FLUIDS; POLYNOMIAL REPRESENTATIONS; VIS-COELASTIC FLUIDS;

NON NEWTONIAN FLOW;

EID: 84949178460     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-642-25295-2     Document Type: Book

References (325)

1. Abid R, Speziale CG (1993) Predicting equilibrium states with Reynolds stress closures in channel flow and homogeneous shear flow. Phys Fluids A 5:1776-1782
2. Abramowitz M, Stegun IA (1972) Handbook of mathematical functions with formulas, graphs, and mathematical tables, 10th edn. Wiley, New York
3. Alvelius K (1999) Studies of turbulence and its modelling through large eddy-and direct numerical simulation. PhD thesis, Department of Mechanics, KTH, Stockholm, Sweden
4. Astarita G (1979) Objective and generally applicable criteria for flow classification. J Non-Newton Fluid Mech 6:69-76
5. Astarita G, Marucci G (1974) Principles of non-Newtonian fluid mechanics. McGraw-Hill, Maidenhead
6. Balakrishnan R (2004) An approach to entropy consistency in second-order hydrodynamic equations. J Fluid Mech 503:201-245
7. Bardina J, Ferziger JH, Reynolds WC (1980) Improved subgrid scale models for large eddy simulation. Paper no. 80-1357, AIAA
8. Barnes HA, Hutton JF, Walters K (1987) An introduction to rheology. Wiley, New York
9. Batchelor GK (1953) Homogeneous turbulence. Cambridge University Press, Cambridge
10. Benjamin TB (1978) Bifurcation phenomena in steady flows of a viscous fluid. II. Philos Trans R Soc A 359:27-43
11. Beris AN, Edwards BJ (1994) Thermodynamics of flowing systems with internal microstructure. Oxford University Press, New York
12. Berselli LC, Iliescu T, Layton WJ (2006) Mathematics of large eddy simulation of turbulent flows. Springer, Berlin
13. Bhatnagar PL, Gross EP, Krook M (1954) A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys Rev 94:511-525
14. Bingham EC (1916) An investigation of the laws of plastic flow. US Bur Stand Bull 13:309-353
15. Bird RB, Armstrong RC, Hassager O (1987a) Dynamics of polymeric liquids, vol 1: Fluid mechanics. Wiley, New York
16. Bird RB, Curtiss CF, Armstrong RC, Hassager O (1987b) Dynamics of polymeric liquids, vol 2: Kinetic theory. Wiley, New York
17. Boger DV, Walters K (1993) Rheological phenomena in focus. Elsevier, Amsterdam
18. Botsis J, Deville M (2006) Mécanique des milieux continus: une introduction. Presses Polytechniques et Universitaires Romandes, Lausanne
19. Boussinesq J (1877) Essai sur la théorie des eaux courantes. Mém Acad Sci Inst Fr 23:46-50
20. Bouzidi M, d'Humières D, Lallemand P, Luo L-S (2001) Lattice Boltzmann equation on a twodimensional rectangular grid. J Comput Phys 172:704-717
21. Burnett D (1935) The distribution of velocities and mean motion in a slight nonuniform gas. Proc Lond Math Soc 39:385-430
22. Carreau PJ (1972) Rheological equations from molecular network theories. Trans Soc Rheol 16:99-127
23. Cercignani C (1988) The Boltzmann equation and its applications. Springer, Berlin
24. Chandrasekhar S (1943) Stochastic problems in physics and astronomy. Rev Mod Phys 15:1-89
25. Chapman S, Cowling TG (1960) The mathematical theory of nonuniform gases. Cambridge University Press, Cambridge
26. Chen S, Doolen GD (1998) Lattice Boltzmann method for fluid flows. In: Annual review of fluid mechanics. Annual Reviews, New York, pp 329-364
27. Chilcott MD, Rallison JM (1988) Creeping flow of dilute polymer solutions past cylinders and spheres. J Non-Newton Fluid Mech 29:381-432
28. Chopard B, Falcone J-L, Latt J (2009) The lattice Boltzmann advection-diffusion model revisited. Eur Phys J 171:245-249
29. Chou PY (1945) On velocity correlations and the solutions of the equations of turbulent fluctuation. Q Appl Math 3:38-54
30. Coleman B, Markowitz H, Noll W (1966) Viscometric flows of non-Newtonian fluids. Springer Tracts in Natural Philosophy, vol 5. Springer, Berlin
31. Coleman BD, Noll JM (1960) An approximation theorem for functionals, with applications in continuum mechanics. Arch Ration Mech Anal 6:355-370
32. Coleman BD, Noll JM (1961) Recent results in the continuum theory of viscoelastic fluids. Ann NY Acad Sci 89:672-714
33. Coles D (1965) Transition in circular Couette flow. J Fluid Mech 21:385-425
34. Collyer AA, Fischer PJ (1976) The Kaye effect revisited. Nature 261:682
35. Cormack DE, Leal LG, Seinfeld JH (1978) An evaluation of mean Reynolds stress turbulence models: the triple velocity correlation. J Fluids Eng 100:47-54
36. Craft TJ, Launder BE (1996) A Reynolds stress closure designed for complex geometries. Int J Heat Fluid Flow 17:245-254
37. Craft TJ, Launder BE (2002) Closure modelling near the two-component limit. In: Launder B, Sandham N (eds) Closure strategies for turbulent and transitional flows. Cambridge University Press, Cambridge, pp 102-126
38. Craft TJ, Launder BE, Suga K (1996) Development and application of a cubic eddy-viscosity model of turbulence. Int J Heat Fluid Flow 17:108-115
39. Craft TJ, Launder BE, Suga K (1997) Prediction of turbulent transitional phenomena with a nonlinear eddy-viscosity model. Int J Heat Fluid Flow 18:15-28
40. Cross MM (1965) Rheology of non-Newtonian fluids: a new flow equation for pseudo-plastic systems. J Colloid Sci 20:417-437
41. Crow SC (1967) Visco-elastic character of fine-grained isotropic turbulence. Phys Fluids 10:1587-1589
42. Crow SC (1968) Visco-elastic properties of fine-grained incompressible turbulence. J Fluid Mech 33:1-20
43. Cruz DOA, Pinho FT (2003) Modeling the new stress for improved drag reduction predictions of viscoelastic pipe flow. J Non-Newton Fluid Mech 114:109-148
44. Cruz DOA, Pinho FT, Resende PR (2004) Modeling the new stress for improved drag reduction predictions of viscoelastic pipe flow. J Non-Newton Fluid Mech 121:127-141
45. Daly BJ, Harlow FH (1970) Transport equations of turbulence. Phys Fluids 13:2634-2649
46. De Angelis E, Casciola CM, Piva R (2002) DNS of wall turbulence: dilute polymers and selfsustaining mechanisms. Comput Fluids 31:495-507
47. Deardorff JW (1970) Turbulence measurements in supersonic two-dimensional wake. J Fluid Mech 41:453-480
48. de Gennes PG (1971) Reptation of a polymer chain in the presence of fixed obstacles. J Chem Phys 55:572-579
49. Dellar PJ (2003) Incompressible limits of lattice Boltzmann equations using multiple relaxation times. J Comput Phys 190:351-370
50. den Toonder JMJ, Nieuwstadt FTM, Kuiken GDC (1995) The role of elongational viscosity in the mechanism of drag reduction by polymer additives. Appl Sci Res 54:95-123
51. Deville MO, Fischer PF, Mund EH (2002) High-order methods for incompressible fluid flow. Cambridge University Press, Cambridge
52. d'Humières D (1992) Generalized lattice-Boltzmann equations. In: Shizgal BD, Weaver DP (eds) Rarefied gas dynamics: theory and applications. Progress in astronautics and aeronautics, vol 159. AIAA, Washington, pp 450-458
53. d'Humières D, Bouzidi M, Lallemand P (2001) Thirteen-velocity three-dimensional lattice Boltzmann model. Phys Rev E 63:066702
54. d'Humières D, Ginzburg I, Krafczyk M, Lallemand P, Luo L-S (2002) Multiple-relaxation-time lattice Boltzmann models in three-dimensions. Philos Trans R Soc Lond A 360:437-451
55. Dimitropoulos CD, Sureshkumar R, Beris AN (1998) Direct numerical simulation of viscoelastic turbulent channel flow exhibiting drag reduction: effect of the variation of rheological parameters. J Non-Newton Fluid Mech 79:433-468
56. Dimitropoulos CD, Sureshkumar R, Beris AN, Handler RA (2001) Budgets of Reynolds stress, kinetic energy and streamwise enstrophy in viscoelastic turbulent channel flow. Phys Fluids 13(4):1016-1024
57. Dimitropoulos CD, Dubief Y, Shakfeh ESG, Moin P, Lele SK (2005) Direct numerical simulation of polymer-induced drag reduction in turbulent boundary layer flow. Phys Fluids 17:011705
58. Dimitropoulos CD, Dubief Y, Shakfeh ESG, Moin P (2006) Direct numerical simulation of polymer-induced drag reduction in turbulent boundary layer flow of inhomogeneous polymer solutions. J Fluid Mech 566:153-162
59. Doi M, Edwards SF (1978a) Dynamics of concentrated polymer systems, part 1. Brownian motion in the equilibrium state. J Chem Soc Faraday Trans 74:1789-1801
60. DoiM, Edwards SF (1978b) Dynamics of concentrated polymer systems, part 2. Molecular motion under flow. J Chem Soc Faraday Trans 74:1802-1817
61. Doi M, Edwards SF (1978c) Dynamics of concentrated polymer systems, part 3. The constitutive equation. J Chem Soc Faraday Trans 74:1818-1832
62. Doi M, Edwards SF (1979) Dynamics of concentrated polymer systems, part 4. Rheological properties. J Chem Soc Faraday Trans 75:38-54
63. Doi M, Edwards SF (1988) The theory of polymer dynamics. Oxford University Press, Oxford
64. Dubief Y, White CM, Terrapon VE, Shakfeh ESG, Moin P, Lele SK (2004) On the coherent drag-reducing and turbulence-enhancing behaviour of polymers in wall flows. J Fluid Mech 514:271-280
65. Durbin PA (1991) Near-wall turbulence closure modeling without 'damping functions'. Theor Comput Fluid Dyn 3:1-13
66. Durbin PA (1993) A Reynolds stress model for near-wall turbulence. J Fluid Mech 249:465-498
67. Durbin PA, Petterson Reif BA (2010) Statistical theory and modeling for turbulent flows, 2nd edn. Wiley, New York
68. El-Kareh AW, Leal LG (1989) Existence of solutions for all Deborah numbers for a non-Newtonian model modified to include diffusion. J Non-Newton Fluid Mech 33:257-287
69. Ericksen JL (1960) Transversely isotropic fluids. Kolloid Z 173:117-122
70. Eringen AC (1980) Mechanics of continua. Krieger, New York
71. Eyink L (1994) The renormalization group method in statistical hydrodynamics. Phys Fluids 6:3063-3078
72. Fasel HF, von Terzi DA, Sandberg RD (2006) A methodology for simulating compressible turbulent flows. J Appl Mech 73:405-412
73. Fattal R, Kupferman R (2004) Constitutive laws for the matrix-logarithm formulation of the conformation tensor. J Non-Newton Fluid Mech 123:281-285
74. Fenstermacher PR, Swinney HL, Gollub JP (1979) Dynamical instabilities and the transition to chaotic Taylor vortex flow. J Fluid Mech 94:103-128
75. Fosdick RL, Serrin J (1979) On the impossibility of linear Cauchy and Piola-Kirchhoff constitutive theories for stress in solids. J Elast 9:83-89
76. FrewerM(2009) More clarity on the concept of material frame-indifference in classical continuum mechanics. Acta Mech 202:213-246
77. Fu S, Launder BE, Tselepidakis DP (1987) Accommodating the effects of high strain rates in modelling the pressure-strain correlation. Technical report TFD/87/5, UMIST
78. Gatski TB (1996) Turbulent flows: model equations and solution methodology. In: Peyret R (ed) Handbook of computational fluid dynamics. Academic Press, London, pp 339-415
79. Gatski TB, Jongen T (2000) Nonlinear eddy viscosity and algebraic stress models for solving complex turbulent flows. Prog Aerosp Sci 36:655-682
80. Gatski TB, Speziale CG (1993) On algebraic stress models for complex turbulent flows. J Fluid Mech 254:59-78
81. Gatski TB, Wallin S (2004) Extending the weak-equilibrium condition for algebraic Reynolds stress models to rotating and curved flows. J Fluid Mech 518:147-155
82. Gatski TB, Rumsey CL, Manceau R (2007) Current trends in modelling research for turbulent aerodynamic flows. Philos Trans R Soc A 365:2389-2418
83. Germano M, Piomelli U, Moin P, Cabot WH (1991) A dynamic subgrid-scale eddy viscosity model. Phys Fluids A 3:1760-1765
84. Geurts BJ (2004) Elements of direct and large-eddy simulation. Edwards, Philadelphia
85. Giesekus H (1966) Die elastizität von flüssgkeiten. Rheol Acta 5:29-35
86. Giesekus H (1982) A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility. J Non-Newton Fluid Mech 11:69-109
87. Giraud L, d'Humières D, Lallemand P (1997) A lattice-Boltzmann model for visco-elasticity. Int J Mod Phys C 8:805-815
88. Giraud L, d'Humières D, Lallemand P (1998) A lattice Boltzmann model for Jeffreys viscoelastic fluid. Europhys Lett 42:625-630
89. Girimaji SS (1996) Fully explicit and self-consistent algebraic Reynolds stress model. Theor Comput Fluid Dyn 8:387-402
90. Gordon RJ, Schowalter WR (1972) Anisotropic fluid theory: a different approach to the dumbbell theory of dilute polymer solutions. Trans Soc Rheol 16:79-97
91. Grad H (1949a) Note on the N-dimensional Hermite polynomials. Commun Pure Appl Math 2:325-330
92. Grad H (1949b) On the kinetic theory of rarefied gases. Commun Pure Appl Math 9:331-407
93. Green AI, Naghdi PM (1965) A general theory of an elastic-plastic continuum. Arch Ration Mech Anal 18:251-281
94. Groisman A, Steinberg V (2000) Elastic turbulence in a polymer solution flow. Nature 405:53-55
95. Groisman A, Steinberg V (2004) Elastic turbulence in curvilinear flows of polymer solutions. New J Phys 6:29. doi:10.1088/1367-2630/6/1/029
96. Gross EP, Jackson EA (1959) Kinetic models and the linearized Boltzmann equation. Phys Fluids 2:432-441
97. Guo Z, Shi B, Zheng C (2002) A coupled lattice BGK model for the Boussinesq equations. Int J Numer Methods Fluids 2:325-342
98. Hallbäck M, Groth J, Johansson AV (1990) An algebraic model for nonisotropic turbulent dissipation rate in Reynolds stress closures. Phys Fluids A 2:1859-1866
99. Hanjalić K (1994) Advanced turbulence closure models: a view of current status and future prospects. Int J Heat Fluid Flow 15:178-203
100. Hanjalić K, Jakirlić S (2002) Second-moment turbulence closure modelling. In: Launder B, Sandham N (eds) Closure strategies for turbulent and transitional flows. Cambridge University Press, Cambridge, pp 47-101
101. Hanjalić K, Launder BE (1972) A Reynolds stress model of turbulence and its application to thin shear flows. J Fluid Mech 52:609-638
102. Hanjalić K, Launder BE (1976) Contribution towards a Reynolds-stress closure for low-Reynoldsnumber turbulence. J Fluid Mech 74:593-610
103. Hanjalić K, Launder BE (2011) Modelling turbulence in engineering and the environment: secondmoment routes to closure. Cambridge University Press, Cambridge
104. Harnoy A (1976) Stress relaxation in elastico-viscous lubricants in gears and rollers. J Fluid Mech 76:501-517
105. Hasimoto H, Sano O (1980) Stokeslet and eddies in creeping flow. Annu Rev Fluid Mech 12:335-363
106. Haworth DC, Pope SB (1986) A generalized Langevin model for turbulent flows. Phys Fluids 29:387-405
107. Herschel WH, Bulkley R (1926) Konsistenzmessungen von gummi-benzollösungen. Kolloid Z 39:291-300
108. Hinze JO (1959) Turbulence. McGraw-Hill, New York
109. Housiadas KD, Beris AN (2003) Polymer-induced drag reduction: effects of the variations in elasticity and inertia in turbulent viscoelastic channel flow. Phys Fluids 15:2369-2384
110. Housiadas KD, Beris AN, Handler RA (2005) Viscoelastic effects on higher order statistics and on coherent structures in turbulent channel flow. Phys Fluids 17:035106
111. Huang K (1987) Statistical mechanics, 2nd edn. Wiley, New York
112. Huilgol RR, Phan-Thien N (1997) Fluid mechanics of viscoelasticity. Elsevier, Amsterdam
113. Hulsen MA, van Heel APG, van den Brule BHAA (1997) Simulation of viscoelastic flows using Brownian configuration fields. J Non-Newton Fluid Mech 70:79-101
114. Ianniruberto G, Marrucci G (1996) On compatibility of the Cox-Merz rule with the model of Doi and Edwards. J Non-Newton Fluid Mech 65:241-246
115. Ianniruberto G, Marrucci G (2000) Convective orientational renewal in entangled polymers. J Non-Newton Fluid Mech 95:363-374
116. Ianniruberto G, Marrucci G (2001) A simple constitutive equation for entangled polymers with chain stretch. J Rheol 45:1305-1318
117. Itô K (1951) On stochastic differential equations. Mem Am Math Soc 4:1-51
118. Jakirlić S, Hanjalić K (2002) A new approach to modelling near-wall turbulence energy and stress dissipation. J Fluid Mech 459:139-166
119. James DF (2009) Boger fluids. In: Annual review of fluid mechanics. Annual Reviews, New York, pp 129-142
120. Jaumann G (1911) Geschlossenes system physikalischer und chemischer differentialgesefze. Sitz Zer Akad Wiss Wien 120:385-530
121. Jeffreys H (1965) Cartesian tensors. Cambridge University Press, Cambridge
122. Jeffreys H (1976) The earth: its origin, history and physical constitution, 6th edn. Cambridge University Press, Cambridge
123. Johansson AV, Hallbäck M (1994) Modelling of rapid pressure-strain in Reynolds-stress closures. J Fluid Mech 269:143-168
124. Jongen T, Gatski TB (1999) A unified analysis of planar homogeneous turbulence using singlepoint closure equations. J Fluid Mech 399:117-150
125. Jongen T, Gatski TB (2005) Tensor representations and solutions of constitutive equations for viscoelastic fluids. Int J Eng Sci 43:556-588
126. Joseph DD (1990) Fluid dynamics of viscoelastic liquids. Springer, Berlin
127. Jovanović J, Pashtrapanska M, Frohnapfel B, Durst F, Koskinen J, Koskinen K (2006) On the mechanism responsible for turbulent drag reduction by dilute addition of high polymers: theory, experiments, simulations and predictions. J Fluids Eng 128:118-130
128. Kampé de Fériet J, Betchov R (1951) Theoretical and experimental averages of turbulent functions. Proc K Ned Akad Wet 53:389-398
129. Kaye A (1963) A bouncing liquid stream. Nature 197:1001
130. Kehrwald D (2005) Lattice Boltzmann simulation of shear-thinning fluids. J Stat Phys 121:223-237
131. Keunings R (2004) Micro-macro methods for the multiscale simulation of viscoelastic flow using molecular models of kinetic theory. In: Rheology reviews 2004. British Society of Rheology, London, pp 67-98
132. Kim J, Moin P, Moser RD (1982) Numerical investigation of turbulent channel flow. J Fluid Mech 118:341-377
133. Kim J, Moin P, Moser RD (1987) Turbulence statistics in fully developed channel flow at low Reynolds number. J Fluid Mech 177:133-186
134. Kolmogorov AN (1941a) The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl Akad Nauk SSSR 30:301-305
135. Kolmogorov AN (1941b) On degeneration of isotropic turbulence in an incompressible viscous fluid. Dokl Akad Nauk SSSR 31:538-541
136. Kolmogorov AN (1942) Equations of turbulent motion in an incompressible fluid. Izv Akad Nauk SSSR, Ser Fiz 6:56-58
137. Koschmieder EL (1993) Bénard cells and Taylor vortices. Cambridge University Press, Cambridge
138. KrafczykM, Tölke J, Luo L-S (2003) Large-eddy simulations with a multiple-relaxation-time LBE model. Int J Mod Phys 17:33-39
139. Kraichnan RH (1964) Kolmogorov's hypothesis and Eulerian turbulence theory. Phys Fluids 7:1723-1734
140. Kreuzinger J, Friedrich R, Gatski TB (2006) Compressibility effects in the solenoidal dissipation rate equation: a priori assessment and modeling. Int J Heat Fluid Flow 27:696-706
141. Lallemand P, Luo L-S (2000) Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys Rev E 61:6546-6562
142. Lallemand P, d'Humières D, Luo LS, Rubinstein R (2003) Theory of the lattice Boltzmann method: three-dimensional model for linear viscoelastic fluids. Phys Rev E 67:021203
143. Lammers P, Beronov KN, Volkert R, Brenner G, Durst F (2006) Lattice BGK direct numerical simulation of fully developed turbulence in incompressible plane channel flow. Comput Fluids 35:1137-1153
144. Larson RG (1988) Constitutive equations for polymer melts and solutions. Butterworth, Boston
145. Larson RJ (1983) Convection and diffusion of polymer network strands. J Non-Newton FluidMech 13:279-308
146. Latt J (2007) Hydrodynamic limit of lattice Boltzmann equations. PhD dissertation, University of Geneva, Geneva, Switzerland. http://www.unige.ch/cyberdocuments/theses2007/LattJ/meta.html
147. Launder BE, Reece GJ, Rodi W (1975) Progress in the development of a Reynolds-stress turbulence closure. J Fluid Mech 68:537-566
148. Lesieur M (2008) Turbulence in fluids, 4th edn. Springer, Dordrecht
149. Lesieur M, Métais O, Comte P (2005) Large-eddy simulations of turbulence. Cambridge University Press, Cambridge
150. Li CF, Gupta VK, Sureshkumar R, Khomami B (2006) Turbulent channel flow of dilute polymeric solutions: drag reduction scaling and an eddy viscosity model. J Non-Newton FluidMech 139:177-189
151. Lien FS, Leschziner MA (1995) Modelling 2D separation from a high lift aerofoil with a non-linear eddy-viscosity model and second-moment closure. Aeronaut J 99:125-144
152. Liepmann HW (1962) Free turbulence. In: Favre A (ed) Mécanique de la turbulence. Colloques Internationaux du CNRS, vol 108, pp 211-227
153. Likhtman AE, Graham RS (2003) Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie-Poly equation. J Non-Newton Fluid Mech 114:1-12
154. Lilly DK (1966) On the application of the eddy-viscosity concept in the inertial sub-range of turbulence. Manuscript 123, NCAR
155. Lilly DK (1992) A proposed modification of the Germano subgrid-scale closure method. Phys Fluids A 4:633-635
156. Lozinski A, Owens RG, Phillips TN (2011) The Langevin and Fokker-Planck equations in polymer rheology. In: Ciarlet PG, Glowinski R, Xu J (eds) Numerical methods for non-Newtonian fluids. Handbook of numerical analysis. Elsevier, Amsterdam, pp 211-303
157. Lumley JL (1967) Rational approach to relations between motions of differing scales in turbulent flows. Phys Fluids 10:1405-1408
158. Lumley JL (1970a) Stochastic tools in turbulence. Academic Press, New York
159. Lumley JL (1970b) Toward a turbulent constitutive relation. J Fluid Mech 41:413-434
160. Lumley JL (1978) Computational modeling of turbulent flows. Adv Appl Mech 18:123-176
161. Lumley JL (1983) Turbulence modeling. J Appl Mech 50:1097-1103
162. Lumley JL, Khajeh-Nouri B (1974) Computational modeling of turbulent transport. In: Turbulent diffusion in environmental pollution. Academic Press, New York, pp 237-248
163. Lumley JL, Newman GR (1977) The return to isotropy of homogeneous turbulence. J Fluid Mech 82:161-178
164. Magnaudet J (1993) Modelling of inhomogeneous turbulence in the absence of mean velocity gradients. Appl Sci Res 51:525-531
165. Malaspinas O (2009) Lattice Boltzmann method for the simulation of viscoelastic fluid flows. PhD dissertation, number 4505. EPFL, Lausanne, Switzerland
166. Malaspinas O, Fiétier N, Deville M (2010) Lattice Boltzmann method for the simulation of viscoelastic fluid flows. J Non-Newton Fluid Mech 165:1637-1653
167. Manceau R, Hanjalić K (2000a) Elliptic blending model: a new near-wall Reynolds stress turbulence closure. Phys Fluids 14:744-754
168. Manceau R, Hanjalić K (2000b) A new form of the elliptic relaxation equation to account for wall effects in RANS modeling. Phys Fluids 12:2345-2351
169. Manceau R, Carlson JR, Gatski TB (2002) A rescaled elliptic relaxation approach: neutralizing the effect on the log layer. Phys Fluids 14:3868-3879
170. Marrucci G, Greco F, Ianniruberto G (2001) Integral and differential constitutive equations for entangled polymers with simple versions of CCR and force balance on entanglements. Rheol Acta 40:98-103
171. Marshall JS, Naghdi PM (1991) Consequences of the second law for a turbulent fluid flow. Contin Mech Thermodyn 3:65-77
172. McComb WD (1990) The physics of fluid turbulence. Clarendon, Oxford
173. McLeish TCB, Larson RG (1998) Molecular constitutive equations for a class of branched polymers: the pom-pom polymer. J Rheol 42:81-110
174. Mellor GL, Herring HJ (1973) A survey of the mean turbulent field closure models. AIAA J 11:590-599
175. Menter F (1994) Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J 32:1598-1605
176. Milner ST, McLeish TCB, Likhtman AE (2001) Microscopic theory of convective constraint release. J Rheol 45:539-563
177. Min T, Yoo JY, Choi H, Joseph DD (2003) Drag reduction by polymer additives in a turbulent channel flow. J Fluid Mech 486:213-238
178. Mompean G (2002) On predicting abrupt contraction flows with differential and algebraic viscoelastic models. Comput Fluids 31:935-956
179. Mompean G, Thais L (2007) Assessment of a general equilibrium assumption for development of algebraic viscoelastic models. J Non-Newton Fluid Mech 145:41-51
180. Mompean G, Jongen T, Deville MO, Gatski TB (1998) On algebraic extra-stress models for the simulation of viscoelastic flows. J Non-Newton Fluid Mech 79:261-281
181. Mompean G, Thompson RL, Souza Mendes PR (2003) A general transformation procedure for differential viscoelastic models. J Non-Newton Fluid Mech 111:151-174
182. Mompean G, Thais L, Tomé MF, Castelo A (2011) Numerical prediction of three-dimensional time-dependent viscoelastic extrudate swell using differential and algebraic models. Comput Fluids 44:68-78
183. Monin AS, Yaglom AM (1971) Statistical fluid mechanics, vols 1 and 2. MIT Press, Boston
184. Morozov AN, van Saarloos W (2007) An introductory essay on subcritical instabilities and the transition to turbulence in visco-elastic parallel shear flows. Phys Rep 447:112-143
185. Moser RD, Kim J, Mansour NN (1999) Direct numerical simulation of turbulent channel flow up to Reτ = 590. Phys Fluids 11:943-945
186. Myong HK, Kasagi N (1990) Prediction of anisotropy of the near-wall turbulence with an anisotropic low-Reynolds-number k-ε turbulence model. J Fluids Eng 112:521-524
187. Nelson E (2001) Dynamical theories of brownian motion. Princeton University Press, Princeton. www.math.princeton.edu/~nelson/books/bmotion.pdf
188. Nie XB, Shan X, Chen H (2008) Galilean invariance of lattice Boltzmann models. Europhys Lett 81(3):34005 (6 pp)
189. Nisizima S, Yoshizawa A (1987) Turbulent channel and Couette flows using an anisotropic k-ε model. AIAA J 25:414-420
190. Noll W (1962) Motions with constant stretch history. Arch Ration Mech Anal 11:97-105
191. Noll W (1976) The representation of monotonous processes by exponentials. Indiana Univ Math J 25:209-214
192. Oberlack M (1997) Non-isotropic dissipation in non-homogeneous turbulence. J Fluid Mech 350:351-374
193. Oceni AG, Manceau R, Gatski TB (2010) Introduction of wall effects in explicit algebraic stress models through elliptic blending. In: Stanislas M, Jimenez J, Marusic I (eds) Progress in wall turbulence: understanding and modelling. Springer, Heidelberg, pp 275-283
194. Oldroyd JG (1950) On the formulation of rheological equations of state. Proc R Soc Lond Ser A 200:523-541
195. Oldroyd JG (1958) Non-Newtonian effects in steady motion of some idealized elastico-viscous liquids. Proc R Soc Lond Ser A 245:278-297
196. Onishi J, Chen Y, Ohashi H (2005) A lattice Boltzmann model for polymeric liquids. Prog Comput Fluid Dyn 5:75-84
197. Onishi J, Chen Y, Ohashi H (2006) Dynamic simulation of multi-component viscoelastic fluids using the lattice Boltzmann method. Physica A 362:84-92
198. Orlandi P (1995) A tentative approach to the direct simulation of drag reduction by polymers. J Non-Newton Fluid Mech 60:277-301
199. Orszag SA (1970) Analytical theories of turbulence. J Fluid Mech 41:59-82
200. Öttinger H-C (1996) Stochastic processes in polymeric fluids: tools and examples for developing simulation algorithms. Springer, Berlin
201. Owens RG, Phillips TN (2002) Computational rheology. Imperial College Press, London
202. Pennisi S (1992) On third order tensor-valued isotropic functions. Int J Eng Sci 30:679-692
203. Peterlin A (1966) Hydrodynamics of macromolecules in a velocity field with longitudinal gradient. J Polym Sci, Polym Phys 4:287-291
204. Peters GWM, Baaijens FPT (1997) Modelling of non-isothermal viscoelastic flows. J Non-Newton Fluid Mech 68:205-224
205. Phan-Thien N (2002) Understanding viscoelasticity basics of rheology. Springer, Berlin
206. Phan-Thien N, Tanner RI (1977) A new constitutive equation derived from network theory. J Non-Newton Fluid Mech 2:353-365
207. Pinho FT (2003) A GNF framework for turbulent flow models of drag reducing fluids and proposal for a k-ε type closure. J Non-Newton Fluid Mech 121:127-141
208. Pinho FT, Li CF, Younis BA, Sureshkumar R (2008a) A low Reynolds number turbulence closure for viscoelastic fluids. J Non-Newton Fluid Mech 154:89-108
209. Pinho FT, Sadanandan B, Sureshkumar R (2008b) One equation model for turbulent channel flow with second order viscoelastic corrections. Flow Turbul. Combust. doi:10.1007/s10494-008-9134-6
210. Pope SB (1975) A more general effective viscosity hypothesis. J Fluid Mech 72:331-340
211. Pope SB (2000) Turbulent flows. Cambridge University Press, Cambridge
212. Prandtl L (1945) Über ein neues formelsystem für die ausgebildete turbulenz. In: Nachr. Akad. Wiss. Göttingen. van den Loerck und Ruprecht, Göttingen, pp 6-19
213. Premnath KN, Pattison MJ, Banerjee S (2009a) Dynamic simulation of multi-component viscoelastic fluids using the lattice Boltzmann method. Physica A 388:2640-2658
214. Premnath KN, Pattison MJ, Banerjee S (2009b) Dynamic simulation of multi-component viscoelastic fluids using the lattice Boltzmann method. Phys Rev E 362:026703
215. Pruett CD (2000) On Eulerian times-domain filtering for spatial large-eddy simulation. AIAA J 38:1634-1642
216. Pruett CD, Gatski TB, Grosch CE, Thacker WD (2003) The temporally filtered Navier-Stokes equations: properties of the residual stress. Phys Fluids 15:2127-2140
217. Ptasinski PK, Boersma BJ, Nieuwstadt FTM, Hulsen MA, Van den Brule HAA, Hunt JCR (2003) Turbulent channel flow near maximum drag reduction: simulations, experiments and mechanisms. J Fluid Mech 490:251-291
218. Reiner M (1964) The Deborah number. Phys Today 62
219. Resende PR, Kim K, Younis BA, Sureshkumar R, Pinho FT (2011) A FENE-P k-ε turbulence model for low and intermediate regimes of polymer-induced drag reduction. J Non-Newton Fluid Mech 166:639-660
220. Reynolds O (1895) On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Philos Trans R Soc Lond A 186:123-164
221. Reynolds WC (1976) Computation of turbulent flows. In: Annual review of fluid mechanics. Annual Reviews, New York, pp 183-208
222. Rivlin RS (1955) Further remarks on the stress-deformation relations for isotropic materials. J Ration Mech Anal 4:681-702
223. Rivlin RS (1957) The relation between the flow of non-Newtonian fluids and turbulent Newtonian fluids. Q Appl Math 15:212-215
224. Rivlin RS, Ericksen JL (1955) Stress-deformation relations for isotropic materials. Arch Ration Mech Anal 4:323-425
225. Rivlin RS, Smith GF (1975) On identities for 33 matrices. Rend Mat 8:348-353
226. Rodi W (1972) The prediction of free turbulent boundary layers by use of a two-equation model of turbulence. PhD thesis, University of London, London
227. Rodi W (1976) A new algebraic relation for calculating the Reynolds stresses. Z Angew Math Mech 56:219-221
228. Rotta JC (1951) Statistiche theorie nichthomogener turbulenz. Z Phys 129:547-572
229. Rubinstein R, Barton JH (1990) Nonlinear Reynolds stress models and the renormalization group. Phys Fluids A 2:1472-1476
230. Rubio P,Wagner MH (1999) Letter to the editor: A note added to Molecular constitutive equations or a class of branched polymers: the pom-pom polymer (J. Rheol., 42:81-110, 1998). J Rheol 43:1709-1710
231. Sadiki A, Hutter K (1996) On the frame dependence and form invariance of the transport equations for the Reynolds stress tensor and the turbulent heat flux vector: its consequences on closure models in turbulence modelling. Contin Mech Thermodyn 8:341-349
232. Saffman PG (1970) A model for inhomogeneous turbulence. Proc R Soc Lond Ser A 317:417-433
233. Sagaut P (2006) Large eddy simulation for incompressible flows. Springer, Berlin
234. Sagaut P (2010) Toward advanced subgrid models for lattice-Boltzmann-based large-eddy simulation: theoretical formulations. Comput Math Appl 59:2191-2199
235. Sagaut P, Cambon C (2008) Homogeneous turbulence dynamics. Cambridge University Press, Cambridge
236. Sagaut P, Deck S, Terracol M (2006) Multiscale and multiresolution approaches in turbulence. Imperial College Press, London
237. Sarkar S, Speziale CG (1990) A simple nonlinear model for the return to isotropy in turbulence. Phys Fluids 29:84-93
238. Schmid PJ, Henningson DS (2001) Stability and transition in shear flows. Springer, New York
239. Schumann U (1977) Realizability of Reynolds stress models. Phys Fluids 20:721-725
240. Schwarz WR, Bradshaw P (1994) Term-by-term tests of stress-transport turbulence models in a three-dimensional boundary layer. Phys Fluids 6:986-998
241. Shan X, Chen H (2007) A general multiple-relaxation-time Boltzmann collision model. Int J Mod Phys C 18:635-643. doi:10.1017/S0022112005008153
242. Shan X, Yuan X-F, Chen H (2006) Kinetic theory representation of hydrodynamics: a way beyond the Navier Stokes equation. J Fluid Mech 550:413-441. doi:10.1017/S0022112005008153
243. Shaqfeh ESG (1996) Purely elastic instabilities in viscometric flows. In: Annual review of fluid mechanics. Annual Reviews, New York, pp 129-185
244. Shih T-H, Zhu J, Lumley JL (1995) A new Reynolds stress algebraic equation model. Comput Methods Appl Mech Eng 125:287-302
245. Shir CC (1973) A preliminary numerical study of atmospheric turbulent flows in the idealized planetary boundary layer. J Atmos Sci 30:1327-1339
246. Shur ML, Spalart PR, Strelets MK, Travin AK (2008) A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities. Int J Heat Fluid Flow 29:1638-1649
247. Simonsen AJ, Krogstad P-A (2005) Turbulent stress invariant analysis: clarification of existing terminology. Phys Fluids 17:088103
248. Sinha K, Candler GV (2003) Turbulent dissipation-rate equation for compressible flows. AIAA J 41:1017-1021
249. Sjögren T, Johansson AV (2000) Development and calibration of algebraic nonlinear models for terms in the Reynolds stress transport equations. Phys Fluids 12:1554-1572
250. Smagorinsky I (1963) General circulation experiments with the primitive equations. I. The basic experiment. Mon Weather Rev 91:99-164
251. Smith GF (1965) On isotropic integrity bases. Arch Ration Mech Anal 18:282-292
252. Smith GF (1994) Constitutive equations for anisotropic and isotropic materials. Mechanics and physics of discrete systems, vol 3. North Holland, Amsterdam
253. Smith GF, Younis BA (2004) Isotropic tensor-valued polynomial function of second-order and third-order tensors. Int J Eng Sci 43:447-456
254. So RMC, Lai YG, Zhang HS, Hwang BC (1991) Second-order near-wall turbulence closures: a review. AIAA J 29:1819-1835
255. So RMC, Aksoy H, Yuan SP, Sommer TP (1996) Modeling Reynolds-number effects in wallbounded turbulent flows. J Fluids Eng 118:260-267
256. Spalart PR, Allmaras SR (1994) A one-equation turbulence model for aerodynamic flows. Rech Aérosp 1:5-21
257. Spalart PR, Jou W-H, Strelets M, Allmaras SR (1997) Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. In: Liu C, Liu Z (eds) Advances in DNS/LES. Greyden Press, Columbus, pp 137-147
258. Spencer AJM (1965) Isotropic integrity bases for vectors and second-order tensors, part II. Arch Ration Mech Anal 18:51-82
259. Spencer AJM (1971) Theory of invariants. Academic Press, New York, pp 239-353
260. Spencer AJM (2004) Continuum mechanics. Dover, Mineola
261. Spencer AJM, Rivlin RS (1959) The theory of matrix polynomials and its application to the mechanics of isotropic continua. Arch Ration Mech Anal 2:309-336
262. Spencer AJM, Rivlin RS (1962) Isotropic integrity bases for vectors and second-order tensors, part I. Arch Ration Mech Anal 9:45-63
263. Speziale CG (1981) Some interesting properties of two-dimensional turbulence. Phys Fluids 24:1425-1427
264. Speziale CG (1987) On nonlinear k-l and k-ε models of turbulence. J Fluid Mech 178:459-475
265. Speziale CG (1991) Analytical methods for the development of Reynolds-stress closures in turbulence. In: Annual review of fluid mechanics. Annual Reviews, New York, pp 107-157
266. Speziale CG (1998a) A consistency condition for non-linear algebraic Reynolds stress models in turbulence. Int J Non-Linear Mech 33:579-584
267. Speziale CG (1998b) A review of material frame-indifference in mechanics. Appl Mech Rev 51:489-504
268. Speziale CG (1998c) Turbulence modeling for time-dependent RANS and VLES: a review. AIAA J 36:173-184
269. Speziale CG, Gatski TB (1997) Analysis and modelling of anisotropies in the dissipation rate of turbulence. J Fluid Mech 344:155-180
270. Speziale CG, Sarkar S, Gatski TB (1991) Modelling the pressure-strain correlation of turbulence: an invariant dynamical systems approach. J Fluid Mech 227:245-27
271. Stolz S, Adams NA (1999) An approximate deconvolution procedure for large-eddy simulation. Phys Fluids 11:1699-1701
272. Stolz S, Adams NA, Kleiser L (1999) The approximate deconvolution model applied to turbulent channel flow. In: Voke P, Sandham N, Kleiser L (eds) Direct and large eddy simulation III. Kluwer Academic, Dordrecht, pp 163-174
273. Stolz S, Adams NA, Kleiser L (2001a) An approximate deconvolution model for large-eddy simulation with application to wall-bounded incompressible flows. Phys Fluids 13:997-1015
274. Stolz S, Adams NA, Kleiser L (2001b) An approximate deconvolution model for large-eddy simulations of compressible flows and its application to shock-turbulent-boundary-layer interaction. Phys Fluids 13:2985-3001
275. Straatman AG (1999) A modified model for diffusion in second-moment turbulence closures. J Fluids Eng 121:747-756
276. Straatman AG, Stubley GD, Raithby GD (1998) Examination of diffusion modeling using zero mean-shear turbulence. AIAA J 36:929-935
277. Succi S (2001) The lattice Boltzmann equation for fluid dynamics and beyond. Oxford University Press, Oxford
278. Succi S, Karlin IV, Chen H (2002) Colloquium: role of the H theorem in lattice Boltzmann hydrodynamic simulations. Rev Mod Phys 74:1203-1220
279. Sureshkumar R, Beris AN (1995) Effect of artificial stress diffusivity on the stability of numerical calculations and the dynamics of time-dependent viscoelastic flows. J Non-Newton FluidMech 60:53-80
280. Sureshkumar R, Beris AN, Handler RA (1997) Direct numerical simulation of the turbulent channel flow of a polymer solution. Phys Fluids 9:743-755
281. Tanner RI (1989) Engineering rheology. Clarendon, Oxford
282. Taulbee DB (1992) An improved algebraic Reynolds stress model and corresponding nonlinear stress model. Phys Fluids A 4:2555-2561
283. Taylor GI (1923) Stability of a viscous liquid contained between two rotating cylinders. Philos Trans R Soc A 223:289-343
284. Tennekes H, Lumley JL (1972) A first course in turbulence. MIT Press, Boston
285. Thais L, Tejada-Martínez AE, Gatski TB, Mompean G (2010) Direct and temporal large eddy numerical simulations of FENE-P drag reduction flows. Phys Fluids 22:013103. doi:10.1063/1.3294574
286. Thais L, Tejada-Martínez AE, Gatski TB, Mompean G (2011) A massively parallel hybrid scheme for direct numerical simulation of turbulent viscoelastic channel flow. Comput Fluids 43:134-142
287. Thrasher M, Jung S, Pang YK, Chuu C-P, Swinney H (2007) The bouncing jet: a Newtonian liquid rebounding off a free surface. Phys Rev E 76:056319
288. Tölke J, Krafczyk M, Schulz M, Rank E (2000) Discretization of the Boltzmann equation in velocity space using a Galerkin approach. Comput Phys Commun 129:91-99
289. Toms BA (1949) Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. In: Proc. of the 1st international congress of rheology, vol 2, pp 135-141
290. Townsend AA (1956) The structure of turbulent shear flows. Cambridge University Press, Cambridge
291. Trouton FT (1906) On the coefficient of viscous traction and its relation to that of viscosity. Proc R Soc Lond Ser A 77:426-440
292. Truesdell C (1955) The simplest rate theory of pure elasticity. Commun Pure Appl Math 8:123-132
293. Truesdell C (1960) The principles of continuum mechanics. Colloquium lectures in pure and applied sciences, vol 5. Socony Mobil Oil Co, Fairfax County
294. Truesdell C (1965) Rational mechanics of deformation and flow. In: Proceedings of the 4th international congress on rheology. Wiley, New York
295. Truesdell C (1991) A first course in rational continuum mechanics, vol 1, 2nd edn. Academic Press, Boston
296. Truesdell C, Muncaster RG (1980) Fundamentals of Maxwell's kinetic theory of monatomic gas, treated as a branch of rational mechanics. Academic Press, New York
297. Truesdell C, Noll W (1992) The nonlinear field theories of mechanics, 2nd edn. Springer, Berlin
298. Truesdell C, Rajagopal KR (2000) An introduction to the mechanics of fluids. Birkhäuser, Boston
299. van Driest ER (1956) On turbulent flow near a wall. J Aeronaut Sci 23:1007-1011
300. Verbeeten WMH, Peters GWM, Baaijens FPT (2001) Differential constitutive equations for polymer melts: the extended pom-pom model. J Rheol 45:823-843
301. Versluis M, Blom C, van der Meer D, van der Weele K, Lohse D (2006) Leaping shampoo and the stable Kaye effect. J Stat Mech P07007
302. Wagner AJ, Giraud L, Scott CE (2000) Simulation of a cusped bubble rising in a viscoelastic fluid with a new numerical method. Comput Phys Commun 129:227-232
303. Wallin S, Johansson AV (2000) An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows. J Fluid Mech 403:89-132
304. Wang C-C (1965) A representation theorem for the constitutive equation of a simple material in motions with constant stretch history. Arch Ration Mech Anal 20:329-340
305. Wang C-C (1970) A new representation theorem for isotropic functions. Arch Ration Mech Anal 36:166-223
306. Warner HR (1972) Kinetic theory and rheology of dilute suspensions of finitely extendible dumbbells. Ind Eng Chem Fundam 11:379-387
307. Wilcox DC (2006) Turbulence modeling for CFD, 3rd edn. DCW Industries, La Cañada
308. Wilson HJ (2011) Graduate lectures on polymeric fluids. University College of London, London. http://www.ucl.ac.uk/~ucahhwi/GM05/index.html
309. Wilson KG (1971) Renormalization group and critical phenomena. 1. Renormalization group and Kadanoff scaling picture. Phys Rev B 4:3174-3183
310. Wolf-Gladrow DA (2000) Lattice-gas cellular automata and lattice Boltzmann models: an introduction. Lecture notes in mathematics, vol 1725. Springer, Berlin
311. Woods LC (1993) An introduction to the kinetic theory of gases and magnetoplasmas. Oxford University Press, Oxford
312. Yakhot A, Orszag SA, Yakhot V, Israeli M (1989) Renormalisation group formulation for largeeddy simulation. J Sci Comput 4:139-159
313. Yakhot A, Orszag SA, TB Gatski ST, Speziale CG (1992) Development of turbulence models for shear flows by a double expansion technique. Phys Fluids A 4:1510-1520
314. Yakhot V, Orszag SA (1986) Renormalisation group analysis of turbulence. I. Basic theory. J Sci Comput 1:3-51
315. Yamamoto M(1956) Anisotropic fluid theory: a different approach to the dumbbell theory of dilute polymer solutions. J Phys Soc Jpn 11:413-421
316. Ying R, Canuto VM (1996) Turbulence modeling over two-dimensional hills using an algebraic Reynolds stress expression. Bound-Layer Meteorol 77:69-99
317. Yoshizawa A (1984) Statistical analysis of the deviation of the Reynolds stress from its eddyviscosity representation. Phys Fluids 27:1377-1387
318. Younis BA, Gatski TB, Speziale CG (2000) Towards a rational model for the triple velocity correlations of turbulence. Proc R Soc Lond A 456:909-920
319. Yu H, Girimaji SS (2005a) DNS of homogeneous shear turbulence revisited with the lattice Boltzmann method. J Turbul 6:N6. doi:10.1080/14685240500103200
320. Yu H, Girimaji SS (2005b) Near-field turbulent simulations of rectangular jets using lattice Boltzmann method. Phys Fluids 17:125106
321. Yu H, Girimaji SS (2006) Direct numerical simulations of homogeneous turbulence subject to periodic shear. J Fluid Mech 566:117-151
322. Yu H, Mei R, Luo L-S, Shyy W (2003) Viscous flow computations with the method of lattice Boltzmann equations. Prog Aerosp Sci 39:329-367
323. Yu H, Girimaji SS, Luo L-S (2005a) DNS and LES of decaying isotropic turbulence with and without frame rotation using the lattice Boltzmann method. J Comput Phys 209:599-616
324. Yu H, Girimaji SS, Luo L-S (2005b) Lattice Boltzmann simulations of decaying homogeneous isotropic turbulence. Phys Rev E 71:061708
325. Yu H, Luo L-S, Girimaji SS (2006) LES of turbulent square jet flow using an MRT lattice Boltzmann model. Comput Fluids 35:957-965