Review of Lattice Boltzmann Method Applied to Computational Aeroacoustics

Shao, Weidong; Li, Jun

doi:10.24425/aoa.2019.128486

Powiadomienia systemowe

Sesja wygasła!

Artykuł - szczegóły

Tytuł artykułu

Review of Lattice Boltzmann Method Applied to Computational Aeroacoustics

Autorzy

Shao Weidong , Li Jun

Treść / Zawartość

Pełne teksty:

Shao_Review of Lattice Boltzmann_2_2019.pdf

Pobierz

Identyfikatory

DOI

10.24425/aoa.2019.128486

Warianty tytułu

Języki publikacji

Abstrakty

This paper presents the research studies carried out on the application of lattice Boltzmann method (LBM) to computational aeroacoustics (CAA). The Navier-Stokes equation-based solver faces the difficulty of computational efficiency when it has to satisfy the high-order of accuracy and spectral resolution. LBM shows its capabilities in direct and indirect noise computations with superior space-time resolution. The combination of LBM with turbulence models also work very well for practical engineering machinery noise. The hybrid LBM decouples the discretization of physical space from the discretization of moment space, resulting in flexible mesh and adjustable time-marching. Moreover, new solving strategies and acoustic models are developed to further promote the application of LBM to CAA.

Słowa kluczowe

lattice Boltzmann method computational aeroacoustics dispersion dissipation perfectly matched layers discontinuous Galerkin method

Wydawca

Instytut Podstawowych Problemów Techniki PAN
Komitet Akustyki PAN
Polskie Towarzystwo Akustyczne

Czasopismo

Archives of Acoustics

Rocznik

2019

Tom

Vol. 44, No. 2

Strony

215--238

Opis fizyczny

Bibliogr. 132 poz., rys., tab., wykr.

Twórcy

autor

Shao Weidong

shilin1225@126.com

Institute of Turbomachinery, Xi’an Jiaotong University, Xi’an 710049, China

autor

Li Jun

junli@mail.xjtu.edu.cn

Institute of Turbomachinery, Xi’an Jiaotong University, Xi’an 710049, China
Collaborative Innovation Centre of Advanced Aero-Engine, Beijing 100191, China

Bibliografia

1. Aidun C. K., Clausen J. R. (2010), Lattice-Boltzmann methods for complex flows, Annual Review of Fluid Mechanics, 42, 439-472.
2. Ashcroft G., Zhang X. (2003), Optimized prefactored compact schemes, Journal of Computational Physics, 190, 2, 459-477.
3. Bailly C., Juve D. (2000), Numerical solution of acoustic propagation problems using linearized Euler equations, AIAA Journal, 38, 1, 22-29.
4. Bassi F., Botti L., Colombo A., Ghidoni A., Massa F. (2015), Linearly implicit Rosenbrock-type Runge-Kutta schemes applied to the discontinuous Galerkin solution of compressible and incompressible unsteady flows, Computers & Fluids, 118, 305-320.
5. Berland J., Bogey C., Marsden O., Bailly C. (2007), High-order, low dispersive and low dissipative explicit schemes for multiple-scale and boundary problems, Journal of Computational Physics, 224, 2, 637-662.
6. Bogey C., Bailly C. (2004), A family of low dispersive and low dissipative explicit schemes for flow and noise computations, Journal of Computational Physics, 194, 1, 194-214.
7. Bres G. A., Freed D., Wessels M. et al. (2012), Flow and noise predictions for the tandem cylinder aeroacoustic benchmark, Physics of Fluids, 24, 036101.
8. Bres G. A., Perot F., Freed D. (2009), Properties of the lattice-Boltzmann method for acoustic, 15th AIAA/CEAS Aeroacoustics Conference and Exhibit, AIAA 09-3395, pp. 1-11, Miami, FL, USA.
9. Buick J. M., Buckley C. L., Greated C. A., Gilbert J. (2000), Lattice Boltzmann BGK simulation of nonlinear sound waves: the development of a shock front, Journal of Physics A: General Physics, 33, 21, 3917-3928.
10. Buick J. M., Greated C. A., Campbell D. M. (1998), Lattice BGK simulation of sound waves, Europhysics Letters, 43, 3, 235-240.
11. Cao N. Z., Chen S. Y., Jin S., Martinez D. (1997), Physical symmetry and lattice symmetry in the lattice Boltzmann method, Physical Review E, 55, 1, 21-24.
12. Capuano F., Coppola G., Balarac G., De Luca L. (2015), Energy preserving turbulent simulations at a reduced computational cost, Journal of Computational Physics, 298, C, 480-494.
13. Casalino D., Lele S. K. (2014), Lattice-Boltzmann simulation of coaxial jet noise generation, Proceedings of the Summer Program 2014, 231-240.
14. Chen L., Yu Y., Lu J. H., Hou G. X. (2014), A comparative study of lattice Boltzmann methods using bounce-back schemes and immersed boundary ones for flow acoustic problems, International Journal for Numerical Methods in Fluids, 74, 439-467.
15. Chen S. Y., Doolen G. D. (1998), Lattice Boltzmann methods for fluid flows, Annual Review of Fluid Mechanics, 30, 329-364.
16. Chen X. P., Ren H. (2015), Acoustic flows in viscous fluid: A lattice Boltzmann study, International Journal for Numerical Methods in Fluids, 79, 4, 183-198.
17. Craig E., Hu F. Q. (2010), On the perfectly matched layer for the Boltzmann-BGK equation and its application to computational aeroacoustics, 16th AIAA/CEAS Aeroacoustics Conference and Exhibit, AIAA 10-3935, pp. 1-18, Stockholm, Sweden.
18. Crouse B., Freed D., Balasubramanian G., Senthooran S., Lew P. T., Mongeau L. (2006), Fundamental aeroacoustic capabilities of the lattice-Boltzmann method, 12th AIAA/CEAS Aeroacoustics Conference and Exhibit, AIAA 06-2571, pp. 1-17, Cambridge, MA, USA.
19. Da Silva A. R., Scavone G. P., Lefebvre A. (2009), Sound reflection at the open end of axisymmetric ducts issuing a subsonic mean flow: A numerical study, Journal of Sound and Vibration, 327, 507-528.
20. De Jong A. T., Bijl H., Hazir A., Wiedemann J. (2013), Aeroacoustic simulation of slender partially covered cavities using a lattice Boltzmann method, Journal of Sound and Vibration, 332, 1687-1703.
21. Dellar P. J. (2001), Bulk and shear viscosities in lattice Boltzmann equations, Physical Review E, 64, 031203.
22. Dellar P. J. (2008), Two routes from the Boltzmann equation to compressible flow of polyatomic gases, Progress in Computational Fluid Dynamics, 8, 1, 84-96.
23. Dhuri D. B., Hanasoge S. M., Perlekar P., Robertsson J. O. (2017), Numerical analysis of the lattice Boltzmann method for simulation of linear acoustic waves, Physical Review E, 95, 043306.
24. Dumbser M., Zanotti O., Loubere R., Diot S. (2014), A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws, Journal of Computational Physics, 278, 1, 47-75.
25. Farassat F. (1981), Linear acoustic formulas for calculation of rotating blade noise, AIAA Journal, 19, 9, 1122-1130.
26. Fares E., Duda B., Khorrami M. R. (2016), Airframe noise prediction of a full aircraft in model and full scale using a lattice Boltzmann approach, 22nd AIAA/CEAS Aeroacoustics Conference and Exhibit, AIAA 16-2707, pp. 1-21, Lyon, France.
27. Ffowcs Williams J. E., Hawkings D. L. (1969), Sound generation by turbulence and surfaces in arbitrary motion, Proceedings of the Royal Society of London Series A – Mathematical and Physical Sciences, 264, 1151, 321-342.
28. Fosso P. A., Deniau H., Sicot F., Sagaut P. (2010), Curvilinear finite-volume schemes using high-order compact interpolation, Journal of Computational Physics, 229, 13, 5090-5122.
29. Freund J. B., Lele S. K., Moin P. (1996), Calculation of the radiated sound field using an open Kirchhoff surface, AIAA Journal, 34, 5, 909-916.
30. Fu S. C., So R. M. C., Leung R. C. K. (2008), Modelled Boltzmann equation and its application to direct aeroacoustics simulation, AIAA Journal, 46, 7, 1651-1662.
31. Gaitonde D., Shang J. S. (1997), Optimized compact-difference-based finite-volume schemes for linear wave phenomena, Journal of Computational Physics, 138, 2, 617-643.
32. Gassner G. J. (2014), A kinetic energy preserving nodal discontinuous Galerkin spectral element method, International Journal for Numerical Methods in Fluids, 76, 1, 28-50.
33. Gassner G., Kopriva D. A. (2011), A comparison of the dispersion and dissipation errors of Gauss and Gauss-Lobatto discontinuous Galerkin spectral element methods, SIAM Journal on Scientific Computing, 33, 5, 2560-2579.
34. Gottlieb S., Shu C. W. (1998), Total variation diminishing Runge-Kutta schemes, Mathematics of Computation, 67, 221, 73-85.
35. Gottlieb S., Shu C. W., Tadmor E. (2001), Strong stability-preserving high-order time discretization methods, SIAM Review, 43, 1, 89-112.
36. Hagstrom T., Hariharan S. I., Thompson D. (2003), High-order radiation boundary conditions for the convective equations in exterior domains, SIAM Journal on Scientific Computing, 25, 3, 1088-1101.
37. Han S. L., Wang G. S., Yu L. S., Wang Y. Y. (2013), Numerical simulation of two-dimensional bluff body aerodynamic noise using lattice Boltzmann method, Advanced Materials Research, 610-613, 2535-2538.
38. Hao J., Kotapati R. B., Pérot F., Mann A. (2016), Numerical studies of acoustic diffraction by rigid bodies, 22nd AIAA/CEAS Aeroacoustics Conference and Exhibit, AIAA 16-2705, pp. 1-10, Lyon, France.
39. Hardin J. C., Hussaini M. Y. (1993), Computational aeroacoustics, Springer-Verlag, New York.
40. Hardin J. C., Pope D. S. (1994), An acoustic/splitting technique for computational aeroacoustics, Theoretical and Computational Fluid Dynamics, 6, 5, 323-340.
41. Hasert M., Bernsdorf J., Roller S. (2011), Towards aeroacoustic sound generation by flow through porous media, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 369, 1945, 2467-2475.
42. Haydock D. (2005), Lattice Boltzmann simulations of the time-averaged forces on a cylinder in a sound field, Journal of Physics A: General Physics, 38, 3265-3277.
43. Haydock D., Yeomans J. M. (2001), Lattice Boltzmann simulations of acoustic streaming, Journal of Physics A: General Physics, 34, 5201-5213.
44. Haydock D., Yeomans J. M. (2003), Lattice Boltzmann simulations of attenuation-driven acoustic streaming, Journal of Physics A: General Physics, 36, 5683-5694.
45. He X., Luo L. S. (1997), Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation, Physical Review E, 53, 6811-6817.
46. He Y. L., Wang Y., LI Q. (2009), Lattice Boltzmann method: Theory and applications [in Chinese], Science Press, Beijing.
47. Heubes D., Bartel A., Ehrhardt M. (2014), Characteristic boundary conditions in the lattice Boltzmann method for fluid and gas dynamics, Journal of Computational and Applied Mathematics, 262, 51-61.
48. Hochbruck M., Ostermann A. (2010), Exponential integrators, Acta Numerica, 19, 209-286.
49. Hsu A. T., Yang T., Lopez I., Ecer A. (2004), A review of lattice Boltzmann models for compressible flows, [in:] Chetverushkin B., Periaux J., Satofuka N., Ecer A. [Eds.], Parallel Computational Fluid Dynamics 2003: Advanced Numerical Methods, Software and Applications, Elsevier, pp. 19-28.
50. Hu F. Q. (2008), Development of PML absorbing boundary conditions for computational aeroacoustics: A progress review, Computers & Fluids, 37, 4, 336-348.
51. Hu F. Q., Hussaini M. Y., Rasetarinera P. (1999), An analysis of the discontinuous Galerkin method for wave propagation problems, Journal of Computational Physics, 151, 2, 921-946.
52. Hu F. Q., Li X. D., Lin D. K. (2008), Absorbing boundary conditions for nonlinear Euler and Navier-Stokes equations based on the perfectly matched layer technique, Journal of Computational Physics, 227, 9, 4398-4424.
53. Izquierdo S., Fueyo N. (2008), Characteristic nonreflecting boundary conditions for open boundaries in lattice Boltzmann methods, Physical Review E, 78, 046707.
54. Ji C. Z., Zhao D. (2014), Lattice Boltzmann investigation of acoustic damping mechanism and performance of an in-duct circular orifice, Journal of the Acoustical Society of America, 135, 6, 3243-3251.
55. Kam E. W. S., So R. M. C., Fu S. C. (2016), One-step simulation of thermoacoustic waves in two-dimensional enclosures, Computers & Fluids, 140, 270-288.
56. Kam E. W. S., So R. M. C., Leung R. C. K. (2009), Acoustic scattering by a localized thermal disturbance, AIAA Journal, 47, 9, 2039-2052.
57. Kam E. W. S., So R. M. C., Leung R. C. K. (2015), Lattice Boltzmann method simulation of aeroacoustics and nonreflecting boundary conditions, AIAA Journal, 45, 7, 1703-1712.
58. Kim J. W., Lee D. J. (1996), Optimized compact finite difference schemes with maximum resolution, AIAA Journal, 34, 5, 887-893.
59. Kok J. C. (2009), A high-order low-dispersion symmetry-preserving finite-volume method for compressible flow on curvilinear grids, Journal of Computational Physics, 228, 18, 6811-6832.
60. Lafitte A., Pérot F. (2009), Investigation of the noise generated by cylinder flows using a direct lattice-Boltzmann approach, 15th AIAA/CEAS Aeroacoustics Conference and Exhibit, AIAA 09-3268, pp. 1-12, Miami, FL, USA.
61. Lahivaara T., Huttunen T. (2011), A non-uniform basis order for the discontinuous Galerkin method of the acoustic and elastic wave equations, Applied Numerical Mathematics, 61, 4, 473-486.
62. Lallier-Daniels D., Moreau S., Sanjose M., Pérot F. (2013), Numerical analysis of axial fans for performance and noise evaluation using the lattice Boltzmann method, CFD Canada 2013, Sherbrooke, Canada.
63. Lee C., Seo Y. (2002), A new compact spectral scheme for turbulence simulation, Journal of Computational Physics, 183, 2, 438-469.
64. Lee T., Lin C. L. (2003), An Eulerian description of the streaming process in the lattice Boltzmann equation, Journal of Computational Physics, 185, 445-471.
65. Lele S. K. (1992), Compact finite difference scheme with spectral-like resolution, Journal of Computational Physics, 103, 1, 16-42.
66. Lele S. K. (1997), Computational aeroacoustics – A review, 35th Aerospace Sciences Meeting and Exhibit, AIAA 97-0018, pp. 1-15, Reno, NV, USA.
67. Li K., Zhong C. W. (2016), Aeroacoustic simulations using compressible lattice Boltzmann method, Advances in Applied Mathematics and Mechanics, 8, 5, 795-809.
68. Li W. D., Li W. (2018), A gas-kinetic BGK scheme for the finite volume lattice Boltzmann method for nearly incompressible flow, Computers & Fluids, 162, 126-138.
69. Li X. M., Leung R. C. K., So R. M. C. (2006a), One-step aeroacoustics simulation using lattice Boltzmann method, AIAA Journal, 44, 1, 78-89.
70. Li Y. B., Shan X. W. (2011), Lattice Boltzmann method for adiabatic acoustics, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 369, 1944, 2371-2380.
71. Li Y. S., Leboeuf E. J., Basu P. K. (2005), Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh, Physical Review E, 72, 046711.
72. Li X. M., So R. M. C., Leung R. C. K. (2006b), Propagation speed, internal energy, and direct aeroacoustics simulation using lattice Boltzmann method, AIAA Journal, 44, 12, 2896-2903.
73. Lighthill M. J. (1952), On sound generated aerodynamically. I. General theory, Proceedings of the Royal Society of London Series A – Mathematical and Physical Sciences, 211, 1107, 564-587.
74. Liu L., Li X. D., Hu F.Q. (2010), Nonuniform time-step Runge-Kutta discontinuous Galerkin method for computational aeroacoustics, Journal of Computational Physics, 229, 19, 6874-6897.
75. Lodato G., Domingo P., Vervisch L. (2008), Three-dimensional boundary conditions for direct and large-eddy simulation of compressible viscous flows, Journal of Computational Physics, 10, 1, 5105-5143.
76. Lv Y., Ihme M. (2015), Entropy-bounded discontinuous Galerkin scheme for Euler equations, Journal of Computational Physics, 295, 715-739.
77. Machrouki H., Ricot D., Coste O. (2012), Lattice Boltzmann aero-acoustics modelling of flow around obstacles, Proceedings of the Acoustics 2012 Nantes Conference, 1297-1301, Nantes, France.
78. Manoha E., Elias G., Troff B., Sagaut P. (1999), Towards the use of boundary element method in computational aeroacoustics, 5th AIAA/CEAS Aeroacoustics Conference and Exhibit, AIAA 99-1980, pp. 1161-1171, Bellevue, WA, USA.
79. Marié S., Ricot D., Sagaut P. (2009), Comparison between lattice Boltzmann method and Navier-Stokes high order schemes for computational aeroacoustics, Journal of Computational Physics, 228, 4, 1056-1070.
80. Mei R. W., Shyy W. (1998), On the finite difference-based lattice Boltzmann method in curvilinear coordinates, Journal of Computational Physics, 143, 426-448.
81. Meskine M. et al. (2013), Community noise prediction of digital high speed train using LBM, 19th AIAA/CEAS Aeroacoustics Conference and Exhibit, AIAA 13-2015, pp. 1-17, Berlin, Germany.
82. Moreau S., Foss J., Morris S. (2016), A numerical and experimental test-bed for low-speed fans, Proceedings of the Institute of Mechanical Engineers Part A – Journal of Power and Energy, 230, 5, 456-466.
83. Murman S. M. (2010), Compact upwind schemes on adaptive octrees, Journal of Computational Physics, 229, 4, 1167-1180.
84. Nannelli F., Succi S. (1992), The lattice Boltzmann equation on irregular lattices, Journal of Statistical Physics, 68, 401-407.
85. Nayafi-Yazdi A., Mongeau L. (2012), An absorbing boundary condition for the lattice Boltzmann method based on the perfectly matched layer, Computers & Fluids, 68, 203-218.
86. Nguyen N. C., Peraire J., Cockburn B. (2015), A class of embedded discontinuous Galerkin methods for computational fluid dynamics, Journal of Computational Physics, 302, 674-692.
87. Patil D. V., Lakshmisha K. N. (2009), Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh, Journal of Computational Physics, 228, 5262-5279.
88. Pérot F. et al. (2011), HVAC blower aeroacoustics predictions based on the lattice Boltzmann method, Proceedings of the ASME-JSME-KSME 2011 Joint Fluids Engineering Conference, AJK 2011-23018, pp. 1-9, Hamamatsu, Shizuoka, Japan.
89. Pérot F., Kim M. S., Le Goff V., Carniel X., Goth Y., Chassaignon C. (2013), Numerical optimization of the tonal noise of a backward centrifugal fan using a flow obstruction, Noise Control Engineering Journal, 61, 3, 307-319.
90. Poinsot T. J., Lele S. K. (1992), Boundary conditions for direct simulations of compressible viscous flows, Journal of Computational Physics, 101, 104-129.
91. Popescu M., Shyy W., Garbey M. (2005), Finite volume treatment of dispersion-relation-preserving and optimized prefactored compact schemes for wave propagation, Journal of Computational Physics, 210, 2, 705-729.
92. Qi J. X., Hasert M., Klimach H., Roller S. (2015), Aeroacoustic simulation of flow through porous media based on the lattice Boltzmann method, [in:] Resch M., Bez W., Focht E. et al. [Eds.], Sustained Simulation Performance, pp. 195-204, Springer, Cham.
93. Reider M. B., Sterling J. D. (1995), Accuracy of discrete-velocity BGK models for the simulation of the incompressible Navier-Stokes equations, Computers & Fluids, 24, 4, 459-467.
94. Sanjose M., Moreau S., Pestana M., Roger M. (2017), Effect of weak outlet-guide-vane heterogeneity on rotor-stator tonal noise, AIAA Journal, 55, 10, 3440-3457.
95. Satti R., Li Y. B., Shock R., Noelting S. (2008), Aeroacoustics analysis of a high-lift trapezoidal wing using a lattice Boltzmann method, 14th AIAA/CEAS Aeroacoustics Conference and Exhibit, AIAA 08-3048, pp. 1-16, Vancouver, British Columbia, Canada.
96. Shao W. D., Li J. (2018a), An absorbing boundary condition based on perfectly matched layer technique combined with discontinuous Galerkin Boltzmann method for low Mach number flow noise, Journal of Theoretical and Computational Acoustics, 26, 4, 1850011.
97. Shao W. D., Li J. (2018b), Three time integration methods for incompressible flows with discontinuous Galerkin Boltzmann method, Computers & Mathematics with Applications, 75, 11, 4091-4106.
98. Shi X., Lin J. Z., Yu Z. S. (2003), Discontinuous Galerkin spectral element lattice Boltzmann method on triangular element, International Journal for Numerical Methods in Fluids, 42, 1249-1261.
99. Sofonea V., Sekerka R. F. (2003), Viscosity of finite difference lattice Boltzmann models, Journal of Computational Physics, 184, 422-434.
100. Spiteri R. J., Ruuth S. J. (2002), A new class of optimal high-order strong-stability-preserving time discretization methods, SIAM Journal on Numerical Analysis, 40, 2, 469-491.
101. Stadler M., Schmitz M. B., Laufer W., Ragg P. (2014), Inverse aeroacoustic design of axial fans using genetic optimization and the lattice-Boltzmann method, Journal of Turbomachinery, 136, 041011.
102. Stanescu D., Habashi W. G. (1998), 2N-storage low dissipation and dispersion Runge-Kutta schemes for computational acoustics, Journal of Computational Physics, 143, 2, 674-681.
103. Stiebler M., Tolke J., Krafczyk M. (2006), An upwind discretization scheme for the finite volume lattice Boltzmann method, Computers & Fluids, 35, 814-819.
104. Stoll S. J. B. (2014), Lattice Boltzmann simulation of acoustic fields, with special attention to non-reflecting boundary conditions, Master thesis, Norwegian University of Science and Technology.
105. Strum M., Sanjose M., Moreau S., Carolus T. (2015), Aeroacoustic simulation of an axial fan including the full test rig by using the lattice Boltzmann method, Fan 2015, pp. 1-12, Lyon, France.
106. Sudo Y., Sparrow V. W. (1995), Sound propagation simulations using lattice gas methods, AIAA Journal, 33, 9, 1582-1589.
107. Tam C. K. W. (1995), Computational aeroacoustics: Issues and methods, AIAA Journal, 33, 10, 1788-1796.
108. Tam C. K. W., Dong Z. (1996), Radiation and outflow boundary conditions for direct computation of acoustic and flow disturbances in a nonuniform mean flow, Journal of Computational Acoustics, 4, 2, 175-201.
109. Tam C. K. W., Webb J. C. (1993), Dispersion-relation-preserving finite difference schemes for computational acoustics, Journal of Computational Physics, 107, 2, 262-281.
110. Tekitek M. M., Bouzidi M., Dubois F., Lallemand P. (2009), Towards perfectly matching layers for lattice Boltzmann equation, Computers & Mathematics with Applications, 58, 5, 903-913.
111. Thompson K. W. (1987), Time dependent boundary conditions for hyperbolic systems, Journal of Computational Physics, 68, 1, 1-24.
112. Tsutahara M. (2012), The finite-difference lattice Boltzmann method and its application in computational aeroacoustics, Fluid Dynamic Research, 44, 045507.
113. Tsutahara M., Kataoka T., Shikata K., Takada N. (2008), New model and scheme for compressible fluids of the finite difference lattice Boltzmann method and direct simulations of aerodynamic sound, Computers & Fluids, 37, 1, 79-89.
114. Uga K. C., Min M., Lee T., Fischer P. F. (2013), Spectral-element discontinuous Galerkin lattice Boltzmann simulation of flow past two cylinders in tandem with an exponential time integrator, Computers & Mathematics with Applications, 65, 239-251.
115. Vergnault E., Malaspinas O., Sagaut P. (2013), Noise source identification with the lattice Boltzmann method, The Journal of the Acoustical Society of America, 133, 3, 1293-1305.
116. Viggen E. M. (2011), Viscously damped acoustic waves with the lattice Boltzmann method, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 369, 1944, 2246-2254.
117. Viggen E. M. (2013), Acoustic multiple source for the lattice Boltzmann method, Physical Review E, 87, 023306.
118. Wang Y., He Y. L., Zhao T. S., Tang G. H., Tao W. Q. (2007), Implicit-explicit finite-difference lattice Boltzmann method for compressible flows, International Journal of Modern Physics C, 18, 12, 1961-1983.
119. Peng G. W., Xi H. W., Duncan C. (1999), Finite-volume scheme for the lattice Boltzmann method on unstructured meshes, Physical Review E, 59, 4, 4675-4682.
120. Xu D., Deng X. G., Chen Y. M., Dong Y. D., Wang G. X. (2016), On the freestream preservation of finite volume method in curvilinear coordinates, Computers & Fluids, 129, 1, 20-32.
121. Xu H., Malaspinas O., Sagaut P. (2012), Sensitivity analysis and determination of free relaxation parameters for the weakly-compressible MRT-LBM schemes, Journal of Computational Physics, 231, 21, 7335-7367.
122. Xu H., Sagaut P. (2011), Optimal low-dispersion low-dissipation LBM schemes for computational aeroacoustics, Journal of Computational Physics, 230, 13, 5353-5382.
123. Xu H., Sagaut P. (2013), Analysis of the absorbing layers for the weakly-compressible lattice Boltzmann methods, Journal of Computational Physics, 245, 1, 14-42.
124. Yoo C. S., Im H. G. (2007), Characteristic boundary conditions for simulations of compressible reacting flows with multi-dimensional, viscous and reacting effects, Combustion Theory and Modelling, 11, 2, 259-286.
125. Yu D. Z., Mei R. W., Luo L. S., Shyy W. (2003), Viscous flow computations with the method of lattice Boltzmann equation, Progress in Aerospace Sciences, 39, 329-367.
126. Zadehgol A., Ashrafizaadeh M., Musavi S. H. (2014), A nodal discontinuous Galerkin lattice Boltzmann method for fluid flow problems, Computers & Fluids, 105, 58-65.
127. Zhang J. Y., Yan G. W., Yan B., Shi X. B. (2011), A lattice Boltzmann model for two-dimensional sound wave in the small perturbation compressible flows, International Journal for Numerical Methods in Fluids, 67, 214-231.
128. Zhang X. X. (2017), On positivity-preserving high order discontinuous Galerkin schemes for compressible Navier-Stokes equations, Journal of Computational Physics, 328, 301-343.
129. Zhong X. L. (1998), High-order finite-difference schemes for numerical simulation of hypersonic boundary-layer transition, Journal of Computational Physics, 144, 2, 662-709.
130. Zhou Y. H., Dong Y. H. (2014), An investigation of the lattice Boltzmann equation-based hybrid approach for simulation of sound generated by isotropic turbulence, Computers & Fluids, 100, 267-277.
131. Zhuang M., Chen R. (1998), Optimized upwind dispersion-relation-preserving finite difference scheme for computational aeroacoustics, AIAA Journal, 35, 11, 2146-2148.
132. Zhuo C. S., Sagaut P. (2017), Acoustic multiple sources for the regularized lattice Boltzmann method: Comparison with multiple-relaxation-time models in the inviscid limit, Physical Review E, 95, 063301.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).

Typ dokumentu

Bibliografia

Identyfikator YADDA

bwmeta1.element.baztech-9d784a87-f887-4fed-a6d2-45ed62f134e5