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A double-distribution-function lattice Boltzmann model for high-speed compressible viscous flows. (English) Zbl 1390.76757
Summary: A lattice Boltzmann model for high-speed compressible viscous flows is presented based on the double-distribution-function lattice Boltzmann method proposed by Q. Li et al. [“Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations”, Phys. Rev. E (3) 76, No. 5, Article ID 056705, 19 p. (2007; doi:10.1103/physreve.76.056705)]. The D2Q17 circle function is introduced to take into account first to fourth order constraints of density equilibrium distribution function, in order for better consistency in the heat flux and the energy dynamics. The corresponding total energy equilibrium distribution function is formed. The present model is tested through three problems, i.e., the Riemann problem, regular shock reflection problem and supersonic boundary layer problem. We also observe improved performance of the new model for a supersonic boundary layer problem in comparison to the original coupled double-distribution-function lattice Boltzmann method.

MSC:
76M28 Particle methods and lattice-gas methods
76J20 Supersonic flows
76L05 Shock waves and blast waves in fluid mechanics
76N20 Boundary-layer theory for compressible fluids and gas dynamics
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[1] Qian, Y. H.; D’Humieres, D.; Lallemand, P., Lattice BGK models for Navier-Stokes equation, Europhys Lett, 17, 6, 479-784, (1992) · Zbl 1116.76419
[2] Chen, S.; Doolen, G. D., Lattice Boltzmann method for fluid flows, Annu Rev Fluid Mech, 30, 329-364, (1998) · Zbl 1398.76180
[3] Xu, A. G.; Zhang, G. C.; Gan, Y. B.; Chen, F.; Yu, X. J., Lattice Boltzmann modeling and simulation of compressible flows, Front Phys, 7, 5, 582-600, (2012)
[4] Xu, A. G.; Zhang, G. C.; Ying, Y. J., Progess of discrete Boltzmann modeling and simulation of combustion system, Acta Phys Sin, 64, 18, 184701, (2015)
[5] Xu, A.; Lin, C.; Zhang, G.; Li, Y., Multiple-relaxation-time lattice Boltzmann kinetic model for combustion, Phys Rev E, 91, 4, 043306, (2015)
[6] Succi, S.; Foti, E.; Higuera, F., Three-dimensional flows in complex geometries with the lattice Boltzmann method, Europhys Lett, 10, 5, 433-438, (1989)
[7] Xu, Y.; Lin, X.; Yang, Y.; Wu, F., Lattice Boltzmann simulation of convection in a porous medium with temperature jump and velocity slip boundary conditions, Commun Theor Phys, 49, 5, 1319-1322, (2008) · Zbl 1392.76064
[8] Chai, Z.; Shi, B., Simulation of electro-osmotic flow in microchannel with lattice Boltzmann method, Phys Lett A, 364, 3-4, 183-188, (2007) · Zbl 1203.76125
[9] Coles, D., A hybrid lattice Boltzmann model for solidâliquid phase transition in presence of fluid flow, Phys Lett A, 351, 45, 359-367, (2006)
[10] Qiu, R.; Wang, A.; Gong, Q.; Jiang, T., Simulation of two-phase fluid mixture flow in rectangular two-inlet cavity using lattice Boltzmann method, Int J Mod Phys C, 25, 04, 1450004, (2014)
[11] Qiu, R. F.; Wang, A. L.; Gong, Q. W.; Jiang, T., Simulation of expanding bubble through a hole in a channel driven by pressure using lattice Boltzmann method, Comput Math Appl, 70, 3, 244-253, (2015)
[12] Gan, Y.; Xu, A.; Zhang, G.; Succi, S., Discrete Boltzmann modeling of multiphase flows: hydrodynamic and thermodynamic non-equilibrium effects., Soft Matter, 11, 26, 5336-5345, (2015)
[13] Qiu, R.; Wang, A.; Jiang, T., Lattice Boltzmann method for natural convection with multicomponent and multiphase fluids in a two-dimensional square cavity, Can J Chem Eng, 93, 6, 1121-1129, (2013)
[14] Qiu, R. F.; Wang, A. L., Numerical investigation of two-component jet flow with heat transfer in a channel by lattice Boltzmann method, Comput Fluids, 138, 1-8, (2016) · Zbl 1390.76756
[15] Chen, F.; Xu, A. G.; Zhang, G. C.; Gan, Y. B.; Ying, Y. J., Highly efficient lattice Boltzmann model for compressible fluids: two-dimensional case, Commun Theor Phys, 52, 10, 681-693, (2009) · Zbl 1253.76114
[16] Gan, Y.; Xu, A.; Zhang, G.; Yu, X.; Li, Y., Two-dimensional lattice Boltzmann model for compressible flows with high Mach number, Phys A Stat Mech Appl, 387, 8-9, 1721-1732, (2008)
[17] Chen, F.; Xu, A. G.; Zhang, G. C.; Ying, Y. J., Multiple-relaxation-time lattice Boltzmann approach to Richtmyer-Meshkov instability, Commun Theor Phys, 55, 2, 325-334, (2011) · Zbl 1264.76092
[18] Lai, H.; Xu, A.; Zhang, G.; Gan, Y.; Ying, Y.; Succi, S., Nonequilibrium thermohydrodynamic effects on the Rayleigh-Taylor instability in compressible flows, Phys Rev E, 94, 2-1, 023106, (2016)
[19] Alexander, F. J.; Chen, S.; Sterling, J. D., Lattice Boltzmann thermohydrodynamics, Phys Rev E, 47, 4, R2249-R2252, (1993)
[20] Yan, G.; Chen, Y.; Hu, S., Simple lattice Boltzmann model for simulating flows with shock wave, Phys Rev E, 59, 1, 454-459, (1999)
[21] Kataoka, T.; Tsutahara, M., Lattice Boltzmann model for the compressible Navier-Stokes equations with flexible specific-heat ratio, Phys Rev E, 69, 2, 035701, (2004)
[22] Watari, M., Finite difference lattice Boltzmann method with arbitrary specific heat ratio applicable to supersonic flow simulations, Phys A Stat Mech Appl, 382, 2, 502-522, (2007)
[23] Sun, C., Lattice-Boltzmann models for high speed flows, Phys Rev E, 58, 6, 7283-7287, (1998)
[24] Yu, H.; Zhao, K., Lattice Boltzmann method for compressible flows with high Mach numbers, Phys Rev E, 61, 4, 3867-3870, (2000)
[25] Qu, K.; Shu, C.; Chew, Y. T., Alternative method to construct equilibrium distribution functions in lattice-Boltzmann method simulation of inviscid compressible flows at high Mach number, Phys. Rev. E, 75, 036706, (2007)
[26] Li, Q.; He, Y. L.; Wang, Y.; Tao, W. Q., Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations, Phys Rev E, 76, 5, 168-206, (2007)
[27] Wang, Y.; He, Y. L.; Li, Q.; Tang, G. H.; Tao, W. Q., Lattice Boltzmann model for simulating viscous compressible flows, Int J Mod Phys C, 21, 3, 383-407, (2010) · Zbl 1386.76128
[28] Li, K.; Zhong, C., A lattice Boltzmann model for simulation of compressible flows, Int J Numer Methods Fluids, 77, 6, 334-357, (2015)
[29] Chen, F.; Xu, A.; Zhang, G.; Li, Y.; Succi, S., Multiple-relaxation-time lattice Boltzmann approach to compressible flows with flexible specific-heat ratio and Prandtl number, Europhys Lett, 90, 5, 1632-1652, (2010)
[30] Chen, F.; Xu, A.; Zhang, G.; Li, Y., Multiple-relaxation-time lattice Boltzmann model for compressible fluids, Phys Lett A, 375, 21, 2129-2139, (2011)
[31] Gan, Y.; Xu, A.; Zhang, G.; Yang, Y., Lattice BGK kinetic model for high speed compressible flows: hydrodynamic and nonequilibrium behaviors, Europhys Lett, 103, 2, 330-337, (2013)
[32] Pieraccini, S.; Puppo, G., Implicit-explicit schemes for BGK kinetic equations, J Sci Comput, 32, 32, 1-28, (2007) · Zbl 1115.76057
[33] Wang, Y.; He, Y. L.; Zhao, T. S.; Tang, G. H.; Tao, W. Q., Implicit-explicit finite-difference lattice Boltzmann method for compressible flows, Int J Mod Phys C, 18, 12, 1961-1983, (2007) · Zbl 1151.82405
[34] Qiu, R.; Chen, R.; You, Y., An implicit-explicit finite-difference lattice Boltzmann subgrid method on nonuniform meshes, Int J Mod Phys C, 28, 4, 1750045, (2017)
[35] He, X.; Luo, L. S., A priori derivation of the lattice Boltzmann equation, Phys Rev E, 55, 6, R6333-R6336, (1997)
[36] Shan, X.; Yuan, X.; Chen, H., Kinetic theory representation of hydrodynamics: a way beyond the Navier-Stokes equation, J Fluid Mech, 550, 413-441, (2006) · Zbl 1097.76061
[37] Qu, K., Development of Lattice Boltzmann Method for Compressible Flows, (2008), Ph.D. thesis in National University of Singapore
[38] Xu, K.; Huang, J., A unified gas-kinetic scheme for continuum and rarefied flows., J Comput Phys, 229, 20, 7747-7764, (2010) · Zbl 1276.76057
[39] Guo, Z.; Xu, K.; Wang, R., Discrete unified gas kinetic scheme for all Knudsen number flows: low-speed isothermal case., Phys Rev E, 88, 3, 033305, (2013)
[40] Li, Q.; He, Y. L.; Wang, Y.; Tang, G., Three-dimensional non-free-parameter lattice-Boltzmann model and its application to inviscid compressible flows, Phys Lett A, 373, 25, 2101-2108, (2009) · Zbl 1229.76090
[41] Qiu, R. F.; You, Y. C.; Zhu, C. X.; Chen, R. Q., Lattice Boltzmann simulation for high-speed compressible viscous flows with boundary layer, Appl Math Model, 48, 567-583, (2017)
[42] Guo, Z.; Zhao, T. S., Explicit finite-difference lattice Boltzmann method for curvilinear coordinates, Phys Rev E, 67, 2, 066709, (2003)
[43] Van Driest, E. R., Investigation of laminar boundary layer in compressible fluids using the crocco method, 10, 15-31, (1952)
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