Abstract
We present an adaptive lattice Boltzmann model to simulate supersonic flows. The particle velocities are determined by the mean velocity and internal energy. The adaptive nature of particle velocities permits the mean flow to have high Mach number. A particle potential energy is introduced so that the model is suitable for the perfect gas with arbitrary specific heat ratio. The Navier-Stokes equations are derived by the Chapman-Enskog method from the BGK Boltzmann equation. As preliminary tests, two kinds of simulations have been performed on hexagonal lattices. One is the one-dimensional simulation for sinusoidal velocity distributions. The velocity distributions are compared with the analytical solution and the measured viscosity is compared with the theoretical values. The agreements are basically good. However, the discretion error may cause some non-isotropic effects. The other simulation is the 29 degree shock reflection.
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References
Chen H, Chen S, Matthaeus W. Recovery of the Navier-Stokes equation using a lattice-gas Boltzmann method.Phys Rev A, 1992, 45(8): R5339–5342
Qian Y H, d'Humières D, Lallemand P. Lattice BGK models for Navier-Stokes equation.Europhys Lett, 1992 17(6): 479–484
Chen Y, Ohashi H, Akiyama M. Heat transfer in lattice BGK modeled fluid.J Stat Phys, 1995, 81(1/2): 71–85
Sun C H. Multispecies Lattice-Boltzmann models for mass diffusion.Acta Mechanica Sinica, 1998, 30(1): 20–26 (in Chinese)
Martinez D, Chen S, Matthaeus W. Lattice Boltzman magneto-hydrodynamics.Phys Plasma, 1994, 1(6): 1850–1867
Chen S, Doolen G D. Lattice Boltzmann method for fluid flows.Annu Rev Fluid Mech, 1998, 30: 329–364
Alexander F J, Chen H, Doolen G D. Lattice Boltzmann model for compressible fluids.Phys Rev A 1992, 46(4): 1967–1970
Xu K. A new class of gas-kinetic relaxation schemes for the compressible Euler equations.J Stat Phys, 1995, 81(1/2): 147–164
Xu K, Martinelli L, Jameson A. Gas-kinetic finite volume methods, flux-vector splitting, and artificial diffusion.J Comput Phys, 1995, 120: 48–65
Nadiga B T. An Euler solver based on locally adaptive discrete velocities.J Stat Phys, 1995, 81 (1/2): 129–146.
Hu S X, Yan G W, Shi W P. Lattice Boltzmann model for compressible perfect gas.Acta Mechanica Sinica, 1997, 13(3): 314–322
Sun C H. Lattice-Boltzmann models for high speed flows.Phys Rev E 1998, 58(6): 7283–7287
Sun C H. Simulations of compressible flows with strong shocks by adaptive lattice Boltzmann model.J Comput Phys, 2000, 161(1): 70–84
Sun C H. Lattice Boltzmann model for compressible fluid on square lattice.Chin Phys Lett, in press
Sun C H. Adaptive lattice Boltzmann model for compressible flows: viscous and conductive properties.Phys Rev E, 2000, 61(3), 2645–2653
Sun C H. Thermal lattice Boltzmann model for compressible fluid.Chin Phys Lett, 2000, 17(3): 209–211
Bernardin D, Sero-Guillaume O, Sun C H. Multi-species 2D lattice gas with energy levels: diffusive properties.Physica D, 1991, 47: 169–188
Colella P. Multidimensional upwind methods for hyperbolic conservation laws.J Comput Phys, 1990, 87: 171–200
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The project supported by the National Natural Science Foundation of China (Grant Nos. 19672030 and 19972037) and by the Scientific Research Foundation for Returned Overseas Chinese Scholars, State Education Ministry
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Chenghai, S. Lattice-Boltzmann model for compressible perfect gases. Acta Mech Sinica 16, 289–300 (2000). https://doi.org/10.1007/BF02487682
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DOI: https://doi.org/10.1007/BF02487682