PMID: 15244972Jul 13, 2004Paper

Lattice Boltzmann method for the compressible Euler equations

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Takeshi Kataoka, Michihisa Tsutahara

Abstract

The lattice Boltzmann model for the compressible Euler equations is proposed together with its rigorous theoretical background. The proposed model has completely overcome the defects of the previous model that the specific-heat ratio cannot be chosen freely. The macroscopic variables obtained from the solution are shown to satisfy, in the limit of the small Knudsen number, the compressible Euler equations if the variation of the solution is moderate. This is the case where no shock waves or contact discontinuities appear. In contrast, when the solution makes steep variation at several localized regions due to the appearance of shock waves and contact discontinuities, the corresponding macroscopic variables satisfy the weak form of the Euler equations. Their derivation is carried out rigorously by taking into account the scale of variation of the solution correctly. This is the first study that has laid the theoretical foundation of the lattice Boltzmann model for the simulation of flows with shock waves and contact discontinuities. Numerical examples and the error estimates are also given, which are consistent with the above theoretical arguments.

References

Oct 1, 1994·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·Y ChenM Akiyama
Apr 20, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Takeshi Kataoka, Michihisa Tsutahara

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Citations

Jul 2, 2010·Chaos·Jianying Zhang, Guangwu Yan
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Aiguo Xu
Jul 7, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yanbiao GanYingjun Li
Jun 30, 2019·The European Physical Journal. E, Soft Matter·Livio Nicola CarenzaAdriano Tiribocchi
Jun 25, 2020·Physical Review. E·Dominik WildeHolger Foysi
Jul 25, 2019·Physical Review. E·S A HosseiniD Thévenin
Mar 4, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Chuandong LinSauro Succi
Jun 4, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Xiaobo NieHudong Chen
Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Takeshi Kataoka, Michihisa Tsutahara
Oct 2, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jianying ZhangXiubo Shi

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